Tunable Surface Topographies via ParticleEnhanced Soft Composites
AfWAES
-MASSACHUSETTS INSTITUTE
OF TECHNOLOLGY
by
Mark A. Guttag
APR 15 2015
B.S. Mechanical Engineering
Brown University, 2012
LIBRARIES
Submitted to the Department of Mechanical Engineering in partial fulfillment of
the requirements for the degree of
Master of Science in Mechanical Engineering
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
February 2015
Massachusetts Institute of Technology 2015. All rights reserved
Author:
Signature redacted
Department of Mechanical EAineering
September 9, 2014
Certified by:
Signature redacted
Mary C. Boyce
Ford Professor of Engineering
It%
Accepted by:
e-)fiesisSepervisor
Signature redacted
David E. Hardt
Ralph E. and Eloise F. Cross Professor in Manufacturing
Chairman, Department Committee on Graduate Students
Tunable Surface Topographies via ParticleEnhanced Soft Composites
by
Mark Guttag
Submitted to the Department of Mechanical Engineering
on September 9, 2014, in partial fulfillment of the
requirements for the degree of
Master of Science in Mechanical Engineering
Abstract
We introduce a new class of particle-enhanced soft composites (PESC) that can generate, on
demand, custom and reversible surface topographies, with surface features that can be highly
localized. These features can be specifically patterned or alternatively can be random in nature.
Our PESC samples comprise a soft elastomeric matrix with stiff particles embedded below the
surface. The surfaces of the samples presented in this thesis are originally smooth and flat but
complex morphologies emerge under application of a stimuli (here we show application of
primarily compressive loading). We demonstrate these adaptive surface topographies with both
physical experiments and finite element simulations which are used to design and to study the
mechanical response. A variety of different surface patterns can be attained by tailoring different
dimensionless geometric parameters (e.g. different particle sizes, shapes, and distributions), as
well as material properties. The design space of the system and the resulting surface
topographies are explored and classified systematically. Given that our method depends
primarily on the geometry of the particle arrays, our mechanism for on-demand custom surface
patterning is applicable over a wide range of length scales. These surfaces can be used in a
variety of different applications including control of fluid flow, adhesion, wettability and many
others.
Thesis Supervisor: Mary C. Boyce
Title: Ford Professor of Engineering
3
Acknowledgements
I would like to thank my advisor, Professor Mary C. Boyce, for all of her support over the
past two years. Her knowledge and direction have shaped me as a student and researcher. I
would also like to thank my co-advisor, Professor Pedro Reis, for his patience over the last year
during a difficult transition period. I look forward to producing great work together in the
coming years.
Thank you to all the members of the Boyce group for all your help. In particular, thank you
to Shabnam Raayai Ardakani and Hansohl Cho for helping me with many technical problems
related to simulations and experiments. Special thanks to Narges Kaynia for helping me make it
through the first two years of grad school and for being the best office mate I could ask for.
Thank you to all the members of the EGS lab for welcoming me into the group. Special
thanks to Khalid Jawed for helping me with my code (and saving me weeks of work in the
process).
I would also like to thank my family and friends for being there for me in good times and
bad. Thank you Michael and David for being the best brothers a guy could ask for, and for
always making me feel better about my short game. Thank you to Andrea for always being there
to lift me up or bring me down a peg when necessary. Thanks Mom for always picking up the
phone and your ability to calm me down when I need it. Thanks Dad for always making time for
me, no matter how busy you are. Without your help the quality of thesis (and everything else I
write) would be much lower than it is now.
4
This work was funded by the Cooperative Agreement between the Masdar Institute of
Science and Technology and the Massachusetts Institute of Technology.
5
Contents
1.
Introduction..................................................................................................................
10
1.1.
Bio-Inspiration and Applications........................................................................
10
1.2.
Overview of technique ........................................................................................
11
1.3.
Contributions.......................................................................................................
12
1.4.
Outline.....................................................................................................................
13
Tunable Surfaces.......................................................................................................
14
2.
2.1.
Wrinkling................................................................................................................14
2.2.
Other tunable surfaces.........................................................................................
19
Finite Elem ent Sim ulation Details ..........................................................................
21
3.
3.1.
General Sim ulation Layout and Boundary Conditions........................................
21
3.2.
Constitutive M odel..............................................................................................
25
3.3.
Num erical Details ...............................................................................................
27
4.
FE: Varying G eom etric Param eters........................................................................
4.1.
Uniform Array of Particles .................................................................................
30
30
4.1.1.
Effect of relative inter-particle ligam ent length ...............................................
31
4.1.2.
Effect of the number of rows of particles.......................................................
37
A
I
+c.
n
,ill
of the aspect ratio of particles..............................................................
6
4U
4.2.
5.
6.
7.
N on-uniform arrays of particles..............................................................................
46
FE: V arying M aterial Properties............................................................................
51
5.1.
V arying com pressibility of the m atrix ................................................................
51
5.2.
Varying Stiffness of Particles ..............................................................................
55
Experim ental Verification .......................................................................................
57
6.1.
M aterials and M ethods.........................................................................................
57
6.2.
Experim ental Results ...........................................................................................
59
Conclusion.....................................................................................................................
67
7.1.
Sum m ary.................................................................................................................
67
7.2.
Extensions ............................................................................................................
69
7.3.
Applications .........................................................................................................
72
7.4.
Conclusions..........................................................................................................
74
References..............................................................................................................................
7
75
Table of Figures
Figure 1-1: Schematic diagram of the mechanism for activation of the skin papillae in Sepia
officinalis.......................................................................................................................................
11
Figure2-1: Mode shapes thatform under equi-biaxial compression ................................
16
Figure2-2: Wrinkling patterns attainedon a sphericalsample.........................................
18
Figure2-3: Wrinkling patterns attainedon a prolate spheroidwith varying k and R/t......... 18
Figure3-1: Basic PESC setup ...........................................................................................
22
Figure3-2: Several RVEs usedfor simulations and their correspondingunit cells ........... 23
Figure3-3: Generalexample ofperiodic boundary conditions on two surfaces ............... 24
Figure 3-4: Experimental validation of neo-Hookean material model ..............................
27
Figure3-5: Validation of mesh density ..............................................................................
28
Figure4-1: Importantdimensions of the uniform arrayof particles.............................
30
Figure 4-2: Effect of a-2fl
on the surface topography......................................................
a
32
Figure 4-3: Normalizedpeak amplitude vs. global strainfor different values of
33
a-2f.........
a
Figure 4-4: Strain contours of different relative inter-particleligament lengths shown at 20%
global comp ressive strain .............................................................................................................
Figure 4-5: Schematic diagram of matrix extrusion due to shearing................................
35
37
Figure 4-6: Effect of number of rows ofparticles on the surface topography ................... 39
Figure4-7: Normalizedpeak amplitude vs. number of rows ofparticles ...........................
8
40
Figure 4-8: Importantdimensions for the investigation of the effect of the particleaspect
ratio ...............................................................................................................................................
41
Figure 4-9: Effect of the aspect ratio ofparticles on the surface topography...................
42
Figure 4-10: Normalizedpeak amplitude vs aspect ratio ofparticles ...............................
43
Figure 4-11: Effect of rotatingparticleson the surface topography .................................
44
Figure 4-12: Effect on the surface topography of non-uniform arrays ofparticles........... 47
Figure 4-13: Demonstrationof localizability of topographicalfeatures of a non-uniform
array ofp articles...........................................................................................................................
Figure 5-1: Effect of compressibility on surface topography.............................................
50
52
Figure 5-2: Comparisonof strainfor the relatively incompressible and compressible case of
different relative inter-particleligament lengths .....................................................................
53
Figure 5-3: Effect ofvarying the stiffness of the particles on the surface topography .....
55
Figure 6-1: Image of a typical experimental setup.............................................................
58
Figure 6-2: Comparisonof simulations and experiments offull RVE.................................
59
Figure 6-3: Comparisonof simulation and experimental resultsfor PESCs with different
num ber of rows ofparticles ..........................................................................................................
62
Figure 6-4: Comparison of simulation and experimental resultsfor PESCs with non-uniform
arrays ofp articles.........................................................................................................................
66
Figure 7-1: Simulation using axisymmetric elements and mismatching thermal expansion
coefficients to mimic the skin papillae of the cuttlefish ............................................................
Figure 7-2: Tensile loading of PESCs................................................................................
71
72
Figure 7-3: Different visual appearanceof identical surfaces with different light sources... 73
9
1. Introduction
In this thesis, we present a new technique to create surfaces that can rapidly and reversibly
change shape. This novel technique involves embedding stiff particles below the surface of an
elastic matrix, creating what we call particle-enhanced soft composites (PESCs). Deforming the
elastic matrix in a prescribed manner via an external or internal stimulus will yield different
surface topographies depending on the size, shape, arrangement, and material properties of the
matrix and particles. The stimulus can be applied in different ways, for example, mechanical
load or displacement, active matrix material controlled by pH change, heat, or electric field.
1.1. Bio-Inspiration and Applications
This work was inspired, in part, by the way cuttlefish camouflage themselves by changing
their surface topography. Some cephalopods, including benthic octopuses and cuttlefish, are
capable of dramatically changing their skin texture (Hanlon and Messenger, 1988). The organs,
SkinI papimae, espunsuiLe fi
nwUginig UI skilLS texiure
are capaDle of rapidly extending and
retracting (Allen et al., 2009). There is considerable variety in the shape and size of skin papillae,
and there may be different mechanisms for extending or retracting them. In a recent study, Allen
et al., 2009 investigated the mechanism behind the activation of dorsal papillae from cuttlefish
(Sepia officinalis). They found that the papillae they investigated were made up of both circular
and horizontal dermal erector muscles. In order to extend the papillae the circular dermal erector
muscles contract lifting the tissue in the center of the muscles toward the surface (Figure 1-1).
Simultaneously, the horizontal dermal erector muscles contract, pulling the skin towards the
middle of the papillae (Allen et al., 2013).
10
dem.h
+#
Figure 1-1: Schematic diagram of the mechanismfor activation of the skin papillae in Sepia
officinalis (Allen et al., 2013).
