Improved coupling of finite element method with material point method based on a particle-to-surface contact algorithm

For extreme deformation problems, material point method (MPM) takes competitive advantages compared with finite element method (FEM) which often encounters mesh distortion. However, for small deformation problems, FEM is still more efficient and accurate than MPM in most cases. Hence, a coupled finite element material point (CFEMP) method and an adaptive finite element material point method (AFEMP) have been proposed by our group to take advantages of both methods. Because the coupling between MPM particles and FEM elements was implemented based on the MPM grid-based contact method, both CFEMP and AFEMP demand a high degree of consistence of meshing between FEM domain and MPM domain. This may lead to over meshing in FEM domain, thus significantly decreases the time step size and increases computational cost as well as data storage. In order to allow arbitrary inconsistent meshing, the CFEMP and AFEMP methods are further improved in this article. The coupling between the MPM particles and FEM elements is implemented based on a particle-to-surface contact algorithm rather than the MPM grid-based contact method, so that the consistent meshing is no more needed. Thus, the meshing of FEM body can be much coarser than the MPM grid. Numerical studies illustrate that the robustness, efficiency and accuracy of the improved CFEMP (ICFEMP) method and the improved AFEMP (IAFEMP) method are much higher than MPM, CFEMP and AFEMP.