Error behaviour in explicit integration algorithms with automatic substepping

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

doi:10.1002/nme.5245

Error behaviour in explicit integration algorithms with automatic substepping

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

Authors

Dr Marti Lloret-Cabot marti.lloret-cabot@durham.ac.uk
Associate Professor

Scott W. Sloan

Daichao Sheng

Andrew J. Abbo

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	May 27, 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

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Copyright Statement
This is the accepted version of the following article: Lloret-Cabot, Martí, Sloan, Scott W., Sheng, Daichao & Abbo, Andrew J. (2016). Error behaviour in explicit integration algorithms with automatic substepping. International Journal for Numerical Methods in Engineering 108(9): 1030-1053 which has been published in final form at https://doi.org/10.1002/nme.5245. This article may be used for non-commercial purposes in accordance With Wiley Terms and Conditions for self-archiving.