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On Lagrangian mechanics and the material point method for large deformation elasto-plasticity [dataset] Open Access

The material point method is ideally suited to modelling problems involving large deformations where conventional mesh-based methods would struggle. However, total and updated Lagrangian approaches are unsuitable and non-ideal, respectively, in terms formulating equilibrium for the method. This is due to the basis functions, and particularly the derivatives of the basis functions, of material point methods normally being defined based on an unformed, and sometimes regular, background mesh. It is possible to map the basis function spatial derivatives using the deformation at a material point but this introduces additional algorithm complexity and computational expense. This paper presents a new Lagrangian statement of equilibrium which is ideal for material point methods as it satisfies equilibrium on the undeformed background mesh at the start of a load step. The formulation is implemented using a quasi-static implicit algorithm which includes the derivation of the consistent tangent to achieve optimum convergence of the global equilibrium iterations. The method is applied to a number of large deformation elasto-plastic problems, with a specific focus of the convergence of the method towards analytical solutions with the standard, generalised interpolation and CPDI2 material point methods. For the generalised interpolation method, different domain updating methods are investigated and it is shown that all of the current methods are degenerative under certain simple deformation fields. A new domain updating approach is proposed that overcomes these issues. The proposed material point method framework can be applied to all existing material point methods and adopted for implicit and explicit analysis, however its advantages are mainly associated with the former.

Descriptions

Resource type
Dataset
Contributors
Creator: Coombs, W.M. 1
Creator: Augarde, C.E. 1
Creator: Brennan, A.J. 2
Creator: Brown, M.J. 2
Creator: Charlton, T.J. 1
Creator: Knappett, J.A. 2
Creator: Ghaffari Motlagh, Y. 3
Creator: Wang, L. 1
1 Durham University, UK
2 University of Dundee, UK
3 University of Sheffield, UK
Funder
Engineering and Physical Sciences Research Council
Research methods
material point method
finite element method
Other description
Figure dataset for "On Lagrangian mechanics and the material point method for large deformation elasto-plasticity"
Keyword
material point method
Lagrangian mechanics
elasto-plasticity
finite deformation mechanics
Subject
Location
Language
Cited in
Identifier
ark:/32150/r2pk02c977f
doi:10.15128/r2pk02c977f
Rights
Creative Commons Attribution 4.0 International (CC BY)

Publisher
Durham University
Date Created
11/07/2019

File Details

Depositor
W.M. Coombs
Date Uploaded
Date Modified
3 September 2019, 15:09:18
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File format: zip (ZIP Format)
Mime type: application/zip
File size: 242983
Last modified: 2019:07:11 08:27:33+01:00
Filename: Data.zip
Original checksum: f62ffff54ef7a53f66e570d44e013045
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User N. Syrotiuk has updated On Lagrangian mechanics and the material point method for large deformation elasto-plasticity [dataset] about 5 years ago