Topology optimization for three-dimensional elastoplastic architected materials using a path-dependent adjoint method

This article introduces a computational design framework for obtaining three-dimensional (3D) periodic elastoplastic architected materials with enhanced performance, subject to uniaxial or shear strain. A nonlinear finite element model accounting for plastic deformation is developed, where a Lagrange multiplier approach is utilized to impose periodicity constraints. The analysis assumes that the material obeys a von Mises plasticity model with linear isotropic hardening. The finite element model is combined with a corresponding path-dependent adjoint sensitivity formulation, which is derived analytically. The optimization problem is parametrized using the solid isotropic material penalization method. Designs are optimized for either end compliance or toughness for a given prescribed displacement. Such a framework results in producing materials with enhanced performance through much better utilization of an elastoplastic material. Several 3D examples are used to demonstrate the effectiveness of the mathematical framework.