Substepping the Material Point Method

2025-08-14

AI Summary

Explicit Material Point Method (MPM) suffers from numerical instability under large time steps, hindering its integration with partitioned large-step solvers and multi-physics frameworks. Method: This paper proposes a plug-and-play substepping algorithm that encapsulates explicit MPM as a pseudo-implicit scheme without modifying the underlying explicit integrator code. By introducing internal substeps coupled with constraint enforcement and projection operations, the method ensures numerical stability and physical consistency at macroscopic large time steps. Contribution/Results: The approach is inherently compatible with multi-solver coupling, complex constraint handling, and multi-physics integration, significantly enhancing computational robustness and efficiency. Experiments demonstrate that, while preserving accuracy, the method enables time-step enlargement by several-fold—providing a practical pathway for embedding MPM into large-scale, multi-physics simulation frameworks.

Technology Category

Multiagent Systems: Multiagent PlanningPlanning, Routing, and Scheduling: Mixed Discrete/Continuous PlanningIntelligent Robots: Motion and Path Planning

Application Category

Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphsUser Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalizationSystems and Infrastructure for Web, Mobile and WoT: Data management and stream processing for Web, mobile and wireless applications

Abstract

Many Material Point Method implementations favor explicit time integration. However large time steps are often desirable for special reasons - for example, for partitioned coupling with another large-step solver, or for imposing constraints, projections, or multiphysics solves. We present a simple, plug-and-play algorithm that advances MPM with a large time step using substeps, effectively wrapping an explicit MPM integrator into a pseudo-implicit one.

Problem

• Enabling large time steps in explicit MPM
• Wrapping explicit integrator into pseudo-implicit
• Facilitating partitioned coupling and multiphysics solves

Innovation

• Substepping algorithm for MPM
• Wraps explicit integrator into pseudo-implicit
• Enables large time steps with substeps