Semi-implicit numerical integration of a highly nonlinear elasto-plastic constitutive model

When implementing a highly nonlinear stress-strain model to solve boundary-valued problems, one of the major challenges is how to reduce the accumulative error and to maintain the effectiveness of the numerical integration. In general, the explicit algorithm tends to have higher accumulative error, and the requirement for accuracy may not be satisfied even when adopting very small increment sizes. When utilizing the Newton-CPPM implicit numerical integration algorithm, the complex Jacobian matrix for a highly nonlinear model may result in non-convergence or even become singular in the modelling process. In order to deal with these challenges, this paper proposes an improved-implicit algorithm, in which a semi-implicit method is used to determine the initial values for the implicit iterations. Using the highly nonlinear SANICLAY model for structured clay as an example, the convergence, the computational efficiency and the accuracy of four algorithms, namely the explicit algorithm, the semi-implicit algorithm, the implicit algorithm and the improved implicit algorithm, are compared via numerical simulations of single element tests. Comparing with the explicit algorithm, the semi-implicit algorithm effectively reduces error accumulation and improves the computation accuracy. The improved implicit algorithm can effectively improve convergence and avoid singularity of Jacobian matrix.