Implicit Stress Integration of Highly Nonlinear Sand Models With Line Search Method and Complex‐Step Jacobian Evaluation

ABSTRACT Although bounding‐surface plasticity models have been extensively studied, robust fully implicit implementations for SANISAND‐type models, especially in boundary‐value analysis, remain limited because of severe nonlinearities and the difficulty of accurate Jacobian evaluation. To address these challenges, this study develops a robust fully implicit stress integration framework for highly nonlinear soil models by combining a line search‐enhanced Newton‐Raphson method (LSNRM) with a complex‐step differentiation method (CSDM), and demonstrates it through the implementation of the SANISAND‐04 model in ABAQUS/Standard. This constitutive model is well known for its ability to capture the complex behavior of sand, which involves strong nonlinearities stemming from state‐dependent dilatancy, kinematic hardening, fabric tensor effects, and stress reversals. The implementation is thoroughly evaluated in terms of correctness, accuracy, and quadratic convergence at both the Gauss point and global structural levels. Finally, the proposed framework is further validated through a benchmark simulation of strip footing bearing capacity, demonstrating its applicability to a representative nonlinear boundary‐value problem.