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A stable poro-mechanical formulation for Material Point Methods leveraging overlapping meshes and multi-field ghost penalisation [dataset] Open Access

The Material Point Method (MPM) is widely used to analyse coupled (solid-water) problems under large deformations/displacements. However, if not addressed carefully, MPM u-p formulations for poro-mechanics can be affected by two major sources of instability. Firstly, inf-sup condition violation can arise when the spaces for the displacement and pressure fields are not chosen correctly, resulting in an unstable pressure field when the equations are monolithically solved. Secondly, the intrinsic nature of particle-based discretisation makes the MPM an unfitted mesh-based method, which can affect the system's condition number and solvability, particularly when background mesh elements are poorly populated. This work proposes a solution to both problems. The inf-sup condition is avoided using two overlapping meshes, a coarser one for the pressure and a finer one for the displacement. This approach does not require stabilisation of the primary equations since it is stable by design and is particularly valuable for low-order shape functions. As for the system's poor condition number, a face ghost penalisation method is added to both the primary equations, which constitutes a novelty in the context of MPM mixed formulations. This study frequently makes use of the theories of functional analysis or the unfitted Finite Element Method (FEM). Although these theories may not directly apply to the MPM, they provide a robust and logical basis for the research. These rationales are further supported by four numerical examples, which encompass both elastic and elasto-plastic cases and drained and undrained conditions.

Descriptions

Resource type

Dataset

Contributors

Creator: Pretti, Giuliano ¹
Creator: Coombs, William M. ¹
Contact person: Coombs, William M. ¹
Creator: Augarde, Charles E. ¹

¹ Durham University, UK

Funder

Engineering and Physical Sciences Research Council

Research methods

Other description

Keyword

Material Point Method
Poro-mechanics
Finite strain
Large deformation analyses
Stability
Inf-sup condition
Mixed formulations

Subject

Material point method

Location

Language

Cited in

Identifier

ark:/32150/r15q47rn80d
doi:10.15128/r15q47rn80d

Rights

Creative Commons Attribution 4.0 International (CC BY)

Publisher

Durham University

Date Created

File Details

Depositor

W.M. Coombs

Date Uploaded

11 November 2024, 11:11:38

Date Modified

18 November 2024, 10:11:50

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File format: zip (ZIP Format)

Mime type: application/zip

File size: 2474976

Last modified: 2024:11:11 11:25:47+00:00

Filename: A_stable_poro-mechanical_formulation_Data.zip

Original checksum: fb6a30603bed8f9595e28885b1869210