An explicit material point finite element method for hyper-velocity impact

In this paper, an explicit material point finite element (FE) method is proposed and a computer code EMPFE-3D is developed for simulating hyper-velocity impact. The material domain is discretized by a mesh of finite elements. The momentum equations are solved on a predefined computational grid (like the material point method) in the large deformation zone, and on the FE mesh (like the traditional FE method) elsewhere. The grid may be fixed in space or moved in a predefined way. The nodes covered by the grid are treated as material particles, and the remaining nodes are treated as FE nodes. The proposed method yields the same results as the traditional FE method if the grid vanishes. On the other hand, it yields the same results as the material point method if the grid covers the entire material domain at all time steps. The method combines the advantages of Eulerian and Lagrangian descriptions of motion while eliminates their drawbacks due to element entanglement and numerical dissipation. The method is computationally efficient and can be easily implemented in an existing explicit FE code like DYNA3D