Three-dimensional soft discrete element method for large-scale simulations of soft spheres

Soft particles are ubiquitous in both nature and industries, yet existing three-dimensional simulation methods remain inefficient. This paper presents a three-dimensional soft discrete element method (3D SDEM) for the efficient large-scale dynamic simulations of soft spherical particles. In the method, each soft sphere is modeled as a truncated ellipsoid with a homogeneous strain field, which requires 12 degrees of freedom only. The dynamic equations of soft spheres are derived by using the Lagrange-d’Alembert principle, and the contact detection between soft spheres is handled via the Common Normal Method. The contact force model and the strain energy function are formulated and validated through various compression scenarios of a single soft sphere. The accuracy and efficiency of the 3D SDEM are verified through two-sphere collision simulations and three-dimensional soft sphere compaction simulations. Notably, the compression of 10,000 soft spheres from a jammed state to 95 % volume fraction is simulated within five hours on a laptop computer with a single GPU only. Finally, the method is used to simulate the shear flow of soft particle glasses comprising 1000 soft spheres and successfully capture individual soft sphere deformations not reported before. These results demonstrate that the 3D SDEM enables the efficient modeling of large-scale soft sphere systems, paving the way for advanced studies in both physics and engineering applications.