ABSTRACT
Since the original, or standard, formulation of the material point method (MPM), there have been many improvements and modifications of the method in an attempt to overcome some numerical drawbacks. The standard MPM uses linear shape functions for the spatial discretisation. The oscillations occur due to the computation of the internal forces when using linear shape functions and the gradient of the shape functions. The spatial derivatives of the shape functions are piecewise constant with a discontinuity at the corresponding central node. The dual domain material point method (DDMP) is an approach to smooth the gradient of the nodal shape functions. Another way to get a smoother gradient for the nodal shape functions is to choose smoother shape functions. The integration within one element in MPM is mostly performed by summing up the values of all MPs inside a given element. The critical time step defines the biggest time increment which can be used for a stable calculation.