Tunable surfaces have potential applications in a number of fields other than camouflage. For
example, Crosby et al. designed a "smart" adhesive (Crosby et al., 2005). They made use of
wrinkling to pattern surfaces that tuned the adhesive properties of the surface. They showed that
by changing the wavelength of the wrinkles they could enhance adhesion. Surface topography
also can affect aerodynamic drag on objects. For example Achenbach showed that changing the
surface roughness on a circular cylinder causes the drag crisis (a dramatic drop in drag
coefficient) to occur at different Reynolds numbers (Achenbach, 1971). It has also been shown
that the wettability of surfaces is strongly influenced by the surface structure (Cassie and Baxter,
1944). With this in mind it is possible to tune the wettability of surfaces by modifying the surface
topography.
1.2. Overview of technique
The deformation of the surface of the PESCs depends upon the material properties of the
embedded particles, their shape, and their geometric arrangement within the soft matrix. In this
11
thesis we use finite element (FE) simulations and physical experiments to investigate the effects
of each of these parameters.
The focus of the first set of FE simulations was understanding the effects on the surface
topography of varying different dimensionless geometric parameters. The results are presented
in terms of dimensionless parameters and are relevant to many different length scales. The
results of the simulations are further examined to understand the mechanics underlying the
formation of different surface features. In a second series of simulations we investigated the
effects of varying the material properties of the embedded particles and matrix.
To validate the results of the simulations we conducted a representative set of physical
experiments. The experiments involved fabrication of prototypes using a multi-material 3D
printer. The prototypes were deformed in a mechanical testing apparatus. We used a high
resolution camera to capture images of the deformed surface and compared the results to the
predictions from the simulations.
1.3. Contributions
*
This thesis presents the novel idea and invention of using particle enhanced soft
composites to create tunable surface topographies. In our studies, the topography
transformations are activated by mechanically compressing the soft composite.
However other activation mechanisms are possible, such as using a responsive
material for the soft matrix that swells upon a change in stimulus.
*
The discovery and elucidation of design principles that can be used to build PESCs
with various desired behaviors.
12
"
The development of finite element simulations and codes that can be used to
investigate different PESC designs.
" Physical validation of the proposed method and material design for tunable surface
topography using physical prototypes and experiments.
1.4. Outline
Chapter 2 presents previous methods of creating tunable surface topography. We discuss
wrinkling in some detail, and several other methods more briefly. Chapters 3, 4 and 5 focus on
the FEA elements of this work. Chapter 3 presents the general setup of the PESCs in the
simulations, the constitutive model used, and the finite element details (e.g. mesh density,
element type, etc.). Chapter 4 presents the results of simulations that were run to investigate the
effect on surface topography of different geometric parameters. The geometric parameters
pertain to the size and shape of the particles as well as the arrangement of the particles in the
matrix. Chapter 5 presents the results of simulations that were run to investigate the effect of
different material properties on surface topography. The effect of changing both the
compressibility of the matrix and the stiffness of the particles were investigated. Chapter 6
discusses the setup and results of physical experiments intended to validate the results of
simulations. The results of the physical experiments are qualitatively compared to the
simulations results. In Chapter 7 we summarize the work, and then discuss some limitations and
suggest future directions.
13
2. Tunable Surfaces
While this thesis will focus on a new method for controlling surface topography, the concept
of creating materials with tunable surfaces is not new. Several different methods exist to create
tunable surfaces.
2.1. Wrinkling
Wrinkling is a term often used to refer to a surface instability that occurs when a stiff film is
attached to a soft substrate and, through the application of some stimulus, compressive stresses
form in the film causing the film to buckle into a wrinkled formation (Allen, 1969). One of the
most common examples of wrinkling occurs as people age. The skin is an organ that is
composed of 3 layers, and the top is thin and stiff compared to the layers below it. During the
gying process the Afferet
1
yr
h
p
cause coprssv srse
t- form
which induce wrinkles (e.g., Genzer and Groenewold, 2006).
The formation of wrinkles can be explained using an energy minimization argument. Under
axial compressive stress it is energetically favorable for a stiff film to buckle. When the stiff film
is not attached to a soft substrate, the film will buckle into the shape of a single half sine wave.
However, with a soft substrate attached, when the stiff film buckles it causes stretching in the
substrate. Because of this, the total energy of the system is a combination of the bending energy
of the film and the stretching energy of the substrate. Buckling of the film into a single half sine
wave would minimize the energy of the film, but it would induce a large stretching energy in the
substrate. For the energy of the entire system to be minimized the film buckles into a higher
14
mode with many sine waves. This causes a higher bending energy in the film, but greatly reduces
the stretching energy in the substrate, thus minimizing the total energy of the system (Allen,
1969).
The simplest case of wrinkling is an initially flat thin stiff film on a compliant substrate
undergoing uniaxial compression. For this case, after the onset of wrinkling, the surface will
form a sinusoidal profile (Allen, 1969). The wavelength, k, of the sinusoidal wrinkles is defmed
by Equation 1 (Huang et al., 2005).
A h= Ef1/3
27
P
Here, E =
EE
where E is the Young's modulus, v is the Poisson's ratio, h is the film
thickness, and the subscripts fand s refer to the film and substrate respectively. As Equation 1
indicates, the wavelength of the wrinkled surface can be varied by changing different material
and geometric parameters. For example, given certain material properties, a thicker film causes a
longer wave length (Li et al., 2012).
In the case of equi-biaxial loading there are a number of possible stable wrinkling modes
(Bowden et al., 1998). Figure 2-1 shows the some of the mode shapes that form under equibiaxial loading (Cai et al., 2011). Cai et al. showed that the lowest energy mode changes
depending on the level of overstress. They define overstress as a, where a, is the equi-biaxial
c
stress in the film at a given strain if the film had not buckled and o- is the critical value of stress
in the film at the onset of buckling. For higher levels of overstress (-
greater than about 1.5) the
herringbone mode is the lowest energy mode, and thus the favorable mode. For lower levels of
overstress ( a less than about 1.5) the square mode is the lowest energy mode. However, for
Uc
15
lower overstresses the square mode is not always seen in experiments. Cai et al. propose that
since the difference in energy of all the modes (other than the herringbone mode) is small, the
initial imperfections in the samples determine which mode the sample will take.
(a)
(b)
(c)
(d)
(e)
Figure2-1: Mode shapes thatform under equi-biaxial compression. (a) ID mode, (b) square
checkerboardmode, (c) hexagonal mode, (d) triangularmode, and (e) herringbonemode (Caiet
al., 2011)
Yin et al., 2012 showed that under equi-biaxial compression the sequence of loading can
affect the surface topography. They showed that for a case where the loading was simultaneous
the surface took a disordered labyrinth pattern. However, when the loading was sequential the
surface took an ordered herringbone pattern (Yin et al., 2012). Yin et al., 2014 expanded on the
previous work on sequential loading with an investigation of the reversibility of the wrinkling
patterns. They found that the transition from the initial flat surface to the ordered herringbone
patterns created through sequential loading were fully reversible upon release/restretching of the
system. However, the transition from the initial flat surface to the disordered labyrinthine pattern
created through simultaneous loading were found to not be reversible because of the formation of
regions of highly concentrated strain (Yin et al., 2014).
The patterns discussed so far are all for samples that are flat in the un-deformed state. Cai et
al., 2011 found that a slight initial curvature in their system caused a strong preference for
certain wrinkling modes to occur (Cai et al., 2011). This is consistent with the work of Cao et al.,
2008 on wrinkling on curved surfaces (Cao et al., 2008). They found that for spherical samples
16
the value of the geometric parameter R/h (where R is the radius of the substrate and h is the
thickness of the film) has a strong influence on the resulting wrinkled surface pattern. They also
found that varying the overstress in the film greatly influences the mode of wrinkling that
appears in the samples. In their investigation Cao et al. found that the surface took the form of
either a "triangularly distributed dentlike pattern" or a "labyrinthlike pattern." They found that
for both smaller values of R/h and overstress the triangular pattern occurred more. For higher
values of R/h and overstress, the labyrinthine pattern was favored.
Figure 2-2 shows these effects (Cao et al., 2008). Wrinkling on prolate spheroids was also
studied by Yin et aL., 2008. They showed that by changing the shape factor of the prolate
spheroid (defined by k = b/a where a and b are the equatorial and polar radius respectively) as
well as changing the ratio R/t (where R is the radius of curvature at the pole and t is the thickness
of the stiff film) both ribbed and reticular patterns could be formed (Yin et aL., 2008). Some of
their results are shown in Figure 2-3.
17
1.2
I
I
I
I
I
~
I
iL]
1.15
0
'3)
1.1
1.05
1
SI
15
w
I
20
30
R/h
50
75
100
Figure 2-2: Wrinkling patterns attainedon a sphericalsample (Cao et al., 2008)
O
L1,30
a
w
20
1~
At
13
1.1 1
,
S.ft
5.4
U
0
0
10
I
I,
15
ow
20
35
Nonntid sim RlI
50
I
75
Figure2-3: Wrinkling patternsattainedon a prolatespheroidwith varying k and R/t. The
black line separatesthe ribbedand the reticularpatterns (Yin et al., 2008)
18
2.2. Other tunable surfaces
One limitation to wrinkling is the fact that it is difficult to control the shape and distribution
of localized surface features. Cabuz et al. (Cabuz et al., 2001) developed a method to get around
this issue. Their method uses a combination of electrostatic and pneumatic forces to control the
surface topography. They mount a flexible cover on top of a series of cavities. The cavities are
then filled with some sort of working fluid (either liquid or gas) and the shape of the cavities are
controlled by a series of electrostatic electrodes used as electrostatic actuators. This method has
the advantage that it allows for individual control of the cavities and thus localized control of the
surface topography. However, this method has drawbacks including the fact that it requires
electrical circuitry throughout the whole sample.
