An unconstrained stress updating algorithm with the line search method for elastoplastic soil models

Abstract

This paper is devoted to developing an efficient and robust stress updating algorithm in a relatively simple computational framework to address the two difficulties of implementing elastoplastic soil models, namely the nonsmoothness and the nonlinearity. In the proposed algorithm, the nonsmoothness caused by the loading/unloading inequality constraints is eliminated by replacing the Karush-Kuhn-Tucker conditions with the smoothing function. The stress updating can be achieved by solving a set of smooth nonlinear algebraic equations in this algorithm. The nonlinear equations are solved using the line search method, which allows a larger convergence radius of the solution in contrast to the standard Newton method. Meanwhile, the smoothing consistent tangent operator corresponding to the unconstrained stress updating strategy ensures the quadratic convergence speed of the global solution. The modified Cam-clay model is used as an example to demonstrate the implementation of this algorithm. The correctness, computational efficiency, and robustness of the algorithm are validated and assessed by comparing it with the analytical solutions in case of cylindrical cavity expansion and the ABAQUS/Standard default integration method. In simulations with large load increment sizes, the CPU time consumed by the new algorithm can be less than half of the ABAQUS default algorithm.