A Variational Formulation for Deformable Particle Simulations and its Level Set Discrete Element Method Implementation

TL;DR

This paper introduces a variational deformable Discrete Element Method that models particle elasticity using level set evolution, matching finite-element accuracy with similar computational efficiency.

Contribution

It develops a novel variational formulation for deformable particles within DEM, extending classical rigid-particle models to include elastic deformation.

Findings

Excellent agreement with finite-element simulations

Supports arbitrary particle geometries and deformation modes

Maintains computational efficiency comparable to rigid DEM

Abstract

We present a deformable Discrete Element Method (DEM) that extends the classical rigid-particle formulation through a reduced-order description of elastic grain-scale deformation. The method hinges on two developments. First, an energetic variational formulation based on the Lagrange--d'Alembert principle extends classical rigid-body dynamics to incorporate particle deformability by embedding translational, rotational, and deformation degrees of freedom within a unified energetic description. Second, particle deformation is realized within the Level Set DEM formalism through evolving level sets. The framework applies broadly to general particle geometries and topologies, and supports arbitrary deformation modes. The resulting deformable DEM retains the robustness, geometric and physical clarity, and scalability of classical DEM, while enabling physically grounded grain-scale deformability at a computational cost of the same order of magnitude as rigid DEM. Comparisons with full finite-element simulations demonstrate excellent agreement at both particle and system scales, establishing a general and extensible variational framework for modeling deformation in particulate systems.