A review of the Material Point Method and its links to other computational methods.

There is considerable interest in development of solid mechanics modelling which can cope with both \nmaterial and geometric nonlinearity, particularly in areas such as computational geotechnics, for applications \nsuch as slope failure and foundation installation. One such technique is the Material Point Method \n(MPM), which appears to provide an efficient way to model these problems. The MPM models a problem \ndomain using particles at which state variables are kept and tracked. The particles have no restriction \non movement, unlike in the Finite Element Method (FEM) where element distortion limits the level of \nmesh deformation. In the MPM, calculations are carried out on a regular background grid to which state \nvariables are mapped from the particles. It is clear, however, that the MPM is actually closely related \nto existing techniques, such as ALE and in this paper we review the MPM for solid mechanics and \ndemonstrate these links.