A Newton-Krylov-based implicit integration algorithm for single and multisurface plasticity

Robust integration schemes for plasticity models allow accurate and efficient numerical simulations of materials such as metals, concrete, soils, and rocks. The Newton-Raphson method is a popular choice for solving systems of nonlinear equations in the context of plasticity problems. However, this method requires calculating the Jacobian matrix of the system of equations defined by the flow rule, the hardening/softening law, and the Karush-Kuhn-Tucker conditions. This task can be cumbersome, especially for complex and multisurface plasticity models. Therefore, this work proposes a novel numerical implicit integration scheme for multisurface plasticity based on a Jacobian-free Newton-Krylov method. Notably, the Karush-Kuhn-Tucker conditions are implemented based on well-established smooth complementary functions to consider multiple yield surfaces properly. The proposed algorithm is vastly versatile since it can be easily applied to diverse single and multisurface models under different stress conditions, including the plane stress condition. The computational efficiency of the proposed method is compared to other common integration schemes, focusing on evaluating different smooth complementary functions. The results highlight the effectiveness of the Jacobian-free Newton-Krylov method for integrating multisurface plasticity equations and its ability to handle challenging finite element problems.