An adaptive finite element material point method and its application in extreme deformation problems

Taking advantages of both Lagrangian and Eulerian methods, material point method (MPM) is suitable for modeling problems with extreme deformation. However, MPM is less accurate and less efficient than finite element method (FEM) for small deformation problems due to particle quadrature and mappings between particles and background grid applied in MPM. To take advantages of both FEM and MPM, an adaptive finite element material point method is developed for modeling the dynamic behavior of material under extreme loading. Bodies are initially discretized by finite elements, and then the elements with large strain are adaptively converted into MPM particles based on their degree of distortion or plastic strain during the solution process. The interaction between the remaining finite elements and MPM particles is implemented based on the background grid in MPM framework. Several numerical examples are presented to validate the efficiency and accuracy of the proposed method, and the numerical results are in good agreement with experiments, while the efficiency of the method is higher than that of both MPM and FEM.