Numerical implementation of the elastoplastic constitutive model based on the improved smoothed GZZ criterion into ABAQUS

The Smoothed Zhang-Zhu(GZZ) criterion is a three-dimensional strength criterion for rocks proposed in recent years，which can reasonably and reliably describe the nonlinear strength characteristics of rock materials. However，only a few finite element software are equipped with this criterion，and most of the existing constitutive model programs based on the GZZ criterion are carried out in the principal stress space，making it difficult to apply in ABAQUS. In addition，the current numerical simulations based on the Smoothed GZZ criterion often use the associated ideal elastoplastic model，ignoring the plastic deformation characteristics and strength nonlinearity of rocks. In this paper，the plastic potential function of the Smoothed GZZ criterion is improved，and a numerical implementation method of the constitutive model based on the Smoothed GZZ criterion in the general stress space is proposed to avoid the problem of principal stress transformation. Meanwhile，a calculation method considering the dilation characteristics and strength variation of rocks is given. Finally，the calculation of this constitutive model is implemented by writing a UMAT subroutine in ABAQUS. Verified by three calculation examples，this model can directly conduct calculations in the general stress space，can reflect the dilation characteristics and strength nonlinearity of rocks，and the numerical solutions are in good agreement with the analytical solutions and the results of model tests，showing a relatively high calculation accuracy.