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
- Physics and Astronomy(all)
- 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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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 AccessFile13 Citations (Scopus)274 Downloads (Pure) -
A cone penetration test (CPT) approach to cable plough performance prediction based upon centrifuge model testing
Robinson, S., Brown, M., Matsui, H., Brennan, A., Augarde, C., Coombs, W. M. & Cortis, M., Oct 2021, In: Canadian Geotechnical Journal. 58, 10, p. 1466-1477 12 p.Research output: Contribution to journal › Article › peer-review
Open AccessFile1 Citation (Scopus)191 Downloads (Pure) -
A Finite Element approach for determining the full load-displacement relationship of axially-loaded shallow screw anchors, incorporating installation effects
Cerfontaine, B., Knappett, J., Brown, M., Davidson, C., Al-Baghdadi, T., Sharif, Y., Brennan, A., Augarde, C., Coombs, W. M., Wang, L., Blake, A., Richards, D. J. & Ball, J. D., Apr 2021, In: Canadian Geotechnical Journal. 58, 4, p. 565-582 18 p.Research output: Contribution to journal › Article › peer-review
Open AccessFile16 Citations (Scopus)259 Downloads (Pure)
Student theses
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Screw piles as offshore foundations : Numerical and physical modelling
Author: Al-Baghdadi, T., 2018Supervisor: Brown, M. (Supervisor) & Knappett, J. (Supervisor)
Student thesis: Doctoral Thesis › Doctor of Philosophy
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Activities
- 1 Invited talk
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Invited speaker, NGI, Norway: Virtual laboratory testing and its applications within offshore wind industry
Michael Brown (Speaker)
22 Sept 2022 → 23 Sept 2022Activity: Talk or presentation types › Invited talk