The Generalized Interpolation Material Point Method
نویسندگان
چکیده
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 generalization permits 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 in MPM calculations. This noise results in nonphysical local variations at the material points, where constitutive response is evaluated. It is shown to destroy the explicit solution in one case, and seriously degrade it in another. History dependent, inelastic constitutive laws 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 is shown to be capable of eliminating cell crossing noise. keyword: MPM, PIC, meshless methods, Petrov– Galerkin discretization.
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