Another method for creating tunable surface topography uses the responsive behavior of
hydrogels (Sidorenko et al., 2007). They combined an "array of isolated high-aspect-ratio
structures" (AIRS) with a hydrogel to form what they call hydrogel-AIRS or HAIRS. These rigid
structures were made of silicon nanocolumns. Their method makes use of the swelling behavior
of hydrogels when exposed to water to activate the surfaces. When the HAIRS are dry the
nanocolumns rest at angles between 600-700 to vertical, however when exposed to humidity the
hydrogel swells causing the nanocolumns to reorient themselves. Depending on the amount of
humidity, the nanocolumns can reach anywhere from the dry rest angle all the way to vertical.
When the hydrogel is dried out the nanocolumns return to their initial position, so the process is
fully reversible. Also this method relies on the swelling of hydrogels as the actuation method,
which means that the humidity of the environment must be controlled.
Another method to create tunable surface topography uses elastomeric materials to
create structures with periodic and random arrangements of voids with a thin-film of the
19
same elastomer on top of the structure (Kozlowski, 2008). Kozlowski found that when the
structure underwent uniaxial compression the film would form convex domes over the
voids in the base structure. Since the material is elastomeric, it can be assumed that upon
unloading, the structure would recover its initial shape, meaning that it is a fully reversible
process.
For the specific application of making surfaces that can switch from wetting to non-wetting,
a variety of methods have been created to change the surface topography. Lahann et al., 2003
created surfaces that were able to transition from hydrophilic to hydrophobic states through the
application of an electrical potential (Lahann et al., 2003). The electrical potential caused a
reorientation of the (1 6-Mercato) hexadecanoic acid (MHA) molecules that formed a monolayer
on the surface of a gold sample. When an electrical potential is applied the molecules reorient
themselves to make the surface hydrophilic, and when the potential is removed the molecules
reorient to make the surface hydrophobic. Minko et al. created surfaces that were capable of
switching from hydrophilic to hydrophobic through exposure to different solvents (Minko et al.,
2003). They used a needlelike structure that was covered in a mix of hydrophobic and
hydrophilic polymers. Exposing the surface to different solvents caused the morphology to
change in different ways. Depending on the solvent used the surface could take on either a
hydrophilic or a hydrophobic shape. Some of these methods for changing the surface shape in
reversible ways only apply to very small length scales (nm - ptm scale) and thus have limited
applications.
20
3.Finite Element Simulation Details
3.1. General Simulation Layout and Boundary Conditions
We simulated several different particle distributions. In each simulation, the PESCs were
made up of a soft matrix with stiff particles embedded below the surface. While we varied the
size, shape and arrangement of the particles from simulation to simulation, we kept many
features the same for all the simulations. Each sample was composed of two arrays of particles
that were symmetric about the horizontal central axis (Figure 3-1a). The space between the two
arrays was sufficiently large that neither array affects the other. The PESCs were all of a similar
size with the particles and the inter-particle spacing on the order of 1cm.
All simulations were run using the commercially available FE software Abaqus 6.11.
In each simulation, periodic boundary conditions were applied to the left and right side of the
PESC. Using periodic boundary conditions ensures that each simulated PESC can be seen as a
representative volume element (RVE) that could be repeated over and over. A displacement
boundary condition was applied to the left and right sides, causing the sample to be compressed
to 20% global strain linearly ramped over the course of the loading step (Figure 3-1b). In all of
the simulations, the top and bottom surfaces were left free to deform, since those are the surfaces
of interest.
21
I
F
(a)
(b)
Figure 3-1: Basic PESC setup. (a) PESC arrangementbefore startingsimulation. (b)
Displacement boundary conditions appliedto the left and rightside of the PESC shown after
compression at 20% global strain
The use of periodic boundary conditions allowed us to simulate the behavior of a large
sample while saving on computation by using a smaller RVE. Some of the RVEs analyzed in this
thesis are shown in Figure 3-2. The figure also shows the unit cells associated with each RVE.
Each of the geometries shown has two different unit cells, and the RVEs were 4 of the first unit
cells shown. Simulating a single unit cell would be sufficient to give the response of the PESC.
For easy visualization and post processing, we chose to conduct simulations with multiple unit
cells.
22
Figure 3-2: Several RVEs usedfor simulations and their correspondingunit cells
A methodology for the implementation of general three-dimensional periodic boundary
conditions for repeating structures was developed by Danielsson, Parks and Boyce (Danielsson
et al., 2002). A simplified version of their methodology was used in our work because the
periodic boundary conditions were two-dimensional and only needed to be applied on two
surfaces. Figure 3-3 shows an example of the general periodicity of the deformation of the two
surfaces. The nodes on the left side are defmed to be a set XI while the nodes on the right side
are defined to be a set X2.
23
2
i
L2
X2
X1
Li
Figure 3-3: General example ofperiodic boundary conditions on two surfaces
The periodic boundary condition was defined mathematically to prescribe a relationship
between the "1" (horizontal) degree of freedom of XI and X2 and the "2" (vertical) degree of
freedom of XI and X2 in Equation 2.
uj
2
_uj1= H
4L
U2
u2=
21L
(2)
In these equations, u'j is the displacement in the i-direction of each node in the!j" node set,
H11 and H 2 1 are the elements of the displacement gradient tensor (Hij =
where Xj is the
specific original position), and L, and L 2 are the lengths of the RVE shown in Figure 3-3. In this
thesis all of the simulations were run under axial compression in the 1-direction. The
displacements H1 1 and H21 were defined in the simulations using virtual nodes. The virtual
nodes are nodes that are not part of the mesh representing the PESC. The nodes were given
displacements of H1 1 = -0.2 and H21 = 0. Using those values in Equation 2 induced axial
compression of 20% global strain in the 1-direction. It was also necessary to fix the displacement
of a single node so that the entire sample would not undergo translation. The way we have
implemented the periodic boundary condition fixing the displacement of a single node also
24
prevents rotation of the system. Since we set H2 1 = 0 the nodes of the XI set are unable to
move vertically relative to the nodes of the X2 set and thus no rotation of the system is allowed.
In this thesis the stationary node was selected to be the top right node, as shown in the deformed
configuration in Figure 3-3.
3.2. Constitutive Model
It is important to assign realistic material properties to both the particles and the matrix in the
PESCs. A compressible neo-Hookean constitutive model was selected for both the particles and
the matrix. The neo-Hookean model used in Abaqus is described using a strain energy potential,
as shown in Equation 3a.
U = C 1 0(f - 3) +
(J
1)2
(a)
G = 2C10
(b)
K =
_2
B
(c)
j= fdetB
F - FT
(d)
The first term in Equation 3a (with
trace (B)(3
t1= (B
(e)
It in it) corresponds to the energy
(f)
stored due to isochoric
change of shape. The second term in Equation 3a (with j in it) corresponds to the energy stored
due to change of volume. The bulk, K, and shear, G, moduli are related to the variables D, and
CIO as shown in Equations 3b and c. The variables I, and j are defined using the left CauchyGreen deformation tensor, B. The Cauchy-Green deformation tensor is defined using the
deformation gradient, F (Fij = x,
where xi is the current position and Xj is the original
position), and its transpose FT, as given in Equation 3d. The term j is the volume ratio and is
defined by Equation 3e. The term I, is called the first deviatoric strain invariant, and is defined
by Equation 3f.
25
The compressible neo-Hookean model requires a bulk modulus and a shear modulus. The
values for the bulk and shear moduli used in most of the simulations were based on the
properties of the materials that were available in the 3D printer that was used for the physical
experiments. In some simulations, described later, we explored the effects of other material
properties. The bulk and shear moduli of the 3D printed materials were estimated by
experimentally determining the elastic modulus and estimating the Poisson's ratio. The measured
elastic modulus of the matrix and particles were approximately IMPa and 1.5GPa respectively.
We assumed that both the matrix and the particle materials were nearly incompressible with
Poisson's ratios of 0.499 and 0.490 respectively. Using these values, we calculated a bulk and
shear moduli for both the matrix and the particles, Table 1.
Particles
G MPa
K MPa
500
25000
Table 1: Materialpropertiesusedfor most simulations
As Table 1 shows, in the simulation the bulk modulus for the matrix is about 500 times
larger than the shear modulus. In reality the ratio of the bulk modulus to the shear modulus (K/G)
is probably much larger since the bulk modulus is likely actually greater than 1GPa. However,
using a more realistic bulk modulus increases the computational time dramatically. After running
simulations with several different bulk moduli we found that increasing the ratio K/G by a factor
of 10 had negligible effects on the results of the strain distribution and topography. This led us
to conclude K/G equal to approximately 500 is large enough to be accurate while being small
enough to keep the computational time reasonably short.
The compressible neo-Hookean model was chosen in large part because of its
computational simplicity. However, there was good agreement between simulations with the
26
neo-Hookean model, and physical experiments with the 3D printed materials. In physical
compression experiments with the matrix material Dr. Hansohl Cho was able to create a true
stress vs. true strain curve (Figure 3-4). Comparing his experiments to simulations shows that
the neo-Hookean model for the matrix material is reasonably accurate up to 100% true strain.
0.8
0
0.6
- Experiment
0.4
OSimulation
0.2
0
0
0.2
0.4
0.6
0.8
1
True Strain
Figure3-4: Experimental validation of neo-Hookean materialmodel. Datagatheredand
compiled by Dr. HansohlCho (personalcommunication, May, 2014).
3.3. Numerical Details
Meshing of the geometry of particles within a matrix was done using meshing algorithms
within Abaqus. The mesh density was defined by applying a global seeding to all edges.
Different seed densities were tested for a few select simulations in order to determine the
smallest mesh density that still gave stable results. The final mesh density was chosen by
selecting a value of the global seeding that when doubled changed the maximum resultant von
Mises stress by less than 5% (Figure 3-5). We performed the meshing in Abaqus with the
element shape defined as "Quad-dominated", the technique was "Free" and we used the
27
"advanced front" algorithm. These were all built in meshing options in Abaqus. The particles
were modelled to be perfectly bonded to the matrix.
