Geometry generation challenges for modelling and analysis of structured materials
Alison McMillan1, Anne Other2 and Joe Bloggs3
1 Glyndwr University, Mold Road, Wrexham, LL11 2AW, UK
2 Another Institution, address, post code, country
3 Yet another Institution, address, post code, country
Engineers evaluating the performance of a component
at the design stage will typically convert Computer
Aided Design (CAD) geometry into a Finite Element
model, and run a Finite Element Analysis (FEA) to
determine deformations and stress levels as a result of
applied loads or displacements. The analysis results
would then be interpreted by comparing with the
required duty of the component.
For metallic
components homogeneous and isotropic material
properties are generally assumed (“macro-scale”
modelling). For components to be manufactured from
composite
materials,
models
may represent
heterogeneity at the ply level, and orthotropic material
properties applied with appropriate directionality. This
ply-level modelling is often termed “meso-scale”
modelling.
Engineering interpretation of failure of materials is
often based on empirical understanding of
experimental data. This approach is generally robust
and safety critical components would always be subject
to validation by means of a suitable programme of
testing. The aspect that is missing is the opportunity to
improve understanding of the material performance by
investigating the material performance at the “microscale”.
Almost all materials exhibit some
heterogeneity at some length scale: for example the
crystal grain structure in metals, or the individual
filaments of fibre in a fibre reinforced composite. Such
details are known to play a role in the material
performance: for example the strength and ductility of
a metal is highly influenced by the crystal grain size
and configuration.
The purpose of this paper is to detail some
computational algorithms for generating random
geometries exhibiting similar characteristics to those
seen at the “micro-scale” in real materials, and use
these for the basis of finite element modelling to
predict the influence of the “micro-scale” structure on
the “macro-scale” material performance.
algorithm has a major influence on the result, a study
of random geometrical forms and a means for
categorising them is essential for further development
of this field. [approx. 350 words]
References
[1] AJ McMillan, “Material strength knock-down
resulting from multiple randomly positioned
voids”, Journal of Reinforced Plastics and
Composites, 31(1), 13-28, 2012.
[2] E Potter, ST Pinho, P Robinson, L Iannucci, AJ
McMillan “Mesh generation and geometrical
modelling of 3D woven composites with variable
tow cross-sections” Computational Materials
Science 51 103–111, 2012.
[3] A McMillan “Defect identification and
characterisation algorithms for assessing effect on
component strength” Proceedings 15th European
Conference on Composite Materials, Venice, Italy,
24-28 June 2012.
[4] M de Berg, M van Krefeld, M Overmars, O
Schwarzkopf, “Computational geometry:
algorithms and applications”, Springer, Berlin,
2000.
[5] H Bohnacker, B Gross, J Laub, Ed. C Lazzeroni,
“Generative design”, Princeton Architectural Press,
New York.
Mini Biography: Alison McMillan studied Maths and
Physics BSc at University College London and Mechanical
Engineering MSc at Cranfield. Her PhD from Staffordshire
University involved computational modelling of vibration
and impact of laminates. Following a series of post-doctoral
positions at the University of Oxford and Keele University
she moved into industry, working almost 15 years at RollsRoyce plc in Derby, on the interface between new product
introduction and capability acquisition. Between 2007-2011
she held a Royal Society Industry Fellowship, based parttime at the University of Bristol. Alison left Rolls-Royce plc
in October 2011, and is currently Professor in Aerospace
Technology at Glyndwr University. [approx. 100 words]
Figure 1 illustrates the formation
of stress banding in a material
containing randomly arranged holes
[1]. A conclusion from this study
was that maximum stress increases
very slowly with the number of holes,
so long as the holes are distributed in
a homogeneously random manner.
Since the geometry generation
Figure 1: Stress bands in a porous material subject to shear loading
Advanced Materials for Demanding Applications, St Asaph, 7-9th April 2014.