Development of the distinct lattice spring model with polyhedral particles

Abstract

Distinct Lattice Spring Model (DLSM) is a microscopic model to overcome the mismatch problem of degrees of freedom when coupling between discrete element method (DEM) and finite element method (FEM). In the original DLSM, the lattice model is composed of a number of same spherical particles, which has the problem of inaccurate geometric description. A polyhedral 3D DLSM was developed to overcome some limitations of the original DLSM. A new pre- and post-processing method is introduced to extend the ability of DLSM on precise geometry description. Following this, a pre-processing method is proposed to generate the lattice model from a 3D Finite Element (FE) Mesh or a 3D Numerical Manifold Method (NMM) Mesh. It is required that the generated mesh can present the precise 3D geometry and consider the spatial morphology of joint surfaces. The 3D FE mesh is generated by using the general mesh software. The FE mesh is generated according to the free surfaces and the joint surfaces defined in the model. To get the 3D NMM mesh, a 3D surface mesh Boolean algorithm is developed. The surface mesh Boolean algorithm is used for solving the Boolean operations between mathematic covers and physical covers in NMM. By using the algorithm, the 3D closed geometry cut by 3D surface and the union of multiple 3D surfaces can be solved. The 3D NMM mesh is ultimately generated through the Boolean intersection of mathematical covers and physical covers, the physical covers include the free surfaces and joint faces. The polyhedral particles generated by the FE mesh or NMM mesh have different shapes and sizes, the springs between polyhedral particles will also have different lengths. The effectiveness, necessity, and correctness of these enrichments are demonstrated from a number of specially designed numerical examples.