Efficient multi-material continuum topology optimization considering hyperelasticity: Achieving local feature control through regional constraints

We introduce a general and efficient multi-material topology optimization framework considering hyperelasticity with many local constraints, which enables flexible control of the design's local features. The proposed framework can effectively distribute multiple candidate materials described by distinct constitutive models according to their respective nonlinear behaviors, and efficiently handle a flexible setting of volume constraints, either global or local. To ensure computational efficiency of the proposed framework, we present a virtual element-based formulation in conjunction with a tailored adaptive refinement and coarsening scheme for multi-material problems, and we adopt the ZPR scheme to update the design variables associated with each constraint in parallel. Three design examples are presented, demonstrating the efficiency and effectiveness of the proposed framework in distributing multiple candidate materials with distinct nonlinear elastic behaviors and handling both global and many (e.g., 1024) local constraints. We envision that the proposed framework enables unique computational capabilities for designing next-generation composite metamaterials and structures with nonlinear behaviors and multi-functionalities.