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

Ghaffari Motlagh, Y. (University of Sheffield, UK); Knappett, J.A. (University of Dundee, UK); Brennan, A.J. (University of Dundee, UK); Brown, M.J. (University of Dundee, UK); Charlton, T.J. (Durham University, UK); Augarde, C.E. (Durham University, UK); Coombs, W.M. (Durham University, UK); Wang, L. (Durham University, UK)

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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
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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

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Depositor: W.M. Coombs
Date Uploaded: 11 July 2019, 07:07:30
Date Modified: 3 September 2019, 15:09:18
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Last modified: 2019:07:11 08:27:33+01:00

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