Optimization of hyperelastic materials with isotropic damage

Abstract

In many practical problems, engineering structures under repeated loading exhibit softening material behaviour. The complex micromechanical processes yielding the observed loss of stiffness are often described phenomenologically on the macroscopic level by damage mechanics. A finite strain elastic constitutive model incorporating an isotropic damage mechanism was developed by Simo (1987). The additional theoretical and computational enhancements for utilizing this damage model and the associated finite element formulation for optimization purposes are outlined in this paper.¶The structural response and its sensitivity expressions at a given time and position depend on the response and the response sensitivities of all previous locations and times. The expressions for variational design sensitivity analysis within damage mechanics are fully stated and related to prior work on history dependent material behaviour such as Prandtl-Reuss elastoplasticity, see Barthold and Wiechmann (1997) and Wiechmann et al. (1997). The theoretical details and the corresponding finite element formulation were described in the paper by Firuziaan (1998).¶New problem functions based on the internal variables are shown to be adequate for controlling and optimizing the damage process.¶Numerical experiments illustrate the method proposed and the efficiency of the overall optimization procedure.