The Finite element method (FEM) has long served as the computational backbone for topology optimization (TO). However, for designing structures undergoing large deformations, conventional FEM-based TO often exhibits numerical instabilities due to severe mesh distortions, tangling, and large rotations, consequently leading to convergence failures. To address this challenge, we present a TO framework based on the Material Point Method (MPM). MPM is a hybrid Lagrangian-Eulerian particle method, well-suited for simulating large deformations. In particular, we present an end-to-end differentiable implicit MPM framework for designing structures undergoing quasi-static hyperelastic large deformations. The effectiveness of the approach is demonstrated through validation studies encompassing both single and multi-material designs, including the design of compliant soft robotic grippers. The software accompanying this paper can be accessed at github.com/UW-ERSL/MOTO.

翻译：有限元法长期以来一直是拓扑优化的计算基础。然而，对于经历大变形的结构设计，传统的基于有限元法的拓扑优化常因严重的网格畸变、缠绕和大旋转而表现出数值不稳定性，从而导致收敛失败。为应对这一挑战，我们提出了一种基于物质点法的拓扑优化框架。物质点法是一种混合拉格朗日-欧拉粒子方法，非常适用于模拟大变形。具体而言，我们提出了一种端到端可微的隐式物质点法框架，用于设计经历准静态超弹性大变形的结构。该方法的有效性通过涵盖单材料与多材料设计的验证研究得到证明，包括柔性软体机器人夹持器的设计。本文附带的软件可在 github.com/UW-ERSL/MOTO 获取。