We use cookies to ensure that we give you the best experience on our website. By continuing to browse this repository, you give consent for essential cookies to be used. You can read more about our Privacy and Cookie Policy.

Durham Research Online
You are in:

B-spline based boundary conditions in the material point method.

Bing, Y. and Cortis, M. and Charlton, T. J. and Coombs, W. M. and Augarde, C. E. (2019) 'B-spline based boundary conditions in the material point method.', Computers and structures., 212 . pp. 257-274.


The material point method is an increasingly popular method for tackling solid mechanics problems involving large deformations. However, there are issues associated with applying boundary conditions in the method and, to date, no general approach for imposing both Neumann and Dirichlet boundary conditions has been proposed. In this paper, a new B-spline based boundary method is developed as a complete methodology for boundary representation, boundary tracking and boundary condition imposition in the standard material point method. The B-spline interpolation technique is employed to form continuous boundaries which are independent of the background mesh. Dirichlet boundary conditions are enforced by combining the B-spline boundaries with an implicit boundary method. Neumann boundary conditions are included by direct integration of surface tractions along the B-spline boundary. This general boundary method not only widens the problems that can be analysed by all variants of the material point method, when implemented using an implicit solver, but is also applicable to other embedded and non-matching mesh approaches. Although the Dirichlet boundary conditions are restricted to implicit methods, boundary representation, tracking and Neumann boundary condition enforcement can be applied to explicit and implicit methods.

Item Type:Article
Additional Information:Figure data available here:
Full text:Publisher-imposed embargo
(AM) Accepted Manuscript
File format - PDF
Full text:(VoR) Version of Record
Available under License - Creative Commons Attribution.
Download PDF
Publisher Web site:
Publisher statement:© 2018 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (
Date accepted:10 November 2018
Date deposited:12 November 2018
Date of first online publication:20 November 2018
Date first made open access:No date available

Save or Share this output

Look up in GoogleScholar