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

TL;DR

This paper introduces a topology optimization framework using an implicit Material Point Method to effectively design structures with large deformations, overcoming FEM limitations like mesh distortion and instability.

Contribution

The paper presents a novel implicit MPM-based topology optimization method capable of handling large deformations, which improves stability and convergence over traditional FEM-based approaches.

Findings

Successfully optimized large deformation structures including soft robotic grippers.

Validated the method on single and multi-material design problems.

Demonstrated improved numerical stability and convergence.

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.