A Coupled Eulerian-Lagrangian Extended Finite Element Formulation for Moving Interface Problems and Damage Transport in Hyperelastic Media

Abstract

A coupled Eulerian- Lagrangian (CEL) formulation is presented to model moving interface problems and damage transport in hyperelastic materials when subjected to large deformations. This formulation is based on Eulerian description of kinematics of deformable bodies along with an updated Lagrangian formulation for transporting deformation gradient tensor. Extended finite element method (XFEM) is used to discretize equilibrium and deformation gradient transport equation in two phase domain separated by a sharp interface. The interface describing the deformed shape of the body is represented by level set function and is evolved using grid based particle method. The performance of the scheme is explored in both one and two dimensions. The numerical results are in good agreement with the theory and with numerical results obtained from the traditional Lagrangian formulation in commercial software Abaqus. In this formulation, the material motion is separate to that of the mesh, so this method can handle large to extreme deformations without any issue of remeshing. Therefore, this method is well suited to handle large deformation problems with hyperelastic media.