Mises (MPa)
I
Mises (MPa)
1.40
11,33
0.028
0.038
(a)
(b)
Figure3-5: Validation of mesh density. For most simulations the mesh density was chosen to
be that of (a). The mesh shown in (b) is twice as dense as the mesh in (a) and the difference in
maximum von Mises stress is less than 5%
Selecting the element shape as quad-dominated made the mesh into a mixture of quadrilateral
and triangular elements. In all simulations, unless otherwise specified, the elements were of the
plane strain family. We did this because of the plane strain nature of the physical experiments
that will be presented later. The majority of simulations used linear, reduced integration
elements. These types of elements were CPE4R and CPE3 (quadrilateral and triangular
respectively). In some cases when the simulation was unable to converge to a solution with the
types of elements described above, the elements were changed to plane strain quadratic elements
(CPE8 and CPE6M). These types of elements were not used for the majority of the simulations
28
because that would have dramatically increased the computational time without increasing the
accuracy of the results.
For all of the simulations, the step type was "Static, General" with non-linear geometry. We
used non-linear geometry because of the large deformations and corresponding large changes in
geometry as well as the nonlinear behavior of the material.
29
4. FE: Varying Geometric Parameters
This chapter will focus on the effect on the surface topography of changing various
geometric parameters of the PESCs. These geometric parameters are related to the size, shape
and distribution of the particles.
4.1. Uniform Array of Particles
We define a uniform array as an array of particles in which all the particles are the same size
and are distributed in a periodic arrangement. We present geometries in a dimensionless way by
computing ratios of geometric features relative to one reference feature.
In this section, all of the PESCs examined are made up of hexagonal arrays of ellipsoidal
particles. Figure 4-1 shows the important dimensions that will be referred to in this section; a is
spacing of the hexagonal array, a is the size of the particle axis perpendicular to the surface,
p is
the size of the particle axis parallel to the surface, and c is the distance between the first row of
particles and the surface.
The first dimensionless geometric parameter that will be investigated in this section is
.
Figure4-1: Important dimensions of the uniform arrayof particles
a
That parameter represents the relative inter-particle ligament length and, for the case of circular
particles,
a
a
is the inter-particle ligament length. The second parameter that will be
30
investigated is the number of rows of particles. The last dimensionless parameter that will be
investigated in this section will be a/p, which is the aspect ratio of the particles. To
systematically investigate the effect of each of these parameters, a number of other
dimensionless parameters were held constant. These parameters will be discussed in more detail
in the following sub-sections.
4.1.1. Effect of relative inter-particle ligament length
The relative inter-particle ligament length is defined by the dimensionless parameter a2f.
In
a
the investigation of the effect of this parameter on the surface topography, other parameters were
held constant. The aspect ratio of the particles (a/0) was held at a constant value of 1, meaning
that the particles were all circular. The parameter c/o was held at a constant value of 0.2,
meaning that the distance between the particles and the surface was 5 times smaller than the
radius of the particles. In this section, we set the number of rows of particles to 3.
The parameter a aa was varied between the values of 0.2 and 0.6, and in all simulations the
PESCs were compressed to 20% global strain. The parameter a-a
was modified by changing
the value of f and holding the value of the hexagonal spacing constant. Figure 4-2 shows the
results of simulations with 4 different relative inter-particle ligament lengths at global
compressive strains of 0%, 10% and 20%. The first thing to notice in the figure is that as the
PESCs are compressed the surface transitions smoothly from the initial flat state to the final
shape without an instability occurring. This is a feature that distinguishes the PESCs from other
methods of creating reversible surface topography, such as wrinkling, which are driven by
instabilities. The smooth transition of the surface shape is important because it means that the
loading can be stopped at any point to get an intermediate surface shape. Figure 4-3 shows the
31
normalized peak amplitude (where peak amplitude is the vertical distance from the highest point
on the surface to the lowest point on the surface) graphed against the global strain for the PESCs
with different relative inter-particle ligament lengths. The graph verifies that the surface changes
smoothly as the global strain is changed. The normalized peak amplitude vs. global strain curves
are fit perfectly by a quadric (shown by the dotted lines). We do not yet understand the reason
for the quadratic fit.
=
4.
4.
0.2
a
a-2=
0.33
-2l=
0.5
a2'=
0.6
a
E =
0.0
Figure 4-2: Effect of
E= -0.10
a
a
E= -0.20
on the surface topography
32
4.
4.
-
Peak Amplitude/a vs Global Strain
0.2
0.18
*
=
0.2
=
0.33
0.16
0.14
+_2a
2
"a 0.12
a
0.1
01
a
5
0.6
=_2
M
0.061
0.04~
40-
.-
0.02
0
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
Global Compressive Strain (IEI)
Figure 4-3: Normalizedpeak amplitude vs. global strainfor different values of
a-2p
a
Another feature present in each simulation shown in Figure 4-2 is the minimum heights of
the surfaces are aligned directly above the particles in the first row. This occurs above the first
row of particles in all of the PESCs that have been examined as part of this research. These
global minima are always aligned directly above the particles in the first row because the
particles near the surface constrain the deformation of the matrix and act as what we call a
"pinning region".
Looking at the top right image in Figure 4-2, we see that between the pinning regions the
surface topography has a single large peak. This peak is aligned directly above the particles in
the second row. As a-2fl is increased to a value of 0.33, there is still a single peak aligned
a
directly above the particles in the second row; however the peak appears to be a bit flatter than
with the smaller relative inter-particle ligament length. When the relative inter-particle ligament
33
a-2#3
length is increased to a a- value of 0.5 or greater, there is no longer a single peak located
above the particles in the second row. Instead what appears is a local minimum aligned at that
location. We refer to these local minima aligned above the particles in the second row as
"bisected peaks."
To understand why the bisected peaks only appear for larger values of a 2#, the mechanics of
a'
the deformation needs to be understood. Figure 4-4 shows strain contours for different cases of
relative inter-particle ligament lengths. The first column in the figure is the normal strain
represented in terms of the X'-Y' coordinate frame, the second column is the shear strain in the
X-Y coordinate frame, and the third column is the volumetric strain. The strain displayed in the
images in the first column corresponds to inter-particle shear strain in the matrix. Notice the
alternating tensile LExx, and compressive LExx, in the matrix at each inter-particle matrix
bridging. This implies that the global compressive strain being applied to the PESC is being
accommodated primarily by local inter-particle shear strain in the matrix. The fact that the strain
in the matrix is primarily shear strain occurs because the matrix is nearly incompressible, so the
global compression causes shape change primarily through inter-particle shear in the PESC
rather than volume change. When we compare the magnitude of the volumetric strain to the
magnitude of the shear strain shown in the contours of Figure 4-4, we see that the volumetric
strain is orders of magnitude smaller than the shear strain. In the figure, the strain in the particles
is not shown because they hardly deform, and instead move as rigid bodies.
34
LErr Compression
LErxr Tension
I+0.97
I0.015
LEXV
LExT
+1.97
0
a-2fl=0.2
a
0
0
I
I0.0
-0.011
-1.98
-1.0
LErr
LExy
+1.21
00.59
0
a-2#= 0.33
0
a
-2.16
-0.60
LErr
-0.0055
LExy
+0.0012
0
a"=
a
0.5
-0.0032
-0.56
-0.30
LExy
LExT
+0.0011
+0.51
f+0.23
0
0
a
10
1-0.47
-0.0030
E.,
= LExx + LEyy
Figure 4-4: Strain contours of different relative inter-particleligament lengths shown at 20%
global compressive strain
Further examination of Figure 4-4 reveals that the shear strain is concentrated primarily in
the inter-particle ligaments. This is especially true for the case of the smaller ligaments, where
well defined shear bands appear. It is clear from the figure that there is a significant difference in
the magnitude of strain for different inter-particle ligament lengths. The magnitude of strain is
much larger for the smaller values than for larger values of
35
a
. This is because the larger the
inter-particle ligament, the more the shear is dispersed throughout the matrix causing a lower
magnitude of shear strain.
Figure 4-5 helps to explain how the difference in magnitude of shear strain in the matrix
leads to different surface topographies. In general what happens is that the concentrated interparticle shearing that was seen in Figure 4-4 (and again in the left most images of Figure 4-5)
leads to the matrix being extruded through the inter-particle ligaments into the region below the
surface. Figure 4-5a shows that when the inter-particle ligaments are smaller, the higher
magnitude of shear strain causes the matrix to be extruded from the region between the particles
in the second row far out into the region directly below the surface between the particles in the
first row. For these smaller inter-particle ligaments, the extrusions from two adjacent regions
merge together above the particles in the second row and push the surface up to form the single
large peak. Figure 4-5b shows that when the inter-particle ligaments are larger and the shear
strain is more dispersed so the magnitude is less, the matrix does not extrude as far into the
region below the surface. Under these conditions the two extruded regions do not merge together
to push the surface up.
36
+0.97
(a)
a
a
0.2
LEXY
= 0.6
Figure4-5: Schematic diagram of matrix extrusion due to shearing. (a) Schematic
correspondingto smaller inter-particleligaments lengths. (b) Schematic correspondingto larger
inter-particleligament lengths.
4.1.2. Effect of the number of rows of particles
To investigate the effect of the number of rows of particles on the surface topography we
arranged the particles in a hexagonal array similar to that used in the investigation of the effect of
the inter-particle ligament length. The important geometric dimensions used in this section are
the same as those seen in Figure 4-1. The parameter c/a was held at a constant value of 0.25,
which means that the ratio of the distance between the particles and the surface to the size of the
particles was unchanged. The aspect ratio of the particles (a/0) was set to a constant value of 1.5.
We set the relative inter-particle ligament length (a-)a
to a constant value of 0.467. The value
of the relative inter-particle ligament length was set by choosing both a constant hexagonal
spacing (a) and a constant semi-minor axis of the particles (p).
Figure 4-6 shows the results of simulations at 0, 10%, and 20% global compressive strains. In
the figure the only parameter that is changed is the number of rows of particles in the PESC. In
37
the top row of the figure, in which the PESC has a single row of particles, the surface develops a
series of single large peaks aligned between the particles in the first row. When a second row of
particles is added (the second row of Figure 4-6), the surface takes on an overall flatter shape.
