Material nonlinear topology optimization considering the von Mises criterion through an asymptotic approach: Max strain energy and max load factor formulations

This paper addresses material nonlinear topology optimization considering the von Mises criterion by means of an asymptotic analysis using a fictitious nonlinear elastic model. In this context, we consider the topology optimization problem subjected to prescribed energy, which leads to robust convergence in nonlinear problems. Two nested formulations are considered. In the first, the objective is to maximize the strain energy of the system in equilibrium, and in the second, the objective is to maximize the load factor. In both cases, a volume constraint is imposed. The sensitivity analysis is quite effective and efficient in the sense that there is no extra adjoint equation. In addition, the nonlinear structural equilibrium problem is solved using direct minimization of the structural strain energy using Newton's method with an inexact line-search strategy. Four numerical examples demonstrate the features of the proposed material nonlinear topology optimization framework for approximating standard von Mises plasticity.