Abstract 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.

中文翻译：

---

考虑超弹性的高效多材料连续体拓扑优化：通过区域约束实现局部特征控制

摘要 我们介绍了一种考虑具有许多局部约束的超弹性的通用且高效的多材料拓扑优化框架，它能够灵活地控制设计的局部特征。所提出的框架可以根据各自的非线性行为有效地分布由不同本构模型描述的多个候选材料，并有效地处理全局或局部体积约束的灵活设置。为了确保所提出框架的计算效率，我们提出了一个基于虚拟元素的公式，并结合针对多材料问题的定制自适应细化和粗化方案，我们采用 ZPR 方案并行更新与每个约束相关的设计变量. 展示了三个设计实例，证明了所提出的框架在分布具有不同非线性弹性行为的多种候选材料以及处理全局和许多（例如，1024）局部约束方面的效率和有效性。我们设想所提出的框架能够为设计具有非线性行为和多功能性的下一代复合超材料和结构提供独特的计算能力。