The single large peak we saw for a single row of particles is replaced by a small bisected peak.
When a third row of particles is added, the surface takes a shape that is somewhere between the
shapes it made with a single row of particles and two rows of particles. After deformation the
PESC with three rows of particles has a flatter surface than that of the PESC with a single row of
particles, but not as flat as the surface of the PESC with two rows of particles. When a fourth
row of particles is added, the surface looks very similar to the surface seen for the PESC with
three rows of particles.
The last column of Figure 4-6 shows the strain contours in the matrix at 20% global strain. In
the case where there is a single row of particles, the shear strain is highest at the surface where
the pinning region exists. When a second row of particles is added, the highest shear strain is
concentrated in bands along the inter-particle ligaments. The magnitude of the shear strain also
increases when a second row of particles is added. When a third row of particles is added, the
highest shear strain is still concentrated in the inter-particle ligaments. The magnitude of the
shear strain also increases when a third row of particles is added. When more rows of particles
are added beyond the third row, the highest shear strain remains concentrated in the inter-particle
ligaments, however the magnitude of the shear strain does not increase by much.
38
LExy
|+0.40
0
-0.43
LExy
+0.82
-0.77
LEy
+1
55
LEn
-0
+1.50
-1.54
0
=-0.10
E= -0.20
E= -0.20
y
Figure4-6: Effect of number of rows ofparticles on the surface topography
To quantify the effect of the number of rows of particles, we looked at the peak amplitude of
the surface. The peak amplitude is again defined as the vertical distance between the highest and
lowest points on the surface. Figure 4-7 shows the effect of the number of rows of particles on
the peak amplitude of the surface. Looking at the images in Figure 4-6, it is no surprise that the
PESCs with one row of particles have the highest peak amplitude. We saw in Figure 4-6 that
when a second row of particles was added the surface dramatically flattened out. That flattening
of the surface causes the peak amplitude to drop dramatically, as seen in Figure 4-7. Each
successive odd row of particles that is added causes an increase in peak amplitude and every
39
even row that is added causes a decrease in peak amplitude. However, every time a new row is
added it causes the peak amplitude to change by less than the previous row did. As the number
of rows grows, the normalized peak amplitude seems to approach a stable value. This is because
each successive row that is added is further from the surface, and will therefore have less of an
effect on the topography.
Peak Amplitude/a vs. Number of Rows
0.2
0.19
Even Number of Rows
-+
-
M 0.18
Odd Number of Rows
0.17 -
0.16
-
.
0.015
<0.14
0.13
0.
0.12
0.11
0.1
0
1
2
4
3
5
6
7
8
Number of Rows
Figure 4-7: Normalizedpeak amplitude vs. number of rows ofparticles
4.1.3. Effect of the aspect ratio of particles
To investigate the effect of the aspect ratio, a/p, of the particles on the surface topography,
we looked at PESCs made up of an array with a single row of particles. Since the particles are
no longer part of a hexagonal array, not all of the dimensions shown in Figure 4-1 still apply.
The dimensions used in this section are shown in Figure4-8. To investigate the effect of the
aspect ratio, other dimensionless parameters were held constant. We set the dimensionless
parameter c/b, i.e. the ratio of the distance between the particles and the surface to particle
spacing, to 0.058. The parameter ac*b was set to 0.27. The numerator of this parameter was held
40
constant meaning that the area of the particles was unchanged. In the denominator we held
constant both the distance from the particles to the surface (c) and particle spacing (b).
Figure4-8: Important dimensionsfor the investigation of the effect of the particleaspect
ratio
Figure 4-9a shows several different simulations in which the aspect ratio of the particles were
varied. It is clear from the figure that changing the aspect ratio of the particles dramatically
changes the surface topography. For the higher values of a/P (the narrower particles) the pinning
regions form sharp valleys while the area between pinning regions form a wide single peak. The
pinning regions of the PESCs with lower values of a/P (the wider particles) form much wider
valleys with narrower peaks in between. This implies that the larger the projected area of the
particles onto the surface, the larger the pinning region will be. This is true because the particles
constrain the deformation of the surface near them, and thus a larger the projected area on the
surface leads to the particle constraining the deformation of a larger area.
41
(a)
LE1
P+ L03
1+.44
+0.21
4MbMOO
=3.43
0
E
4M
E -0.2
-0.1
__=_-0.2
(b)
0
_.0_57
IEX
at- 0.21
0
-2.00
0.40
I
a0.86
1.044
a
-0i
= 3.43
LEV
mm
*.60
at4e4
m0
-0.55
0
-0.2
=-0.2
LEV~
-1.35
= 0.21
4O
41
0
LEV
5
S+0.85
*4**0
-=0.86
a0
=
3.43
0 0.5
01+.80
-
..3
0
=-0.2
E= -0.2
Figure 4-9: Effect of the aspect ratio ofparticles on the surface topography
Figure 4-9b shows simulations in which the particles were changed from the usual ellipsoidal
shape to either diamonds or rectangles. In these simulations the aspect ratio of the particles were
varied in the same way as in the simulations of ellipsoidal particles, and the same constant values
42
were used for dimensionless parameters. In the case of both the diamond and the rectangular
particles, fillets were added to the corners because without them the simulations were not able to
converge to a solution. As was true for the ellipsoidal particles, the larger the projected area of
the particles the larger the pinning region. One notable difference is that for the diamond-shaped
particles at smaller values of a/p, the particles deform by bending at the tips, where the particle is
thinnest.
The last columns in Figure 4-9a and b show shear strain contours in the matrix. For all
shapes of particles the magnitude of the shear strain is the largest for the case with the widest
particles. For the cases with the widest particles, the shear strain is concentrated primarily on the
surface of the particles near the sides. When the particles are narrower (for both - = 0.86 and
3.43) the magnitude of the shear strain is much smaller than for the widest particles. We believe
that this is because the wider particles have less space between them, and thus interact with one
another more, causing higher magnitudes of shear strain.
Peak Amplitude/b vs u/
0.1
0.095
0.09
0.085
C
0.08
0.075
0.07
0.065
0.061
0
-1
0.5
1
1.5
2
2.5
3
3.5
4
a/P
Figure4-10: Normalizedpeak amplitude vs aspect ratio ofparticles
43
To quantify the effect of the aspect ratio on the surface topography, we again examined the
peak amplitudes. Figure 4-10 is a plot of the peak amplitude normalized by the particle spacing
against the aspect ratio of the particles. All of the data points in the figure are based on PESCs
made up of ellipsoidal particles. The PESCs were all compressed to 20% global strain. The
figure shows that the narrower particles (highest values of a/0) induce a larger peak amplitude.
As the particles become wider the normalized peak amplitude appears to decay nearly linearly
until a/P reaches a value of 0.5. Below that value of a/p, the normalized peak amplitude climbs
as the particles become wider. The blue point on the curve corresponds to the simulation in
which the particles had an aspect ratio of 0.15. The sudden large jump in peak amplitude from
an aspect ratio of 0.21 to 0.15 can be explained by looking at Figure 4-11.
(a)
LExy
=
0.1
$
$ $$
#$
$
+1.18
1***W
f*1
0
S0.15
I
-1.61
LExy
+1.03
a0
0.21
_ _
_
0
_ _
_
_ _
_
_
_
_
_
e=-0.19
=-0.18
_
_
_
c=-0.20
=-0.20
101
Peak Amplitude/b vs Global Strain
(b)
0.12
0.1
0.08
1
X0.04
0.04
0.
0
0.05
0.1
0.15
0.2
Global Compressive Strain ( E1)
Figure4-11: Effect of rotatingparticles on the surface topography. (a) Resultant surface
topographyfor PESC with a/8 = 0.15. (b) Graph of the normalizedpeak amplitude vs the global
compressive strainfor a/3=O. 15.
44
Figure 4-1la shows the results of the simulation for PESCs with particles of two different
aspect ratios. For global compressive strains up to 18%, the results of the simulations for both
aspect ratios show that the deformation in the matrix is symmetric. However, somewhere
between 18% and 19% global strain the particles with the smaller aspect ratio rotate in the
matrix, while the particles with a higher aspect ratio do not rotate. The rotation causes the
particles to pull the surface down near the right side of each particle and push the surface up near
the left side of each particle. This pushing up and pulling down causes a larger peak amplitude
to form, which explains the large jump in normalized peak amplitude seen in Figure 4-10.
Looking at the shear strain contours, we again see that for the wider particles the magnitude of
the shear strain is larger.
This effect can be seen in Figure 4-1 lb, where the normalized peak amplitude is plotted
against the global compressive strain for an aspect ratio of 0.15. The blue points correspond to all
the strains before the particles rotate and the red points correspond to the strains after the
particles rotate. In the figure the black line is a quadratic fit to the blue points with an R2 value of
0.9999. It is clear from the figure that the rotation of the particles causes the normalized peak
amplitude to increase more than it would have if the particles simply moved closer to one
another without rotating.
While Figure 4-11 a helps to explain why there is a large jump in normalized peak amplitude
for the smallest aspect ratio, it also reveals several important details about that particular
simulation. First, the rotation of the wider particles indicates an instability in the system that was
not seen for higher values of a/p. This instability causes the surface to suddenly change from a
symmetric shape to a non-symmetric shape. This means that even with an initially symmetric
arrangement of particles, it is possible to create surface topographies that are not symmetric.
45
Also the fact that the instability did not occur until a certain amount of strain was reached means
that with certain arrangements of particles it is possible to create both symmetric and nonsymmetric surface topographies. While this instability was only seen for the smallest aspect
ratio, we conjecture that a similar instability may occur for other aspect ratios if the PESCs were
compressed to more than 20% global strain.
4.2. Non-uniform arrays of particles
To this point, we have only investigated uniform arrays in which all of the particles are
identical. In this section, we investigate non-uniform arrays of particles in which there can be a
mixture of particles with different sizes and shapes.
We look first at a mixture of circular particles of different sizes. In these arrangements the
smaller particles are embedded in the matrix between the larger particles that would make up a
uniform array. Figure 4-12 shows the results of several simulations of the non-uniform arrays
along with the original uniform arrays.
