Compatible coupling of discrete elements and finite elements using Delaunay–Voronoi dual tessellations

Abstract

The Voronoi cell lattice model (VCLM) is a discrete approach for simulating the behavior of solids and structures, based on a Voronoi cell partitioning of the domain. In this study, the duality between Voronoi and Delaunay tessellations is used to couple distinct regions represented by VCLM and the finite element method (FEM). By introducing an edge-based smoothing scheme in the FEM, the element frame is transformed from the conventional triangular body to the edge entity. Therefore, along each of the Delaunay edges, both the lattice and finite elements can be defined, which provides several advantages: (a) The regions modeled by each respective approach are clearly distinguished without the need for interface elements, (b) algorithmic efficiency is enhanced during element-wise computations during explicit time integration, and (c) the element performance of the three-node triangular element is improved by introducing the edge-based strain smoothing technique. Selected examples are used to validate the VCLM–FEM coupling approach. Simulations of elastic behavior, geometric nonlinearity, and fracture are conducted. The simulation results agree well with the corresponding theoretical, numerical, and experimental results, which demonstrates the capabilities of the proposed compatible coupling scheme.