Coupling of finite element method with material point method by local multi-mesh contact method

As a Lagrangian particle method, the material point method (MPM) has the potential to model extreme deformation of materials, where the traditional finite element method (FEM) often encounters mesh distortion and element entanglement which lead to numerical difficulties. However, FEM is more accurate and efficient than MPM for problems with small deformation. It is therefore desirable to model the body with extreme deformation by MPM and the body with small deformation by FEM, respectively. In this paper, a method to handle the contact interaction between the MPM body and the FEM body is proposed, which is implemented on the background grid of MPM. By this method, FEM is coupled with MPM and a hexahedral element is incorporated into our 3D explicit MPM code MPM3D®. Several numerical examples, including plate impact, sphere rolling, perforation of thick plate, and fluid-structure interaction problems, are studied and the numerical results are in good agreement with analytical solution and results available in the literature. The coupling of FEM and MPM offers advantages of both FEM and MPM.