Imposition of essential boundary conditions in the material point method (figure data)

Cortis, Michael (Durham University, UK); Brennan, Andrews (Dundee University, UK); Augarde, Charles (Durham University, UK); Robinson, Scott (Dundee University, UK); Coombs, William (Durham University, UK); Brown, Michael (Dundee University, UK)

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Imposition of essential boundary conditions in the material point method (figure data) Open Access

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, to the MPM, expanding its capabilities to 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 non-zero 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: (i) the boundaries are independent of the background mesh, (ii) artificially stiff regions of material points are avoided and (iii) the method does not rely on spurious mirroring of the problem domain to imposed symmetry. The main contribution of this work is equally applicable to standard finite elements and the MPM.

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Resource type: Dataset
Contributors: Creator: Cortis, Michael ¹
Contact person: Cortis, Michael ¹
Data collector: Cortis, Michael ¹
Data curator: Cortis, Michael ¹
Creator: Augarde, Charles ¹
Creator: Coombs, William ¹
Creator: Robinson, Scott ²
Creator: Brennan, Andrews ²
Creator: Brown, Michael ²

¹ Durham University, UK
² Dundee University, UK
Funder: Engineering and Physical Sciences Research Council
Research methods: Material Point Method
Implicit Boundary Method
Other description
Keyword: material point method
embedded boundaries
non-matching meshes
Subject
Location
Language
Cited in: https://doi.org/10.1002/nme.5606
Identifier: ark:/32150/r1h415p9531
doi:10.15128/r1h415p9531
Rights: Open Data Commons - Open Database (ODC-ODbL)
Publisher: Durham University
Date Created

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Depositor: M. Cortis
Date Uploaded: 22 June 2017, 19:06:27
Date Modified: 23 June 2017, 10:06:17
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User M. Cortis has updated Imposition of essential boundary conditions in the material point method (figure data).zip	almost 7 years ago
User M. Cortis has updated Imposition of essential boundary conditions in the material point method (figure data).zip	almost 7 years ago
User M. Cortis has updated Imposition of essential boundary conditions in the material point method (figure data).zip	almost 7 years ago