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

TY - JOUR

T1 - On the use of domain-based material point methods for problems involving large distortion

AU - Wang, Lei

AU - Coombs, William M.

AU - Augarde, Charles E.

AU - Cortis, Michael

AU - Charlton, T. J.

AU - Brown, Michael

AU - Knappett, Jonathan

AU - Brennan, Andrew

AU - Davidson, Craig

AU - Richards, David

AU - Blake, Anthony

N1 - This work was supported by the Engineering and Physical Sciences Research Council [grant numbers EP/K502832/1, EP/M017494/1 and EP/M000397/1] as indicated in the paper’s acknowledgements. The fifth author (Charlton, T.J.) was supported by the Engineering and Physical Sciences Research Council [grant number EP/K502832/1].

PY - 2019/10/1

Y1 - 2019/10/1

N2 - 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.

AB - 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.

KW - Material Point Method

KW - Convected Particle Domain Interpolation

KW - large deformation mechanics

KW - elasto-plasticity

KW - distortion

KW - Elasto-plasticity

KW - Large deformation mechanics

KW - Distortion

KW - Material point method

KW - Convected particle domain interpolation

UR - https://www.scopus.com/pages/publications/85068967423

UR - https://discovery.dundee.ac.uk/en/publications/68d187a7-1e0b-4575-97eb-58bba92d75b1

U2 - 10.1016/j.cma.2019.07.011

DO - 10.1016/j.cma.2019.07.011

M3 - Article

SN - 0045-7825

VL - 355

SP - 1003

EP - 1025

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

ER -