Error behaviour in explicit integration algorithms with automatic substepping

Lloret-Cabot, Martí; Sloan, Scott W.; Sheng, Daichao; Abbo, Andrew J.

Abstract

This paper studies the behaviour of the error incurred when numerically integrating the elasto‐plastic mechanical relationships of a constitutive model for soils using an explicit substepping formulation with automatic error control. The correct update of all the variables involved in the numerical integration of the incremental stress–strain relationships is central to the computational performance of the integration scheme, and, although often missed in the literature, all variables (including specific volume) should be explicitly considered in the algorithmic formulation. This is demonstrated in the paper by studying, in the context of the Cam clay formulations for saturated soils, the influence that the updating of the specific volume has on the accuracy of the numerical solution. The fact that the variation of the local error with the size of the integrated strain depends on the order of local accuracy of the numerical method is also used in the paper to propose a simple and powerful strategy to verify the correctness of the implemented mathematical formulation.

Citation

Lloret-Cabot, M., Sloan, S. W., Sheng, D., & Abbo, A. J. (2016). Error behaviour in explicit integration algorithms with automatic substepping. International Journal for Numerical Methods in Engineering, 108(9), 1030-1053. https://doi.org/10.1002/nme.5245

• Journal Article Type: Article
• Acceptance Date: Feb 21, 2016
• Online Publication Date: May 27, 2016
• Publication Date: 2016
• Deposit Date: Oct 2, 2018
• Publicly Available Date: Nov 21, 2018
• Journal: International Journal for Numerical Methods in Engineering
• Print ISSN: 0029-5981
• Electronic ISSN: 1097-0207
• Publisher: Wiley
• Peer Reviewed: Peer Reviewed
• Volume: 108
• Issue: 9
• Pages: 1030-1053
• DOI: https://doi.org/10.1002/nme.5245
• Public URL: https://durham-repository.worktribe.com/output/1317822