46
LEky
+0.65
(a)
0
I
-0.65
LExy
(b)
01
I
I
+0.65
-0.65
i+050
LEny
0
I
(c)
-0.49
LEny
1+0.90
4.
*
I
I
(d)
1-0.90
LEXy
+1.16
(e)
4.
I
I
0
-1.09
LExy
+0.58
4.
I
0
-0.55
E= 0
E = -0.20
E = -0.10
E = -0.20
Figure 4-12: Effect on the surface topography of non-uniform arrays ofparticles
Figure 4-12 shows several simulations of both uniform and non-uniform arrays of particles.
Figure 4-12a and b are both made up of smaller particles that are embedded into the matrix
between larger particles that are arranged as the uniform array shown in Figure 4-12c. Similarly,
Figure 4-12d and e are both made up of smaller particles that are embedded into the matrix
between larger particles that are arranged as the uniform array shown in Figure 4-12f. For both
Figure 4-12c and f, the uniform array is defined with constant values of the dimensionless
parameters: a/c = 20, a/u = 4 and a/P = 1. In those parameters the dimensions a,c, and a are
47
defined as described in Figure 4-1. For all of the non-uniform arrays shown in the figure we set
the parameter a/r, where r is the radius of the smaller particles, to 2.
In Figure 4-12a, the smaller particles are aligned such that the distance between the smaller
particles and the surface (c as defined in Figure 4-1) is the same as those for the larger particles
and the surface. In Figure 4-12b the smaller particles were aligned such that the centers of both
the smaller and larger particles lay on the same horizontal plane. As shown in Figure 4-12c, with
the uniform array of a single row of particles a single large peak forms on the surface at a
location directly between the particles. When smaller particles are added a bisected peak appears
aligned directly above the smaller particles where the single large peak was seen for the uniform
array. For the case in Figure 4-12a, the valley aligned above the smaller particles has a larger
radius of curvature than that of the valley seen at the same location in Figure 4-12b. This is
because when the smaller particles are closer to the surface those particles more easily constrain
the deformation of the matrix causing the pinning region to be larger. The larger pinning region
leads to a wider valley, i.e., the radius of curvature is larger.
Figure 4-12d, e and f show the results of simulations nearly identical to Figure 4-12a, b and
c, but with two rows of larger particles instead of a single row. In the case of Figure 4-12f, the
PESC forms a bisected peak without the addition of the smaller particles. This is because the
second row of particles is pinning the surface, as was discussed in section 4.1.2. When the
smaller particles are added to the array, the bisected peak becomes much more pronounced. As
we saw for the single row of particles, the valley located above the smaller particles has a larger
radius of curvature for the case where the distance c is constant than for the case where the
central horizontal axis of the smaller particles is aligned with the central horizontal axis of the
48
larger particles. This can be explained with the same reasoning used for the single row of
particles.
Looking closely at Figure 4-12e, we see that as the PESC is compressed the smaller particles
move down relative to the larger particles in the first row. This movement is not seen in Figure
4-12b where there is a single row of particles. For the case with two rows of larger particles, the
smaller particles move down because they are being pulled down by the larger particles below
them. The combined effects of both the smaller particles and the larger particles in the second
row cause the surface to be pulled down further in the region where the bisected peak appears.
This in turn causes the bisected peak to appear sharper than the case shown in Figure 4-12d.
The last column of Figure 4-12 shows the shear strain in the matrix for each case. Looking at
the contours we see that for both one and two rows of particles, the magnitude of the shear strain
is larger for the case where the smaller particles are in the matrix. It should also be noted that for
two rows of particles, when there are no small particles the shear strain forms bands between the
particles. However, when the smaller particles are added there is a concentration of high
magnitude shear strain located on the bottom surface of the small particles and the shear bands
are not as prominent.
Another non-uniform array of particles is shown in Figure 4-13. The PESC shown in this
figure have a mixture of particles with different sizes, shapes, and orientations. Looking at the
deformed surface of the PESC it is clear that a variety of different topographical features are
formed in a single PESC. The shape of each topographical feature is controlled primarily by the
particles in the immediate vicinity of the feature. For example, looking at the region shown in
the red circle, the surface forms a shape similar to that seen in Figure 4-12e. This is because in
49
the region near that topographical feature the particle distribution is similar to that seen in Figure
4-12e. Looking at the shear strain contours, we see a similar shear strain distribution in the
region associated with that surface feature. Also in the shear strain contours we see bands of
shear strain forming in the regions where the particles form a staggered array. Similar regions of
shear bands were seen in previous cases with a staggered array of particles. The fact that the
shape of topographical features is controlled primarily by the particles near the feature is
important because it means that this method of creating tunable surfaces allows for highly
localized control of the surface topography, which is difficult to do through other methods such
as wrinkling.
0
LExy
E
L~xy
=-0.2
j+0.60
-0.60
Figure 4-13: Demonstrationof localizability of topographicalfeatures of a non-uniform
arrayofparticles
50
5. FE: Varying Material Properties
In previous chapters, we explored the effect on the surface topography of changing different
geometric parameters. The coefficients used for the material model in the simulations were
chosen to mimic the material properties of the materials used by the Objet5OO Connex MultiMaterial 3D printer that made the samples used in the physical experiments.
In this chapter, we address the effect of changing the material properties of both the matrix
and the particles. We do this using simulation only.
5.1. Varying compressibility of the matrix
As discussed in section 3.2, the material used by the 3D printer to create the matrix was
relatively incompressible compared to the amount it could be sheared. In this section we focus on
investigating the effects of a more compressible matrix. Table 2 shows the pertinent material
properties of the two materials used for the matrix. The material that was based on the 3D printed
samples will be referred to as relatively incompressible, while the other material will be referred
to as compressible. For the relatively incompressible material, the bulk modulus was about 500
times larger than the shear modulus, whereas for the compressible material the bulk and shear
moduli were of the same order of magnitude.
K (MPaL
K/G
N
G (MPa)
Relativelyl ncmressible
0.33166J
5 52
09
0.250
1.65
0.66
0.4
Compressible
Table 2: Materialproperties of the matrix with different compressibility
We now examine the effect of the compressibility for two different particle arrays with
different relative inter-particle ligament lengths, (a-).
Figure 5-1 shows the results of the
a
simulation for the four combinations of relative inter-particle ligament length and material
51
models. Notice that the relatively incompressible matrix leads to larger changes in surface
topography. Note also that changing the compressibility of the matrix affects the two different
relative inter-particle ligament lengths differently.
(a)
a-2= 0.2
a a2?=
0.6
Relatively
Incompressible
Compressible
(b)
a-2# = 0.2
a-2= 0.6
a
Figure 5-1: Effect of compressibility on surface topography. All simulations are shown at
20% global compressive strain. (b) The portions of the compressible cases seen in the red ovals
in (a)
For the larger ligaments, the surface topography for both the relatively incompressible and
compressible matrices form a similar shape in which the there is a local minimum aligned
directly above each particle. For the smaller ligaments, the surface topographies are different in
morphology as well as magnitude. Looking at Figure 5-lb we can see that for compressible
matrix with the smaller ligaments a bisected peak forms.
52
Figure 5-2 sheds light on why changing the compressibility of the matrix affects the surface
topography of the PESCs with smaller ligament lengths more than the PESCs with larger
ligament lengths.
LEx
LEx
(a)
1+1.97
=-fl0.2
+1.21
0
0
1.98
-1.21
LExy
+0.30
LEx
+0.52
a-2fl
0.6
0
a
Y
iRelatively
1-0.47
1-0.30
Compressble
Incompressible
(b)
+0.015
+0. 2 7
0
a-2f=0.2
10
a
1-0.69
1-0.011
+0.001
= 0.6
0
Relatively
Incompressible
*
a-2
EV0
003
Compressible
0.34
Figure 5-2: Comparison of strainforthe relatively incompressible and compressible case of
different relative inter-particleligament lengths shown at 20% global compressive strain. (a)
Shear strain in the relatively incompressiblecase. (b) Volumetric strainfor both materialmodels
53
Figure 5-2a shows the strain along the X'-axis in the relatively incompressible case for the
two different relative inter-particle ligament lengths. As it was pointed out in section 4.1.1, the
shear strain for both inter-particle ligament lengths is concentrated primarily in the inter-particle
ligaments. It should be noted however, that the magnitude of the shear strain is much larger for
the PESC with the smaller inter-particle ligaments. Since in both of those models the matrix was
relatively incompressible the global compressive strain was accommodated almost exclusively
by local shear strain rather than by volumetric strain.
Figure 5-2b shows the volumetric strain in the matrix for both the relatively incompressible
and compressible cases with both relative inter-particle ligament lengths. The relatively
incompressible matrix case shows negligible volumetric strain. Looking at the scale bars, we see
that for the compressible cases the magnitude of the volumetric strain is more than an order of
magnitude larger than for the relatively incompressible cases and is of similar magnitude to the
shear strain of the incompressible case. This is because in the relatively incompressible case the
material has a strong preference to change shape rather than volume. However in the
compressible case, where the bulk and shear moduli are on the same order of magnitude, the
matrix material does not have a strong preference for shape change or volume change.
In general, the matrix will deform in the most energetically efficient way to accommodate the
global compressive strain. In the relatively incompressible case this means that the matrix
undergoes shear strain with very little volumetric strain. This leads to a higher magnitude of
localized shear strain, as seen in the case with the smaller inter-particle ligaments. In the
compressible case, it is more energetically efficient for the matrix to volumetrically strain than to
accommodate the global compressive strain through high magnitudes of local shear strain. In the
relatively incompressible case with the larger inter-particle ligaments, the shear strain was not
54
nearly as large as the shear strain for the smaller inter-particle ligaments. Therefore, when the
matrix was changed to the compressible material the difference in the surface topography was
not as large for the PESC with the larger inter-particle ligaments.
