Novel Consistent Tangent Operator for Runge–Kutta‐Based Explicit Stress Integration for Elasto‐Plastic Models: Application to the Modified Cam Clay Model

Abstract

Explicit stress integration techniques for elasto‐plastic constitutive models have demonstrated high‐order accuracy, efficiency, and robustness. However, there is a notable absence of a proposed expression for the consistent tangent operator, which is essential to guarantee the quadratic convergence of the Newton–Raphson algorithm used in solving the global problem. Therefore, when employing explicit stress integration, the typical convergence rate of the global problem is linear. In this work, we introduce a novel expression for the consistent tangent operator specifically formulated for Runge–Kutta‐based explicit stress integration techniques. The Gauss point integration algorithm involves substepping, finding the intersection of the stress path with the yield surface, and implementing a yield surface drift correction algorithm. All of these numerical procedures are linearised and integrated into the expression of the consistent tangent matrix. The assessment of the consistent tangent matrix expression is conducted through a various element tests and finite element simulations using the Modified Cam Clay model. In all the simulations, a quadratic rate of asymptotic convergence is consistently achieved with the iterative solver used in the global problem. The proposed consistent tangent operator significantly enhances the computational efficiency of explicit stress integration techniques, positioning them as a viable, high‐order alternative to implicit stress integration.