Application of Conjugate Gradient Method in Numerical Implementation of Elasto-plastic Model

Abstract:

Based on the singularity and non-convergence characteristics of the Jacobian matrix， the composition and the algorithm of the elasto-plastic constitutive model were comprehensively analyzed. The problem of solving the highly nonlinear equations in Newton-closest point projection method（Newton-CPPM） implicit algorithm was transformed into a seeking minimum value problem by the conjugate gradient method， and the improvement of traditional implicit method was eventually accomplished. Finally， according to the calculations of single unit， the Saniclay model considering the structural properties of soft soils was set as an example， which is involved in different strain paths and initial stress states. In this process， the calculation convergence， the accuracy and the efficiency between traditional implicit algorithm and improved implicit algorithm were separately compared. In addition， the differences between traditional and improved implicit algorithm were examined by engineering example. Results show that， compared with the traditional implicit algorithm， the improved implicit algorithm can effectively improve the computational efficiency and convergence.