An Evaluation of the Material Point Method

The theory and algorithm for the Material Point Method (MPM) are documented, with a detailed discussion on the treatments of boundary conditions and shock wave problems. A step-by-step solution scheme is written based on direct inspection of the two-dimensional MPM code currently used at the University of Missouri-Columbia (which is, in turn, a legacy of the University of New Mexico code). To test the completeness of the solution scheme and to demonstrate certain features of the MPM, a one-dimensional MPM code is programmed to solve one-dimensional wave and impact problems, with both linear elasticity and elastoplasticity models. The advantages and disadvantages of the MPM are investigated as compared with competing mesh-free methods. Based on the current work, future research directions are discussed to better simulate complex physical problems such as impact/contact, localization, crack propagation, penetration, perforation, fragmentation, and interactions among different material phases. In particular, the potential use of a boundary layer to enforce the traction boundary conditions is discussed within the framework of the MPM.