Implicit MPM with second-order convected particle domain interpolation

Wang, L.; Coombs, W.M.; Augarde, C.E.; Brown, M.

Abstract

An implicit material point method (MPM) with the second-order convected particle interpolation (CPDI2) is presented in this paper. In the MPM a body is described by a number of Lagrangian material points, at which state variables are stored and tracked. Calculations are then carried out on a background Eulerian computational mesh. A mapping and re-mapping algorithm is employed, to allow the state variables and other information to be mapped back and forth between the material points and background mesh nodes during an analysis. To reduce the error during these mappings, there are several extensions. The latest extension is termed CPDI2, which uses a quadrilateral particle domain to replace a material point. The CPDI2 extension has been implemented explicitly with using regular grids in published papers. This work develops an implicit CPDI2 method with an elasto-plastic material model. The motivation is that an implicit scheme can reduce the computational cost by allowing a large time step, while enforcing the yield condition accurately and increase stability. Both quadrilateral and triangular particle domains are used. An example shows that the use of a triangular particle domain is more flexible than the quadrilateral particle domain.

Citation

Wang, L., Coombs, W., Augarde, C., & Brown, M. (2017, April). Implicit MPM with second-order convected particle domain interpolation. Presented at 25th Conference on Computational Mechanics UKACM 2017., Birmingham, UK

• Presentation Conference Type: Conference Paper (published)
• Conference Name: 25th Conference on Computational Mechanics UKACM 2017.
• Start Date: Apr 11, 2017
• End Date: Apr 13, 2017
• Publication Date: Apr 13, 2017
• Deposit Date: Jun 7, 2017
• Publicly Available Date: Nov 22, 2024
• Publisher: University of Birmingham
• Pages: 264-267
• Book Title: Proceedings of the 25th Conference on Computational Mechanics (UKACM 2017) : 11th – 13th April 2017, School of Engineering, University of Birmingham, Birmingham, UK.
• Public URL: https://durham-repository.worktribe.com/output/1147091
• Publisher URL: http://ukacm2017.ukacm.org/wp-content/uploads/2017/04/Proceedings-UKACM2017-compressed.pdf