Abstract:SUMMARYA new algorithm is developed to improve the accuracy and efficiency of the material point method for problems involving extremely large tensile deformations and rotations. In the proposed procedure, particle domains are convected with the material motion more accurately than in the generalized interpolation material point method. This feature is crucial to eliminate instability in extension, which is a common shortcoming of most particle methods. Also, a novel alternative set of grid basis functions is … Show more
“…This idea was first developed in the Generalized Interpolation Material Point (GIMP) method [8] and has since been applied to wide variety of engineering problems, e.g., [16,[30][31][32]56]. A similar variant of the MPM, the Convected Particle Domain Interpolation (CPDI) technique [43], effectively combats the discontinuous gradient issue by introducing a parallelogram-shaped particle domain that is consistently updated using the deformation gradient at the particle. Unfortunately these approaches do not address or alleviate kinematic locking.…”
Section: Overview Of the Materials Point Methodsmentioning
“…This idea was first developed in the Generalized Interpolation Material Point (GIMP) method [8] and has since been applied to wide variety of engineering problems, e.g., [16,[30][31][32]56]. A similar variant of the MPM, the Convected Particle Domain Interpolation (CPDI) technique [43], effectively combats the discontinuous gradient issue by introducing a parallelogram-shaped particle domain that is consistently updated using the deformation gradient at the particle. Unfortunately these approaches do not address or alleviate kinematic locking.…”
Section: Overview Of the Materials Point Methodsmentioning
“…The full version of GIMP requires tracking the supports of the characteristic functions of the material 0021-9991/$ -see front matter Ó 2011 Elsevier Inc. All rights reserved. doi:10.1016/j.jcp.2011.04.032 points [4][5][6]. For brevity, in this paper we call the support of the characteristic function the shape of the material point.…”
“…1). Although aligning particle centers always helped the calculations, shearing the domains only influences the results when using shape function methods that account for domain deformation (e.g., convected particle domain integration or CPDI [21]). All calculations here using uniform, generalized interpolation methods (or uGIMP [12]) where the integration domain remains a square, but translates with the particles; uGIMP was used for all simulations because it was more efficient and accounting for domain shearing (with CPDI) had very little effect.…”
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