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

2026-03-15

AI Summary

This work proposes a novel topology optimization framework that integrates the implicit Material Point Method (MPM) to address numerical instabilities arising from mesh distortion and large rotations in large-deformation problems. For the first time, MPM is incorporated into topology optimization within an end-to-end differentiable pipeline, leveraging automatic differentiation and hyperelastic constitutive models to enable stable and efficient quasi-static optimization of structures undergoing finite deformations. The approach naturally supports both single- and multi-material designs and demonstrates robust performance on complex geometries, including soft robotic grippers. By circumventing the limitations of traditional finite element–based methods, the proposed framework significantly enhances the robustness and applicability of topology optimization in highly nonlinear deformation regimes.

Technology Category

• Intelligent Robots: Learning & Optimization for ROB
• Search and Optimization: Sampling/Simulation-based Search
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Responsible Web: Machine-in-the-loop, human agency and autonomy

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.

Problem

• topology optimization
• large deformations
• numerical instability
• mesh distortion
• convergence failure

Innovation

• Material Point Method
• Topology Optimization
• Large Deformations
• Implicit Differentiable Framework
• Soft Robotics