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On the use of domain-based material point methods for problems involving large distortion

On the use of domain-based material point methods for problems involving large distortion
On the use of domain-based material point methods for problems involving large distortion

Challenging solid mechanics problems exist in areas such as geotechnical and biomedical engineering which require numerical methods that can cope with very large deformations, both stretches and torsion. One candidate for these problems is the Material Point Method (MPM), and to deal with stability issues the standard form of the MPM has been developed into new domain-based techniques which change how information is mapped between the computational mesh and the material points. The latest of these developments are the Convected Particle Domain Interpolation (CPDI) approaches. When these are demonstrated, they are typically tested on problems involving large stretch but little torsion and if these MPMs are to be useful for the challenging problems mentioned above, it is important that their capabilities and shortcomings are clear. Here we present a study of the behaviour of some of these MPMs for modelling problems involving large elasto-plastic deformation including distortion. This is carried out in a unified implicit quasi-static computational framework and finds that domain distortion with the CPDI2 approaches affects some solutions and there is a particular issue with one approach. The older CPDI1 approach and the standard MPM however produce physically realistic results. The primary aim of this paper is to raise awareness of the capabilities or otherwise of these domain-based MPMs.

Convected particle domain interpolation, Distortion, Elasto-plasticity, Large deformation mechanics, Material point method
0045-7825
1003-1025
Wang, L.
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Coombs, W.M.
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Augarde, C.E.
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Cortis, M.
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Charlton, T.J.
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Brown, M. J.
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Knappett, J.
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Brennan, A.
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Davidson, C.
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Richards, D.
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Blake, A.
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Wang, L.
ffdc9d25-25fb-48d6-95dc-9db51a7a65c9
Coombs, W.M.
b0ab888c-8404-4f5b-abcc-f2cc5b462cae
Augarde, C.E.
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Cortis, M.
3242806a-5c41-4615-9da1-2021c85507f0
Charlton, T.J.
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Brown, M. J.
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Knappett, J.
cda30027-553d-4310-8a05-e48d8989a545
Brennan, A.
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Davidson, C.
bce1f209-790b-46f1-8c0c-4d744d2941bb
Richards, D.
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Blake, A.
e0438bea-cfc4-4373-b100-8b9768ddc56f

Wang, L., Coombs, W.M., Augarde, C.E., Cortis, M., Charlton, T.J., Brown, M. J., Knappett, J., Brennan, A., Davidson, C., Richards, D. and Blake, A. (2019) On the use of domain-based material point methods for problems involving large distortion. Computer Methods in Applied Mechanics and Engineering, 355, 1003-1025. (doi:10.1016/j.cma.2019.07.011).

Record type: Article

Abstract

Challenging solid mechanics problems exist in areas such as geotechnical and biomedical engineering which require numerical methods that can cope with very large deformations, both stretches and torsion. One candidate for these problems is the Material Point Method (MPM), and to deal with stability issues the standard form of the MPM has been developed into new domain-based techniques which change how information is mapped between the computational mesh and the material points. The latest of these developments are the Convected Particle Domain Interpolation (CPDI) approaches. When these are demonstrated, they are typically tested on problems involving large stretch but little torsion and if these MPMs are to be useful for the challenging problems mentioned above, it is important that their capabilities and shortcomings are clear. Here we present a study of the behaviour of some of these MPMs for modelling problems involving large elasto-plastic deformation including distortion. This is carried out in a unified implicit quasi-static computational framework and finds that domain distortion with the CPDI2 approaches affects some solutions and there is a particular issue with one approach. The older CPDI1 approach and the standard MPM however produce physically realistic results. The primary aim of this paper is to raise awareness of the capabilities or otherwise of these domain-based MPMs.

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Accepted/In Press date: 6 July 2019
e-pub ahead of print date: 17 July 2019
Published date: 1 October 2019
Keywords: Convected particle domain interpolation, Distortion, Elasto-plasticity, Large deformation mechanics, Material point method

Identifiers

Local EPrints ID: 432757
URI: http://eprints.soton.ac.uk/id/eprint/432757
ISSN: 0045-7825
PURE UUID: 9d0a05e2-989a-4817-bab9-0326eeb8f4ae

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Date deposited: 26 Jul 2019 16:30
Last modified: 07 Oct 2020 00:38

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Contributors

Author: L. Wang
Author: W.M. Coombs
Author: C.E. Augarde
Author: M. Cortis
Author: T.J. Charlton
Author: M. J. Brown
Author: J. Knappett
Author: A. Brennan
Author: C. Davidson
Author: D. Richards
Author: A. Blake

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