Deformable Particles: Modeling and Applications

Abstract

Particulate materials, such as granular materials, foams, emulsions, and packings of cells, including epithelial monolayers and tissues, are composed of “particles” that can change their shapes under external stresses. Computational methods for modeling the structural and mechanical properties of particulate materials either prescribe a fixed shape for each particle, or construct volumetric particle meshes that can be computationally expensive. In this chapter, we review the recently developed deformable particle model, which only requires a surface mesh to describe arbitrary changes in particle shape. We introduce the shape-energy function for the deformable particle model, which can be tuned to model the mechanics of bulk elastic particles, elastic shells, particles governed by surface tension, and particles that undergo plastic shape changes. In addition, we specify the particle interactions, including frictional interactions between contacting rough and smooth deformable particle surfaces. We compare the compressive force between a flat wall and a deformable particle to that between two contacting bulk elastic particles and elastic shells as a function of the particle deformation. We also illustrate how to perform calculations of the pressure, packing fraction, and vibrational density of states for static packings of deformable particles. In addition, we describe extensions of the deformable particle model to flexible, tesselated granular materials, which have applications in soft robotics.