5.2. Varying Stiffness of Particles
In all of the simulations shown so far, the material model for the particles has been based on
the stiffest material available from the 3D printer. The material available in the 3D printer used
for the particles has a Young's modulus of approximately 150OMPa while the material used for
the matrix has a Young's modulus of approximately IMPa. In this section we investigate how
changing the stiffness of the particles can change the surface topography.
Figure 5-3 shows the results of simulations in which we varied the Young's modulus of the
particles over several orders of magnitude.
=
EU
=
0
-0.2
Epart = 1500MPa
Epart = 15OMPa
Epart = 15MPa
Epart = 1.5MPa
Epart =
0.15MPa
Figure5-3: Effect of varying the stiffness of the particles on the surface topography. The
Young's modulus of the matrix is JMPafor each simulation.
The stiffest particles are representative of the materials available from the 3D printer.
Looking at the figure it is clear that reducing the stiffness of the particles from the stiffest by a
single order of magnitude has very little effect on the results of the simulation. However, when
55
the particle stiffness is reduced by another order of magnitude, to 15MPa, the particles start to
deform when we apply the compressive load. The deformation of the particles causes a slight
variation in the surface topography. When the stiffness is reduced by yet another order of
magnitude, to 1.5MPa, the particles deform a large amount and cause the surface to change shape
dramatically. As the particle stiffness approaches the stiffness of the matrix the surface becomes
much flatter. This makes sense because if the particles and the matrix have the same material
properties, the addition of particles is irrelevant.
The rightmost image corresponds to particles with a Young's modulus of 0.15MPa, i.e., the
particles are softer than the matrix. This causes a dramatic change in the surface topography. It
appears that when the particles are softer than the matrix, and therefore deform more than the
matrix, the particles no longer pin the matrix down. Instead, of being a local minimum the
surface above the particles is a local maximum.
While the work done so far has primarily investigated PESCs with particles stiff enough to
be considered nearly rigid, the ability to have the particles deform presents new opportunities for
creating novel surface topographies that should be studied going forward. This also suggests the
potential to use materials that will plastically deform at low yield stress thus creating a
permanently deformed topography.
56
6. Experimental Verification
In previous chapters we described FE simulations that explored the effects of geometric and
material parameters on the surface topography of the PESCs. In this chapter, we describe
physical experiments designed to validate some of the simulations. Because of the high cost of
the materials, we only validated a subset of the simulations.
6.1. Materials and Methods
The prototype PESCs used in the experiments were made with an Objet500 Connex MultiMaterial 3D printer. This printer is capable of printing multiple materials in a single part with
good bonding between the different materials. The materials available as outputs from the printer
are all proprietary materials. For our PESCs, the matrix was made out of the TangoPlus material,
which the company describes as a "rubber-like material." The material used for the particles in
the PESCs was the VeroBlack material, which the company describes as a "rigid opaque
material." While the VeroBlack is not completely rigid, it is significantly stiffer than the matrix.
The Young's moduli for the TangoPlus and VeroBlack were measured using compressive and
tensile tests by other members of the Boyce Group and found to be approximately IMPa and
1500MPa respectively.
A typical image of the experimental setup is shown in Figure 6-1. Since the simulations
were all run with plane strain elements, it was important that the experiments be performed under
plane strain conditions. To enforce the plane strain condition, the 3D printed sample (Figure
6-la) was sandwiched between two clear acrylic plates (Figure 6-ib). The plates were secured
together using four bolts that went through both plates. The holes for the bolts, as well as the
plates themselves were cut using a laser cutter. We chose acrylic as the material for the plates
57
because it is transparent and thus allowed us to use a camera to get clear images of the sample
throughout the experiments. Two pieces of acrylic (Figure 6-1c) were also cut to the thickness of
the 3D printed samples and were used as spacers between the two plates to ensure that the plates
were secured the same distance apart in each experiment. Another piece of acrylic (Figure 6-1d)
was cut to go on top of the sample, between the two plates and extend above the plates. This
piece was used to transfer the compressive load from the cross head of the Zwick mechanical
tester (Figure 6-1 e) to the sample. All of the contacting surfaces between the sample and the
acrylic were lubricated using mineral oil.
(e)
-
1 cm
Figure6-1: Image of a typical experimental setup
The experiments were all performed using a Zwick mechanical tester with which a
compressive load was applied using the displacement control feature of the machine. All of the
samples were compressed to 20% global strain. Since the TangoPlus material used in the matrix
58
of the samples is highly viscoelastic, the tests were performed at very low strain rates
(approximately 10-4/second) to reduce any time dependent effects the samples may have
introduced. During the tests a high resolution camera was setup on a tripod in front of the
sample, and set to take a picture every half second. The camera was a Point Grey CMLN- 13 S2M
camera with a Nikon AF Micro-Nikkor 60mm f/2.8D lens.
6.2. Experimental Results
The geometries selected to be validated were some of the PESCs used in the investigation of
the effect of the number of rows of particles from section 4.1.2 as well as some of the nonuniform arrays of particles discussed in section 4.2. Figure 6-2 shows simulation and
experimental results of the full RVE of a non-uniform array of particles at various global
compressive strains.
Simulation
Experiment
Simulation
S=-.09
Experiment
Simulation
Experiment
Figure6-2: Comparisonof simulations and experiments offull RVE
59
As the figure shows, the simulated RVE's exhibit a periodicity not seen in the experiments.
We believe that the lack of periodicity in the experiments is attributable to friction in the system.
Friction played no role in the simulation. However, the introduction of the plates, which were
needed to enforce the plane strain condition in the physical experiments, introduced friction into
the system. The introduction of the mineral oil helped, but did not eliminate the friction. The
friction appears to be more significant at the right edge (which was the bottom surface of the test
machine). Although we attempted to reduce the friction, we were not successful.
The left sides of the images in the figure correspond to the top of the samples in the
experiments, i.e., the part of the sample closest to the region where the compressive force is
applied. If we look only at the left most unit cell there is good qualitative agreement between
with the simulations and the experiments. For the rest of this section will focus on the
experimental unit cells closest to the compressor head.
Figure 6-3 shows simulation and experimental results for tests that were part of the
investigation of the effect of the number of rows of particles on the surface topography. On the
whole, we see good qualitative agreement between the simulations and experiments. Looking at
the case with a single row of particles in Figure 6-3a, a single large peak appears aligned
between the two particles for the simulation and the physical experiment. For the case with two
rows of particles, shown in Figure 6-3b, a bisected peak appears aligned above the particles in
the second row for both the simulations and physical experiments. With three rows of particles
(Figure 6-3c), the surface for both sets of experiments takes on a shape that is flatter than the
case with a single row of particles, but does not have the bisected peak seen for the PESC with
two rows of particles.
60
(a)
Simulation
Experiment
E = -0.10
E=
2cm
-
E = -0.20
Surface Profiles at 20% Global Compressive Strain
3
R2 = 0.994
2.5
- Simula tion
Experi ment
2. S.O
2
*
S
0
0
0.
0.5*-
0
is
10
s
20
X position (mm)
Simulation
Experiment
-
E= 0
2 cm
E = -0.10
E = -0.20
Surface Profiles at 20% Global Compressive Strain
2
R2
R220=
Simulation 20% Strain
2
0.968
simulation 21% Strain
1.r
Experiment
0.5
0!
0
5
10
X position (mm)
61
15
20
(c)
Simulation
f
Experiment
-
2 cm
E=0
E = -0.10
E
-0.20
Surface Profiles at 20% Global Compressive Strain
R 220
=
"221=
2.5
0.912
0.984
Simulation 20% strain
. simulation 21% Strain
SEper
ment
2
o
v
4..
0
5
10
is
20
X position (mm)
Figure 6-3: Comparisonof simulation and experimental resultsfor PESCs with different
number of rows ofparticles
The graphs in Figure 6-3a, b and c show the surface profiles of both the simulations and
experiments at 20% global compressive strain. The X-Y coordinates of the surface of the
experiments were extracted by first tracing the surface in Photoshop to remove the background.
After the background was removed, we used custom Matlab code to extract the surface
coordinates in pixels. To get the experimental surface coordinates in mm, we found dimensions
of a single particle in pixels and, since we knew the dimensions in mm, we were able to convert
the units of the surface profile into mm. Once we had the surface profile of the experimental
surfaces, we were able to compare them to the surface profiles found in the simulations. We
62
compared the two profiles by calculating the coefficient of determination (R 2 ) defined by
Equation 4.
R = 1-
_(4)
The R 2 values are shown on each plot. The plots in Figure 6-3b and c show the curves of the
simulations at both 20% and 21% global compressive strain. The R2 values which compare the
experiments to both simulation curves are shown. We found that for those cases experimental
profiles fit the simulation profiles at 21% global compressive strain better than the simulation
profiles at 20% strain. We believe that this is because the friction in the experiments may cause
local strains in near the compressor head to be higher than 20% and the local strains far away
from the compressor head to be lower than 20%, while still combining to 20% global
compressive strain. The best R2 value for all of the cases in Figure 6-3 are above 0.96, indicating
that the experimental and simulation surface profiles are similar to one another.
We show the results of the simulations and physical experiments of the non-uniform arrays
of particles in Figure 6-4. For all cases, we again see reasonably good qualitative agreement
between the simulations and experiments. Figure 6-4a shows the case in which the smaller
particles and the larger particles are the same distance from the surface. As we saw in the
simulations, the experiments show the smaller particles moving up relative to the larger particles,
which causes higher peak amplitude. Figure 6-4b shows the case in which the horizontal axes of
the smaller and larger particles are aligned. We see that upon compression the particles stay
aligned with one another. Figure 6-4c and d depict experiments with two rows of particles. .In
both the simulations and the physical experiments, the local minimum aligned above the smaller
particles has a larger radius of curvature when the smaller and larger particles were the same
63
distance from the surface than the case where the horizontal axes were aligned. The same
method that was used to create the plots shown in Figure 6-3 was used to create the plots shown
in Figure 6-4. We see that for each case (with the exception of Figure 6-4b and d) the R2 values
are all above 0.95 indicating a very good fit. Even for the case shown in Figure 6-4b and d the
R 2 values of 0.901 and 0.915 indicate a moderately good fit, and the major patterns that were
seen in the simulations also appeared in the experiments. These results indicate that our
simulations are capturing the important aspects of the behavior of the PESCs.
