Multimaterial topology optimization of elastoplastic composite structures

Plasticity is indispensable for wide-ranging structures as a protection mechanism against extreme loads. Tailoring elastoplastic behaviors such as stiffness, yield force, and energy dissipation to optimal states is therefore crucial for safety and economics. Recent studies have optimized either geometry or material phase for desired energy dissipating capacities; however, integrating both in design optimization is essential but thus far not achieved, impeding a comprehensive understanding of the interplay among structural geometry, material heterogeneity, and plasticity. Here, we propose a general topology optimization framework for discovering lightweight, multimaterial structures with optimized elastoplastic responses under small deformations. This framework features a multiobjective optimization formulation that simultaneously enhances initial stiffness, delays plastic yielding, and maximizes energy absorption/dissipation. The approach is built upon rigorous elastoplasticity theory and the celebrated return mapping algorithm, incorporating both isotropic and kinematic hardening. We analytically derive the history-dependent sensitivities using the reversed adjoint method and automatic differentiation. Employing the proposed framework, we investigate several composite structures and demonstrate the non-intuitive optimized geometries and material distributions that deliver diverse superior elastoplastic performances, including maximized plastic energy dissipation and various degrees of yield resistance. Furthermore, our findings reveal underlying mechanisms that enhance structural elastoplastic performance, such as leveraging sequential yielding to prolong post-yielding resistance and prevent catastrophic failure. These optimized designs and discovered mechanisms reveal the principles for creating the next generation of resilient engineering structures accounting for elastoplastic behaviors.