A convected particle domain interpolation technique to extend applicability of the material point method for problems involving massive deformations

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 proposed for efficiently calculating nodal force and consistent mass integrals on the grid. Specifically, by taking advantage of initially parallelogram-shaped particle domains, and treating the deformation gradient as constant over the particle domain, the convected particle domain is a reshaped parallelogram in the deformed configuration. Accordingly, an alternative grid basis function over the particle domain is constructed by a standard 4-node finite element interpolation on the parallelogram. Effectiveness of the proposed modifications is demonstrated using several large deformation solid mechanics problems.

Material point method enhanced by modified gradient of shape function

“…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.…”

Numerical simulation of orthogonal cutting using the material point method

“…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.…”

Avalanche and landslide simulation using the material point method: flow dynamics and force interaction with structures

“…There is a large literature base considering MPM applications-the interested reader is referred to three recent publications [13,14,22] that summarize previous applications, extensions, and numerical implementation details. In the specific context of granular flow, it is important to recognize the works of [15,32,33] in which the MPM is used to simulate granular media in various contexts.…”