Caveats on the implementation of the generalized material point method

The material point method (MPM) is a numerical method for the Solution of problems in continuum mechanics, including Situations of large deformations. A generalization (GMPM) of this method was Introduced by Bardenhagen and Kober (2004) in order to avoid some computational instabilities inherent to the original method (MPM). This generalization leads to a method more akin of the Petrov-Galerkin procedure. Although It is possible to find in the literature examples of the deduction and applications of the MPM/GMPM to specific problems, its detailed Implementation is yet to be presented. Therefore. this paper attempts to describe all steps required for the explicit Implementation of the material point method, Including its generalization. Moreover, some caveats during the implementation are addressed. For example, the setting up of boundary conditions and the steps for the computation of Values at nodes and material points are discussed. The Influences of the time and space discretization are also verified, basing oil numerical analyses. Two strategies for the update of stress. known as Update stress first (USF) and update stress last (USL) are numerically investigated. It is shown that both the order for the computation of boundary conditions and the way that the,rid values are extrapolated have high impact on the accuracy of the Solution. The complete 3D algorithm is detailed and summarized in order to make easier the implementation of the GMPM/MPM