On the return mapping algorithms in structural optimization of biomorphic ceramics

The paper deals with structural optimization of biomorphic microcellular ceramics involving an elastoplasticity with the von Mises yield criterion in the macroscopic model. The return mapping algorithms introduced by Simo and Ortiz in 1985 are applied for the numerical solution of the problem. The latter methods are computationally effective, robust, and stable, and have recently become the most popular means of numerically solving elasto-plastic equations. Based on the operator splitting methodology, the return mapping algorithm can be defined by first solving the elastic equations to obtain an elastic predictor and then taken as an initial condition for the plastic equations by using a projection of the trial elastic stress onto the constraint set of admissible stresses. Finite element discretized von Mises plasticity with isotropic strain hardening is included in the state equation as an equality constraint in the structural optimization problem