Projects per year
Abstract
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 of 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 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.
Original language | English |
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Article number | 112622 |
Pages (from-to) | 1-32 |
Number of pages | 32 |
Journal | Computer Methods in Applied Mechanics and Engineering |
Volume | 358 |
Early online date | 28 Sept 2019 |
DOIs | |
Publication status | Published - 1 Jan 2020 |
Keywords
- Elasto-plasticity
- Finite deformation mechanics
- Generalised interpolation
- Lagrangian mechanics
- Material point method
ASJC Scopus subject areas
- Computational Mechanics
- Mechanics of Materials
- Mechanical Engineering
- General Physics and Astronomy
- Computer Science Applications
Fingerprint
Dive into the research topics of 'On Lagrangian mechanics and the implicit material point method for large deformation elasto-plasticity'. Together they form a unique fingerprint.Projects
- 1 Finished
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Supergen Wind Challenge 2015: Screw Piles for Wind Energy Foundation Systems (Joint with Universities of Durham and Southampton)
Brennan, A. (Investigator), Brown, M. (Investigator) & Knappett, J. (Investigator)
Engineering and Physical Sciences Research Council
26/02/16 → 25/07/19
Project: Research
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An implicit material point-to-rigid body contact approach for large deformation soil-structure interaction
Bird, R. E., Pretti, G., Coombs, W. M., Augarde, C., Sharif, Y., Brown, M., Carter, G., Macdonald, C. & Johnson, K., Oct 2024, In: Computers and Geotechnics. 174, 16 p., 106646.Research output: Contribution to journal › Article › peer-review
Open AccessFile2 Citations (Scopus)94 Downloads (Pure) -
Cone Penetration Tests (CPTs) in layered soils: a Material Point approach
Bird, R., Coombs, W. M., Augarde, C., Brown, M., Sharif, Y., Carter, G., Johnson, K. & Macdonald, C., 2023. 6 p.Research output: Contribution to conference › Paper › peer-review
Open AccessFile150 Downloads (Pure) -
Physical modelling to demonstrate the feasibility of screw piles for offshore jacket supported wind energy structures
Davidson, C., Brown, M., Cerfontaine, B., Knappett, J., Brennan, A., Al-Baghdadi, T., Augarde, C., Coombs, W. M., Wang, L., Blake, A., Richards, D. & Ball, J. D., Feb 2022, In: Geotechnique. 72, 2, p. 108-126 19 p.Research output: Contribution to journal › Article › peer-review
Open AccessFile40 Citations (Scopus)501 Downloads (Pure)
Student theses
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Screw piles as offshore foundations : Numerical and physical modelling
Al-Baghdadi, T. (Author), Brown, M. (Supervisor) & Knappett, J. (Supervisor), 2018Student thesis: Doctoral Thesis › Doctor of Philosophy
File
Activities
- 1 Invited talk
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Invited speaker, NGI, Norway: Virtual laboratory testing and its applications within offshore wind industry
Brown, M. (Speaker)
22 Sept 2022 → 23 Sept 2022Activity: Talk or presentation types › Invited talk
Datasets
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On Lagrangian mechanics and the material point method for large deformation elasto-plasticity [dataset]
Coombs, W. M. (Creator), Augarde, C. E. (Creator), Brennan, A. J. (Creator), Brown, M. (Creator), Charlton, T. J. (Creator), Knappett, J. A. (Creator), Ghaffari Motlagh, Y. (Creator), Wang, L. (Creator), University, D. (Contributor), University, D. (Contributor) & Council, E. A. P. S. R. (Contributor), Durham University, 2019
DOI: 10.15128/r2pk02c977f, http://collections.durham.ac.uk/files/r2pk02c977f
Dataset