On the Simulation of Deformable Bodies Using Combined Discrete and Finite Element Methods

Abstract

In discrete element methods (DEM, [2] and [4]) the simulated bodies are typically assumed to be infinitely rigid in order to reduce the computational cost. However, there are multibody systems where it is useful to take into account the deformability of the simulated bodies in order to enable the evaluation of their stress and strain distributions. This paper focuses on the simulation of systems of multiple deformable bodies using a combination of discrete and finite element methods (FEM), with some simplifying assumptions that are necessary to make the solution of the problem feasible. In traditional mixed FE formulations the contact effects can be taken into account using Lagrange multipliers methods and keeping the contact surfaces and forces as unknowns together with the unknown displacements. This approach results in huge systems of highly nonlinear coupled equations due to geometric as well as boundary nonlinearities. Furthermore, the parts of the bodies that may come in contact, typically, have to be identified before performing the simulation. However, no prior knowledge of the upcoming contacts is available in the multibody systems under consideration. Considering the excessive computational requirements, due to the huge number of degrees-of-freedom (DOF) and the high nonlinearities of the coupled systems of equations, it is unrealistic to solve problems involving many interacting bodies using such classical contact FE approaches. Simulations of deformable bodies with reasonable computational cost are enabled by incorporating FEM in DE analyses using certain assumptions that uncouple the contact interactions from the equations of dynamic equilibrium. In particular, the DEM are employed to identify, at each simulation step, the bodies in contact and determine the contact forces. Then, either a FE or a DE formulation is used at the individual body level to describe the equations of motion, depending