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The Aggregated Material Point Method (AgMPM) [dataset] Open Access

The Material Point Method (MPM) has been shown to be an effective approach for analysing large deformation processes across a range of physical problems. However, the method suffers from a number of spurious artefacts, such as a widely documented cell crossing instability, which can be mitigated by adopting basis functions with higher order continuity. The larger stencil of these basis functions exacerbate a less widely discussed issue - small cuts. The small cut issue is linked to the arbitrary interaction between the physical body and the background mesh that is used to assemble and solve the governing equations in the MPM. There is the potential for degrees of freedom near the boundary of the body to have very small contributions from material points, which causes two problems: (i) artificially large accelerations/displacements at the boundary and (ii) ill conditioning of the global linear system. This paper provides a new mesh Aggregated MPM, or AgMPM, that mitigates the small cut issue by forming aggregated elements, tying the ill-behaved degrees of freedom to well posed interior elements. Implicit quasi-static and explicit dynamic formulations are provided and demonstrated through a series of numerical examples. The approach does not introduce any new numerical parameters and can be applied to implementations that adopt a lumped mass matrix. Aggregation is shown to significantly improve the stability of implicit implementations of the MPM, often at a lower computational cost compared to standard, non-aggregated, implementations. The technique improves the energy conversation and the stress field of explicit dynamic MPMs.

Descriptions

Resource type

Dataset

Contributors

Creator: Coombs, William ¹
Contact person: Coombs, William ¹
Creator: Bird, Robert ¹
Creator: Pretti, Giuliano ¹

¹ Durham University, UK

Funder

Engineering and Physical Sciences Research Council

Research methods

Material Point Method

Other description

Keyword

Material point method
Finite deformation mechanics
Mesh aggregation
Implicit quasi-static
Explicit dynamic

Subject

Material point method

Location

Language

English

Cited in

Identifier

ark:/32150/r1gm80hv42k
doi:10.15128/r1gm80hv42k

Rights

Creative Commons Attribution 4.0 International (CC BY)

Publisher

Durham University

Date Created

File Details

Depositor

W.M. Coombs

Date Uploaded

8 April 2025, 08:04:01

Date Modified

8 April 2025, 11:04:46

Audit Status

Audits have not yet been run on this file.

Characterization

File format: zip (ZIP Format)

Mime type: application/zip

File size: 281463477

Last modified: 2025:04:08 09:36:23+01:00

Filename: FigureData.zip

Original checksum: f492b38a83f34225c5140dcdacab4f0f