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

M. Steffen1, P.C. Wallstedt2, J.E. Guilkey2,3, R.M. Kirby1, M. Berzins1
School of Computing, University of Utah, Salt Lake City, UT, USA. {msteffen,kirby,berzins}@cs.utah.edu
Departmentof MechanicalEngineering,Universityof Utah, Salt Lake City, UT, USA.{philip.wallstedt,james.guilkey}@utah.edu
Corresponding Author

Computer Modeling in Engineering & Sciences 2008, 31(2), 107-128. https://doi.org/10.3970/cmes.2008.031.107

Abstract

The Material Point Method (MPM) has shown itself to be a powerful tool in the simulation of large deformation problems, especially those involving complex geometries and contact where typical finite element type methods frequently fail. While these large complex problems lead to some impressive simulations and solutions, there has been a lack of basic analysis characterizing the errors present in the method, even on the simplest of problems. The large number of choices one has when implementing the method, such as the choice of basis functions and boundary treatments, further complicates this error analysis.\newline In this paper we explore some of the many choices one can make when implementing an MPM algorithm and the numerical ramifications of these choices. Specifically, we analyze and demonstrate how the smoothing length within the Generalized Interpolation Material Point Method (GIMP) can affect the error and stability properties of the method. We also demonstrate how various choices of basis functions and boundary treatments affect the spatial convergence properties of MPM.

Keywords

Material Point Method, GIMP, Meshfree Methods, Meshless Methods, Particle Methods, Smoothed Particle Hydrodynamics, Quadrature.

Cite This Article

Steffen, M., Wallstedt, P., Guilkey, J., Kirby, R., Berzins, M. (2008). Examination and Analysis of Implementation Choices within the Material Point Method (MPM). CMES-Computer Modeling in Engineering & Sciences, 31(2), 107–128.



This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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