Multimaterial topology optimization for finite strain elastoplasticity: theory, methods, and applications

18th U.S. National Congress on Computational Mechanics (USNCCM18)

Plasticity is inherent in many engineering materials, such as metals. It can either degrade the load-carrying capacity of structures due to material yielding or protect structures through plastic energy dissipation. To fully harness plasticity, we propose a topology optimization framework that simultaneously optimizes structural geometries and material phases to customize the stiffness, strength, and toughness of designs experiencing finite-strain elastoplasticity. The framework accurately predicts structural responses by employing a rigorous, mechanics-based elastoplasticity theory that ensures isochoric plastic flow. It also effectively identifies optimal material distributions using a gradient-based optimizer, where gradient information is obtained via a reversed adjoint method to address history dependence, along with automatic differentiation to compute the complex partial derivatives. Using this framework, we optimize a range of elastoplastic structures with real-world applications, including energy-dissipating dampers, load-carrying beams, impact-resisting bumpers, and cold-working profiled sheets. These optimized structures reveal important mechanisms for enhancing design performance, such as the transition from kinematic to isotropic hardening with increasing displacement amplitudes and the formation of twisted regions that concentrate stress and improve plastic energy dissipation. Based on the superior performance of these designs, we demonstrate the framework’s effectiveness in tailoring elastoplastic responses across various spatial dimensions, material types, hardening behaviors, and combinations of candidate materials. Ultimately, this work offers a systematic approach for optimizing the next generation of elastoplastic structures subjected to large deformations.