A Runge–Kutta Enhancement Strategy Based on the Return Mapping Method

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.