Imposition of essential boundary conditions in the material point method

By M. Cortis, William M. Coombs, Charles E. Augarde, Michael Brown, A. Brennan, S. Robinson. 2018

70 citations recorded by the source corpus.

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.

Subfields: Computational Mechanics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/68aff02d1f3f0da724cabd924ecc1972cd000055

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In Computational Mechanics

1. M. Cortis
2. Y. Bing
3. William M. Coombs
4. T. J. Charlton
5. Charles E. Augarde

In Mechanics of Materials

1. M. Cortis
2. Y. Bing
3. William M. Coombs
4. T. J. Charlton
5. Charles E. Augarde
6. Xiaoying Zhuang
7. Hong Zheng

Citations in the corpus

• B-spline based boundary conditions in the material point method (2019, methodology): “The outer layer of the material points were identified as the problem boundaries which were approximated using B-splines. boundary conditions on the left boundary ware applied by the B-spline based IBM and the pressure applied through 5 equal load steps.”