The Generalized Interpolation Material Point Method

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 generalizationperm...

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Bibliographic Details
Published in:Computer modeling in engineering & sciences 2004, Vol.5 (6), p.477-495
Main Authors: Bardenhagen, S G, Kober, E M
Format: Article
Language:English
Subjects:
Computational grids
Finite element method
Galerkin method
Identification methods
Interpolation
Mathematical analysis
Meshless methods
Noise
Smoothness
Solid mechanics
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Summary: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.
ISSN:1526-1492
1526-1506
DOI:10.3970/cmes.2004.005.477