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.

Mitigating kinematic locking in the material point method

“…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.…”

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.…”