Material Point Method

The Material Point Method (MPM), is an extension of the Particle-in-cell (PIC) Method in computational fluid dynamics to computational solid dynamics, and is a Finite element method (FEM)-based particle method. It is primarily used for multiphase simulations, because of the ease of detecting contact without inter-penetration. It can also be used as an alternative to dynamic FEM methods to simulate large material deformations, because there is no re-meshing required by the MPM.

In the MPM, Lagrangian point masses, or material points, are moved through a Eulerian background mesh. At the end of each calculation cycle, a ‘convective’ step occurs, in which the mesh is reset to its original position, while material points remain in their current positions. There are two key differences between the PIC and MPM. The first one is that the MPM is formulated in the weak form similar to that for the FEM so that the FEM and MPM could be combined together for large-scale simulations. The second one is that history-dependent constitutive models could be formulated on the material points, which results in a robust spatial discretization method for multiphase and multi-physics problems.