Currently

locally non-differential piecewise functions

the explicit forward Euler method (EFEM)

and the Newton-Raphson iteration method (NRIM) are commonly adopted plastic yield criterions for implicit finite element solution. However

the EFEM will cause stress deviation from the yield surface and lead to non-convergent result

and the NRIM needs to frequently calculate derivative of yield criterion. They are both inconvenient for non-differential functions. A method combining the semi-implicit backward Euler method and the Steffensen iterative method is proposed for these piecewise yield criterions to update stress and consistent tangent modulus. The combination method is applied to write code in ANSYS’s UserMat module for an elastic-perfect plastic constitutive model

based on a composite unified strength criterion with unified strength theory and tension cut-off. Then the custom constitutive model is applied to simulate excavation process of a deep circular tunnel

and the numerical simulation results fit well with the theoretical solutions

which verifies the correctness and practicability of the model and the combination method. The combination method can prevent stress deviation from the yield surface and does not need to solve partial derivatives of the plastic flow function. It is simple and easy for popularization and application.