Structure Optimization of Elastoplastic Multiphase Hierarchical Systems
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Path-dependent structure (or topology) optimization of elastoplastic hierarchical materials is computationally intensive due to the necessity of consistently propagating microscale plastic deformation and internal state variables to the structural scale. In this work, we circumvent these computational challenges by embedding analytically derived continuum micromechanics-based estimates of effective macroscale elastoplastic properties, including isotropic hardening, directly into the structural optimization problem. Macroscale elastoplastic constitutive responses and hardening evolution laws are derived analytically from microscale phase descriptions, eliminating the need for explicit computational homogenization while preserving the inherent path dependence of the response. The optimization problem involves history-dependent design sensitivities governed by evolving internal state variables, which are efficiently handled using an adjoint-based sensitivity formulation. Numerical results on a cantilever benchmark problem demonstrate that, the proposed algorithm allocates additional material toward the clamped region to control the plastic strain growth through isotropic hardening, thereby delaying excessive strain accumulation. These results confirm that incorporating isotropic hardening fundamentally alters the optimization mechanism, enabling controlled plastic accommodation while preserving load-carrying capacity of the structure throughout the optimization process.
