A Runge–Kutta Enhancement Strategy Based on the Return Mapping Method
- 1POWERCHINA Chengdu Engineering Corporation Limited, Chengdu 610072, China
- 2State Key Laboratory of Hydroscience and Engineering, Department of Hydraulic Engineering, Tsinghua University, Beijing 100084, China
Abstract
Accurate stress integration at large strain increments requires control of both trajectory error and yield-surface drift. This study presents RK-RM, a hybrid strategy combining explicit Runge–Kutta integration with cutting-plane return mapping. A forward–backward calculation constructs complementary internal variables, which are combined with the forward stress to initialize the correction. The method is examined with the Modified Cam-Clay and Unified Hardening (UH) models in material-point tests, triaxial simulations, and a foundation loading example. The UH triaxial comparisons show smaller deviatoric-stress errors than the tested closest point projection (CPPM) implementation, while additional undrained material-point comparisons show lower local constitutive cost. Accuracy depends on the loading path, step size, and correction strategy. The results support RK-RM as a practical stress-integration option for the constitutive models and loading conditions considered.
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BibTeX
@article{dou2026rungekutta,
title = {{A Runge–Kutta Enhancement Strategy Based on the Return Mapping Method}},
author = {Xiangxian Dou and Li Wan and Jinlong Xie and Qianhui Liu and Yuzhen Yu},
journal = {Mathematics},
year = {2026},
month = oct,
doi = {10.3390/math14203831},
url = {https://www.mdpi.com/2227-7390/14/20/3831},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - A Runge–Kutta Enhancement Strategy Based on the Return Mapping Method
AU - Xiangxian Dou
AU - Li Wan
AU - Jinlong Xie
AU - Qianhui Liu
AU - Yuzhen Yu
PY - 2026
DA - 2026/10/21
JO - Mathematics
DO - 10.3390/math14203831
UR - https://www.mdpi.com/2227-7390/14/20/3831
AB - Accurate stress integration at large strain increments requires control of both trajectory error and yield-surface drift. This study presents RK-RM, a hybrid strategy combining explicit Runge–Kutta integration with cutting-plane return mapping. A forward–backward calculation constructs complementary internal variables, which are combined with the forward stress to initialize the correction. The method is examined with the Modified Cam-Clay and Unified Hardening (UH) models in material-point tests, triaxial simulations, and a foundation loading example. The UH triaxial comparisons show smaller deviatoric-stress errors than the tested closest point projection (CPPM) implementation, while additional undrained material-point comparisons show lower local constitutive cost. Accuracy depends on the loading path, step size, and correction strategy. The results support RK-RM as a practical stress-integration option for the constitutive models and loading conditions considered.
SN - 2227-7390
ER -