An open-source unconstrained stress updating algorithm for the modified Cam-clay model

Abstract

This paper presents an unconstrained stress updating algorithm for a critical state plastic model of clay soil, where the loading/unloading estimations and the consideration of the stress behaviour transition from elasticity to plasticity can be bypassed by using the Fischer–Burmeister smoothing function instead of the Kuhn–Tucker complementarity conditions. A smoothing tangent operator consistent with the unconstrained stress updating strategy is derived from preserving the quadratic convergence speed for the global solution. Specifically, the relationship and difference between the consistent and continuum tangent operators are analysed from the perspectives of algebra and geometry. In addition, the nonlinear constitutive equations obtained by the backward Euler integration scheme are solved by the double dogleg trust region method (improved by non-monotonic technology), where a larger strain increment than that of the newton method is allowed for the stress updating. Then, the modified Cam-clay model for soil is implemented in ABAQUS/Standard by the proposed algorithm. The results of numerical examples show that the algorithm has significant advantages in terms of computation efficiency and robustness in contrast to the ABAQUS/Standard default integration algorithm, especially for the condition of large load increments and cyclic loadings. More than twice the computational efficiency of the ABAQUS/Standard default integration algorithm can be observed in the representative numerical examples. The source code of the proposed algorithm is freely available at https://github.com/zhouxin615/NMTR_Method.