Optimal microstructures of elastoplastic cellular materials under various macroscopic strains

Topology optimization has been applied widely in cellular material design by optimizing the microstructure of periodic base cell (PBC). So far, most works are focused on the design of microstructures with linear material properties using the inverse homogenization method. When accounting elastoplastic constitutive behaviors, there is in usual no overall closed-form constitutive expression for the cellular microstructure as the case of linear elasticity, the design is therefore dependent on the specific applied loading. Due to the importance of topology optimization concerning elastoplastic material, the microstructural topology optimization procedure of elastoplastic cellular material with the objective of maximizing their nonlinear responses in terms of the strain energy density is proposed by using the bi-directional evolutionary structural optimization (BESO) method in this paper. Analytical sensitivity analysis is derived in a clear and rigorous manner using the adjoint method and incorporated into the BESO algorithm. The effectiveness of the proposed approach is validated through a series of numerical examples for various macroscopic strain loadings.