MOTO: Topology Optimization for Large Deformations via an Implicit Material Point Method

Abstract: 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.