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Premium 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 year2011
Publication title
international journal for numerical methods in engineering
Resource typeJournals
PublisherJohn Wiley & Sons
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.
Subject(s)boundary value problem , calculus (dental) , classical mechanics , computer science , dentistry , domain (mathematical analysis) , engineering , finite element method , geology , geometry , interpolation (computer graphics) , material point method , mathematical analysis , mathematics , mechanics , medicine , motion (physics) , oceanography , particle (ecology) , particle method , physics , point (geometry) , point particle , smoothed particle hydrodynamics , structural engineering
Language(s)English
SCImago Journal Rank1.421
H-Index168
eISSN1097-0207
pISSN0029-5981
DOI10.1002/nme.3110

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