Projects per year
Abstract
There is increasing interest in the material point method (MPM) as a means of modelling solid mechanics problems in which very large deformations occur, e.g. in the study of landslides and metal forming; however, some aspects vital to wider use of the method have to date been ignored, in particular methods for imposing essential boundary conditions in the case where the problem domain boundary does not coincide with the background grid element edges. In this paper, we develop a simple procedure originally devised for standard finite elements for the imposition of essential boundary conditions, for the MPM, expanding its capabilities to model boundaries of any inclination. To the authors' knowledge, this is the first time that a method has been proposed that allows arbitrary Dirichlet boundary conditions (zero and nonzero values at any inclination) to be imposed in the MPM. The method presented in this paper is different from other MPM boundary approximation approaches, in that (1) the boundaries are independent of the background mesh, (2) artificially stiff regions of material points are avoided, and (3) the method does not rely on mirroring of the problem domain to impose symmetry. The main contribution of this work is equally applicable to standard finite elements and the MPM.
Original language | English |
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Pages (from-to) | 130-152 |
Number of pages | 23 |
Journal | International Journal for Numerical Methods in Engineering |
Volume | 113 |
Issue number | 1 |
Early online date | 21 Jun 2017 |
DOIs | |
Publication status | Published - 6 Jan 2018 |
Keywords
- embedded boundaries
- material point method
- nonmatching meshes
ASJC Scopus subject areas
- Numerical Analysis
- General Engineering
- Applied Mathematics
Fingerprint
Dive into the research topics of 'Imposition of essential boundary conditions in the material point method'. Together they form a unique fingerprint.Projects
- 1 Finished
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Seabed Ploughing: Modelling for Infrastructure Installation (Joint with Durham University)
Brennan, A. (Investigator) & Brown, M. (Investigator)
Engineering and Physical Sciences Research Council
1/10/14 → 31/12/17
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 AccessFile1 Citation (Scopus)71 Downloads (Pure) -
An efficient and locking-free material point method for three dimensional analysis with simplex elements
Wang, L., Coombs, W. M. (Lead / Corresponding author), Augarde, C., Cortis, M., Brown, M. J., Brennan, A. J., Knappett, J. A., Davidson, C., Richards, D., White, D. J. & Blake, A. P., 15 Aug 2021, In: International Journal for Numerical Methods in Engineering. 122, 15, p. 3876-3899 24 p.Research output: Contribution to journal › Article › peer-review
Open Access14 Citations (Scopus) -
On Lagrangian mechanics and the implicit material point method for large deformation elasto-plasticity
Coombs, W. M. (Lead / Corresponding author), Augarde, C., Brown, M., Brennan, A., Charlton, T., Knappett, J., Motlagh, Y. & Wang, L., 1 Jan 2020, In: Computer Methods in Applied Mechanics and Engineering. 358, p. 1-32 32 p., 112622.Research output: Contribution to journal › Article › peer-review
Open AccessFile45 Citations (Scopus)435 Downloads (Pure)
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DeepOcean, UK lunch and learn session, Physical modelling of seabed ploughing for cable and pipeline installation
Brown, M. (Invited speaker)
14 Dec 2018Activity: Talk or presentation types › Invited talk
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Hidetake Matsui
Brown, M. (Host)
1 Mar 2017 → 30 Mar 2018Activity: Hosting a visitor types › Hosting an academic visitor