Theory and analysis techniques for the use
of a DCB specimen for determining the
toughness of PC-3 Prostate Cancer
Justin Babcock
Department of Aerospace Engineering and Engineering Mechanics
The University of Texas at Austin
justin.babcock@gmail.com
What?

PC-3 Prostate cancer is a human prostate cancer
cell line
Biological supply companies
 Provides for repeatability

What?

The critical energy release rate allows us to
determine the toughness
Why?

Understanding metastasis important
Normally fatal
 Prevent onset


Metastasis?


Spreading
Adhesion dependent

Toughness
The specimen / A basic model


Bilayer of cells
Beams polycarbonate microscope slides
Experimental / modeling method I


Displace specimen
Recording force – displacement to failure



Multiple values of a  dC/da
Determine critical G
U, A, P, C, a, b
Modeling method II

Basic finite element model
Apply the predicted, or measured, critical load
 Compute J integral (Rice 1968)  G

Modeling method III


Nonlinear spring foundation
Song & Waas (1994)
Modeling method III

Constitutive properties (σ-ε plot)
Modeling method III

Energy Criterion for failure

General form
Modeling method III

Energy Criterion for failure

Strain energy formulated
Spring foundation
Elastic beam
Modeling method III

FE implementation


Code developed
Potential Energy
Modeling method IV


Cohesive element model
Finite element model


Cells modeled as cohesive elements
Test data
Traction-separation information
 Bridging zone size



Implement via cohesive elements abaqus
Crack propagation
Conclusions


Each model progressively adds complexity
Model I


Model II


Finite element of model I
Model III


Simplest, unbonded
Adhesive  spring foundation
Model IV


Adhesive de-bonding
Crack propagation
References


Rice, J. R. (1968). "A path independent integral
and the approximate analysis of strain
concentration by notches and cracks." ASME
Journal of Applied Mechanics 35: 379-386
Song, S. J., Waas, A. M. (1994). " A spring
foundation model for mode I failure of
laminated composites based on an energy
criterion." J. Eng. Mater. Technol. (Trans.
ASME) 116(4): 512-516.