When using an implicit numerical integration algorithm to implement a highly nonlinear elasto-plastic constitutive models in FEM simulations, some difficulties would encounter including Jacobian matrix singularity and non-convergence. Based on the composition of the elastoplastic constitutive model and the characteristics of the traditional implicit algorithms, this paper proposes three improved implicit algorithms, namely the Homotopy-Newton-CPPM algorithm, the CG-Newton-CPPM algorithm and the two-stage algorithm, which would contribute to improve the convergence and deal with singularity of the Jacobian matrix. Besides, the convergence and the computational efficiency as well as the accuracy of five algorithms, including a conventional explicit algorithm, a conventional implicit algorithm and three improved implicit algorithms, are compared with reference to numerical simulations of single element tests and multi-element analysis.

当在FEM仿真中使用隐式数值积分算法来实现高度非线性的弹塑性本构模型时，会遇到一些困难，包括雅可比矩阵奇异性和不收敛性。根据弹塑性本构模型的组成和传统隐式算法的特点，提出了三种改进的隐式算法，分别是同伦-牛顿-CPPM算法，CG-牛顿-CPPM算法和两阶段算法。将有助于改善收敛性并处理雅可比矩阵的奇异性。此外，包括常规显式算法，常规隐式算法和三种改进的隐式算法在内的五种算法的收敛性，计算效率以及准确性，