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

• DOI: 10.3970/cmes.2008.031.107
• Publication Date: 2008-06-01
• Authors: Michael Steffen; P. C. Wallstedt; James E. Guilkey; Robert M. Kirby; Martin Berzins
• Keywords: Smoothing; Material Point Method; Basis (linear algebra)

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 problems lead some impressive simulations solu- tions, there been lack basic analysis char- acterizing errors present method, even on simplest problems. number choices one when implementing suchas thechoiceofbasisfunctionsandboundary treatments,furthercomplicates thiserroranalysis. In thispaperweexploresomeofthemany can make an MPM al- gorithm numerical ramifications choices. Specifically, we analyze demonstrate how smoothing length within General- ized InterpolationMaterial (GIMP) affect error stability properties method. We also various basis functions boundary treat- ments spatial convergence MPM.