64
(a)
Simulation
Experiment
2 cm
-
E=0
E
E
-0.1
-0.2
Surface Profiles at 20% Global Compressive Strain
2
R-2Simulation
R20.95Ep8i n
n
ri
Experiment
0.5
0
t
P
20 iv
r
X position (mm)
mi.i41
Simulation
*
Experiment*
E=O
-2cm
E=-0.1
E= -0.2
Surface Profiles at 20% Global Compressive Strain
R 2 = 0.901
- Simulation
-is
,.Experiment
.
0.5
0
0
5
2
10
X position (m
65
15
20
Simulation
-
E=O
2 cm
*
*
*
Experiment
*
ION
E=-0.1
E=-0.2
Surface Profiles at 20% Global Compressive Strain
1.6
R 2 =0.979
- Simulation
.Experiment
B
*
.*
0.2010
15t
i 20
X position (mm)
(d)
Simulation
Experiment
cm
-2
E= 0
E-
M.1
E=
-0.2
Surface Profiles at 20% Global Compressive Strain
R 2 =0.915
2
Simulation
5
I
. Experiment
aN
s
o.s
p
p
05
0
5
10
15
20
X position (mm)
Figure6-4: Comparison of simulation and experimental resultsfor PESCs with non-uniform
arrays ofparticles
66
7. Conclusion
7.1. Summary
In this thesis we presented a new method to dynamically create surface topography through
the use of particle-enhanced soft composites. The deformation of the surface of the PESCs
depends upon the material properties of the embedded particles, their shape, and their geometric
arrangement within the soft matrix. The impact of each of these was explored through finite
element simulations that were validated using physical experiments.
Throughout our investigation we found a number of commonalities that were independent of
the particular geometric arrangement of particles. First we found that in general, the stiff
particles constrain the deformation of the matrix. This caused a pinning region to occur directly
above the particles in the first row for each PESC. We also found through the compression of the
PESCs the surface gradually changes from the initial flat shape to different curved shapes
depending on the amount of global deformation applied and these topographies are the result of
inter-particle shearing. This is an important difference between our method and methods such as
wrinkling that rely on instabilities to form different regular sinusoidal surface topographies. In
some cases there was a considerable period of gradual topographical change before instabilities
occurred. These instabilities give a clear asymmetry to the topography, which could be used to
produce anisotropic directionally biased surfaces.
In our investigation of the effect on the surface topography of the relative inter-particle
ligament length there were a number of interesting findings. We found that for smaller ligament
lengths the surface formed a series of large peaks that were aligned between the particles in the
67
first row. However, for larger ligament lengths the surface took on a flatter shape, and if the
ligaments were large enough bisected peaks occurred.
We also found that, in a uniform staggered array, the number of rows of particles has a
significant effect on the surface topography. When there is a single row of particles, a series of
large peaks appear on the surface, and each peak is between adjacent particles. When a second
row of particles is added, they have a pinning effect on the surface causing a flatter shape with
some bisected peaks. We showed that each additional odd row of particles caused the peak
amplitude to increase and each additional even row caused the peak amplitude to decrease.
Furthermore, each successive row that was added had a smaller effect on the surface topography
than the row before it.
In our investigation into the effect on the surface topography of the aspect ratio of the
particles we showed that the larger the projected area of the particles is on the surface, the larger
the pinning region will be. This was shown to be true for ellipsoidal particles as well as
rectangular and diamond shaped particles. We found that with enough global compression a
PESC with sufficiently wide particles underwent an instability causing the particles to rotate and
inducing a non-symmetric surface shape. This was an important finding because it showed that
the surface of a single PESC can be made into a symmetric or non-symmetric shape by simply
varying the amount of applied deformation.
We also showed that by using non-uniform arrays of particles (arrays in which the particles
were not all the same size and/or shape) a number of interesting topographical features can be
formed. We showed the shape of each surface feature is controlled primarily by the particles near
68
those features. This is an important finding because it shows that using PESCs provides highly
localizable control of the surface topography, unlike other methods such as wrinkling.
In addition to investigating the effect on surface topography of different geometric
parameters we investigated the effect of changing material properties. We showed that a PESC
with a relatively incompressible matrix has more dramatic topographical features than a PESC
with a relatively compressible matrix. We also showed that changing the compressibility of the
matrix affects the surface topography more for PESCs with smaller relative inter-particle
ligaments than PESCs with larger ligaments. We also showed that changing the stiffness of the
particles can substantially affect the surface topography. In particular, we showed that if the
stiffness of particles is above a threshold, the particles behave like rigid bodies and making them
stiffer does not change the behavior of the PESCs. However, when the particles are soft enough
to deform they can cause dramatically different surface topographies.
We also performed physical experiments to validate the results of the simulations. In the unit
cell closest to the compressor head, we saw good qualitative agreement between the simulations
and experiments. Similar topographical features were seen in both the simulations and physical
experiments. However, unlike in the simulations, the effect of the particles was dampened with
distance from one of the compression edges. We speculate that this was attributable to failure to
successfully eliminate friction in the physical experiments.
7.2. Extensions
In this work we investigated PESCs constructed using an elastic material for the matrix.
Since the matrix never deformed plastically the surface changes were fully reversible. The use of
69
materials that would deform in an elastic-plastic manner would allow for permanent
(irreversible) changes to the surface topography.
This thesis has only presented 2D geometries, however, particle-enhanced soft composites
can be extended to 3D. The extra degree of freedom would increase the number of useful
arrangements of the particles, and the particles themselves could be spheres, ellipsoids, plates,
blocks, etc. This would allow for a richer set of surface topographies.
In this thesis, we examined PESCs with a single activation mechanism; uniaxial compression
applied by an external crosshead. When the PESCs are extended to 3D the loading could be
biaxial or using some other 3D loading. The method of activation through the application of an
external compressive force is simple to apply in the laboratory on 2D samples. However when
PESCs are used for applications in 3D with larger samples, activation through applying an
external compressive force may not be practical. One other possible method of activating PESCs
is the use of swelling. Figure 7-1 shows the results of preliminary simulations designed to mimic
the behavior of the skin papillae of cuttlefish, which was discussed in section 1.1.
70
-AT
Figure 7-1: Simulation using axisymmetric elements and mismatching thermal expansion
coefficients to mimic the skin papillae of the cuttlefish
In the simulation, we consider an axisymmetric structure of a ring surrounded by a matrix.
This was constructed using axisymmetric elements in the simulation. The particles form a stiff
circular ring (shown in black) embedded in a soft matrix (grey). The ring was assigned a nonzero thermal expansion coefficient while the matrix was assigned a thermal expansion coefficient
of 0. Over the course of the loading step, the temperature was dropped, causing the ring to
contract. The contraction of the ring acts to extrude the matrix upwards forming the surface
protrusion. Different shaped "rings" would form different shaped protrusions.
By using thermally responsive materials, we can activate PESCs in different ways. It may be
possible to activate PESCs in a similar way using materials that swell with other stimuli. These
are areas of research to be addressed going forwards.
Along with swelling and uniaxial compression, we also conducted preliminary simulations
on activating the PESCs using uniaxial tension (Figure 7-2). The figure shows a PESC loading in
uniaxial tension at 0, 10%, and 20% global strain. We can see that as the PESC is stretched,
71
peaks are aligned directly above the particles in the first row. This is the opposite of what we saw
for in the case of uniaxial compression when the pinning region was formed. Looking at the
shear strain contours we see shear bands between the particles that are similar to those that were
seen under axial compression. Applying tensile loading is another way to activate the surfaces of
*
PESCs that warrants a more thorough investigation going forwards.
E = 0.2
LE*y
+0.49
E = 0.2
0
-0.53
tx
Figure 7-2: Tensile loading of PESCs
7.3. Applications
The potential applications for controlling surface topography through the use of PESCs are
numerous and are relevant in a number of different fields. One possible application relates to the
visual appearance of the surfaces. Figure 7-3 shows two images each with the exact same
72
surface. The position of the light source is different for the two images. The figure demonstrates
that by varying the position of the light source, identical surfaces can appear to be different.
PESCs could be used to tune a surface topography to make it appear unchanged even under
changing light conditions, which could have applications in camouflage.
Figure 7-3: Different visual appearanceof identicalsurfaces with different light sources
PESCs could also be used to create surfaces with tunable wettability. Through the
application of a load, the surface could change from wetting to non-wetting and back again. The
ability to change a surface to non-wetting could be used to reduce biofouling.
Since the shape of contacting surfaces affects friction and adhesion, PESCs could be used to
control the amount of friction between two surfaces. The ability to change surface topography
could also be used to study the way cells move through changing environments. This could be
useful, for example, in understanding cellular flow through capillaries.
Working with Professor Pedro Reis, we intend to investigate the effect of surface topography
on aerodynamic drag. The idea is to create PESCs that can tune the surface topography in order
to dynamically minimize the drag at different Reynolds numbers. A potential application would
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be coating vehicles with "smart" surfaces so that when they are traveling at different speeds the
surface would change to minimize the drag and thus increase fuel efficiency. Professor Reis has
already done some work on this concept with post-doctoral fellows Denis Terwagne and Miha
Brojan; who used wrinkling to control the surface topography (Terwagne et al., 2014). We
hypothesize that extending this work to use PESCs will allow additional applications. To confirm
this, further understanding of the mechanisms behind the deformation of the PESCs is required,
especially in 3D.
7.4. Conclusions
This thesis presented a powerful new tool to create tunable surface topographies. The use of
PESCs allows for a wide variety of surface topographies to be formed. It also allows for highly
localized control of topological features, which is a major benefit of this method. We believe
that flexibility offered by PESCs will make them useful for applications across a wide range of
length scales. Controlling surfaces with PESCs could be particularly useful for applications in
which the environment surrounding the surface is changing. The PESCs offer the freedom to
adapt the surface topography in order to optimize performance under changing conditions.
74
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