ARUP; ISBN: 978-0-9562121-5-3 - CMBBE 2012 - Cardiff University

Cook’s equation (Eqn 1). In this, Ai and Ai 0 represents the
total and quasi static values of the material parameters, is the strain rate and Ci is a
scaling parameter. The reference strain rate for quasi-static response was assumed to be
0.001/s. However, a constitutive model that can take into account of this behavior is not
readily available in commercial packages. Therefore a VUSDFLD subroutine was
written in Abaqus/Explicit TM ε
. Most material properties in ABAQUS/Explicit can be
defined as functions of field variables, fi. Subroutine VUSDFLD allows the user to
define fi at every integration point of an element. In the subroutine, the material
properties can be a function of parameters like σ, ε, εpl, ε ̇, computed at solution time.
The computed material properties inside VUSDFLD routine are then passed to the main
code for stress updation. The user subroutine developed was validated using single
element simulations and compiled in double precision along with the main model.
.
3.4. Optimisation module
0 ε
Ai = Ai 1+ log
.
⎛ ⎞
⎜ ⎟
⎝
⎜ 0.001
⎠
⎟ *C ⎡
⎤
⎢
⎥
i
⎢
⎥
⎣
⎦
Genetic algorithms (GA) are widely used in search and optimisation problems. They use
procedures motivated by evolution such as selection, inheritance, mutation and
crossover. When the location of the optimum of the problem cannot be analytically
reduced to a subset of the solution space, GA can be used to extract a good solution
though a reduced search process. For the current study an open source C++ GA code
developed by Sastry and Goldberg [12] was used. Some studies have used optimization
techniques to derive material parameters for bones under impact starting with CT scan.
The present study differs in that subject specific material assignment and analysis was
done instead of working with a nominal geometric model and establishing nominal
material properties. A schematic diagram of the workflow of the optimisation procedure
is shown in Figure 1.
Figure 1 Schematic diagram of the workflow of the optimisation procedure.
4. RESULTS AND DISCUSSIONS
The material property sets arrived at are listed in Table 1, where C1, C2 and C3 are the
scaling parameters for modulus of elasticity, yielding and failure used in Eqn 1
respectively. Using the obtained material parameters individual tests were simulated by