Implicit numerical integration of an elasto-plastic constitutive model for structured clays

Compared with the general constitutive models, the highly nonlinear elasto-plastic constitutive models for structured clays are more complex, which leads to the problems of Jacobian matrix singularity and nonconvergence more easily when the implicit algorithm of Newton-CPPM is used for the numerical implementation. To solve the problems, two implicit algorithms are proposed in this paper. Considering the Newton-CPPM implicit algorithm is a local convergence algorithm, the homotopy continuation algorithm of global convergence is introduced to improve the iterative initial value of the Newton-CPPM algorithm, so the method can be called as homotopy-Newton-CPPM algorithm. Considering that the calculation of every iteration for the Newton-CPPM implicit algorithm is too large, a two-stage iterative algorithm based on the idea of the fully explicit algorithm is presented. The consistency parameter is calculated in the first-stage, taking the consistency parameter as a known quantity and the algorithm similar to the explicit algorithm is used to solve the values of state variables in the second-stage. Then, taking the SANICLAY model that including destructuration as an example, from the two aspects of the composition of the elasto-plastic constitutive model and the characteristics of the algorithm, the reasons for Jacobian matrix singularity and nonconvergence are analyzed. The convergence, accuracy and cost of four algorithms, including the explicit algorithm, traditional implicit algorithm and two kinds of improved implicit algorithms, are compared with reference to the numerical simulations of single element tests. Finally, the homotopy-Newton-CPPM algorithm and the traditional implicit algorithm are applied to the multielement calculation of subgrade bearing capacity. The results show that the homotopy-Newton-CPPM algorithm can effectively improve convergence and avoid singularity of Jacobian matrix compared with the traditional implicit algorithm.