On structural topology optimization considering material nonlinearity: Plane strain versus plane stress solutions

We present a structural topology optimization framework considering material nonlinearity by means of a tailored hyperelastic formulation. The nonlinearity is incorporated through a hyperelastic constitutive model, which is capable of capturing a range of nonlinear material behavior under both plane strain and plane stress conditions. We explore both standard (i.e. quadrilateral) and polygonal finite elements in the solution process, and achieve smooth convergence in both the optimization process and the solution of nonlinear state equations. Numerical examples are presented, which demonstrate that the topology optimization framework can effectively capture the influence of various material behaviors, load levels and loading conditions (i.e. plane stress versus plane strain) on the optimal topologies.