Numerical performance of different order explicit integration schemes with substepping and automatic error control

Lloret-Cabot, M; Sheng, D

Abstract

The numerical integration of the incremental stress-strain relations of a constitutive model for soils plays a central role in the overall computational performance of geotechnical finite element analyses and it is, therefore, desirable to have an efficient integration scheme that ensures accurate solutions with a reasonable computational effort. Substepping integration schemes with automatic error control are precisely aimed at providing such numerical efficiency. Against this background, this paper discusses the numerical performance of low and high order accurate explicit substepping and implicit integration schemes when integrating, numerically, the constitutive relations of the Modified Cam Clay (MCC) for typical stress paths. The discussion is presented in the context of the performance maps which are useful and simple verification tools to check that the algorithm performs as expected at a single integration as well as when the substepping is active and, in addition, provide information about the appropriate value of the tolerance to be used in the substepping scheme (STOL) to reach a prescribed level of accuracy, while also anticipating the associated approximate computational cost.

Citation

Lloret-Cabot, M., & Sheng, D. (2023, June). Numerical performance of different order explicit integration schemes with substepping and automatic error control. Presented at 10th European Conference on Numerical Methods in Geotechnical Engineering, London

• Presentation Conference Type: Edited Proceedings
• Conference Name: 10th European Conference on Numerical Methods in Geotechnical Engineering
• Start Date: Jun 26, 2023
• End Date: Jun 28, 2023
• Acceptance Date: Apr 13, 2023
• Online Publication Date: Aug 1, 2023
• Publication Date: 2023
• Deposit Date: Oct 2, 2024
• Peer Reviewed: Peer Reviewed
• Keywords: Integration schemes; Explicit; Substepping; automatic error control
• Public URL: https://durham-repository.worktribe.com/output/2941966