Open Access

ARTICLE

The Generalized Interpolation Material Point Method

S. G. Bardenhagen^1,2, E. M. Kober³

1 Dept. of Mechanical Engineering, University of Utah, Salt Lake City, UT 84112, USA, Graduate Engineering Research Center, University of Florida, 1350 Poquito Rd., Shalimar, FL 32579, USA.
2 Correspondence address: Group T–14, MS B214, Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA.
3 Group T–14, MS B214, Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA.

Computer Modeling in Engineering & Sciences 2004, 5(6), 477-496. https://doi.org/10.3970/cmes.2004.005.477

Abstract

The Material Point Method (MPM) discrete solution procedure for computational solid mechanics is generalized using a variational form and a Petrov–Galerkin discretization scheme, resulting in a family of methods named the Generalized Interpolation Material Point(GIMP) methods. The generalizationpermits identification with aspects of other point or node based discrete solution techniques which do not use a body–fixed grid, i.e. the “meshless methods”. Similarities are noted and some practical advantages relative to some of these methods are identified. Examples are used to demonstrate and explain numerical artifact noise which can be expected inMPM calculations. Thisnoiseresultsin non-physical local variations at the material points, where constitutive response is evaluated. It is shown to destroy the explicit solutionin one case, and seriouslydegrade it in another. Historydependent, inelasticconstitutivelaws can be expected to evolve erroneously and report inaccurate stress states because of noisy input. The noise is due to the lack of smoothness of the interpolation functions, and occurs due to material points crossing computational grid boundaries. The next degree of smoothness available in the GIMP methods isshown tobe capable of eliminatingcell crossing noise.

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