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A convected particle domain interpolation technique to extend applicability of the material point method for problems involving massive deformations
Author(s) -
Sadeghirad A.,
Bran R. M.,
Burghardt J.
Publication year - 2011
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.3110
Subject(s) - parallelogram , material point method , interpolation (computer graphics) , grid , domain (mathematical analysis) , deformation (meteorology) , particle (ecology) , mathematics , point (geometry) , meshfree methods , mathematical analysis , smoothed particle hydrodynamics , finite element method , geometry , classical mechanics , mechanics , motion (physics) , physics , structural engineering , engineering , geology , oceanography , hinge , meteorology
Abstract A 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. Copyright © 2011 John Wiley & Sons, Ltd.