Examination and Analysis of Implementation Choices within the Material Point Method (MPM)

The Material Point Method (MPM) has shown itself to be a powerful tool in the sim- ulation of large deformation problems, especially those involving complex geometries and contact where typical finite element type methods fre- quently fail. While these large complex problems lead to some impressive simulations and solu- tions, there has been a lack of basic analysis char- acterizing the errors present in the method, even on the simplest of problems. The large number of choices one has when implementing the method, suchas thechoiceofbasisfunctionsandboundary treatments,furthercomplicates thiserroranalysis. In thispaperweexploresomeofthemany choices one can make when implementing an MPM al- gorithm and the numerical ramifications of these choices. Specifically, we analyze and demonstrate how the smoothing length within the General- ized InterpolationMaterial Point Method (GIMP) can affect the error and stability properties of the method. We also demonstrate how various choices of basis functions and boundary treat- ments affect the spatial convergence properties of MPM.