A unified Minkowski sum model for largely deformed granular materials with arbitrary morphologies

Abstract

Since deformable granular materials with arbitrary morphologies constructed by different dilated non-spherical models in complex structures remain challenging for numerical simulations using the discrete element method (DEM), a unified Minkowski sum model was proposed for calculating collision forces and large deformations of arbitrarily shaped granular materials and structures. In this model, dilated superquadric equations, dilated spherical harmonic functions, and dilated polyhedrons were developed to construct arbitrarily shaped particles, and Fibonacci and automatic mesh simplification algorithms were established to determine the surface meshes of the particles with controlled accuracy. Subsequently, the Minkowski sum model based on chain-linked meshes and granular skeletons was proposed to calculate collision forces and large deformations of rigid and deformable granular materials. To investigate the conservation, accuracy, and robustness of the proposed model, six sets of numerical examples were conducted and compared with the theoretical and finite element results, which included the static analysis of a deformable granular skeleton, the mechanical analysis of a single deformable structure, a single deformable particle impacting a rigid wall, the collision between two rigid and deformable particles, the accumulation of multiple rigid particles on a deformable structure, and compression of multiple deformable particles within a deformable structure. The corresponding numerical results are in good agreement with the theoretical and finite element results, which verifies that the present DEM model can accurately predict the large deformation characteristics of different dilated DEM models and can be extensively applied to the dynamic flows and deformation behaviors of arbitrarily shaped granular materials involving multiple DEM models in deformable structures.