Inhomogeneous Neumann boundary conditions for MPM and GIMP

Abstract

As the Material Point Method (MPM) uses both a mesh and a point discretisation scheme, the application of boundary conditions is difficult, currently limiting the flexibility of the method. While many boundary condition options have been used in the literature, the accuracy of Neumann boundary condition options has not yet been studied. Four options have here been evaluated for 1D and 2D benchmarks, although none of the options were found to be both accurate and generally applicable in MPM. However, for the generalised interpolation material point method (GIMP), the application of surface tractions on support domain boundaries or on a detected surface are valid options. Large differences between these two accurate options and the application of tractions at surface material points, a method regularly used in the literature, have been observed.