An exact implementation of the generalized Zhang-Zhu criterion for elasto-plastic finite element calculations

The generalized Zhang-Zhu (GZZ) strength criterion was proposed as an extension to the Hoek-Brown criterion and the Mogi criterion. The introduction to mean normal stress results in a non-smooth and non-convex yield surface, which presents a challenge for updating plastic stress. Current research primarily focuses on modified smooth GZZ criteria or approximate solutions, which inevitably lead to increased computational costs or inaccuracies. In this paper, an accurate stress updating algorithm is proposed based on the original GZZ criterion. The algorithm operates entirely in the principal stress space, where numerical singularities at the intersection of yield surfaces are avoided by defining four different types of stress updating. This approach simplifies the GZZ criterion compared to its formulation in general stress space. The return mapping is employed to compute the updated stress and consistent stiffness matrix, facilitating calculations using both finite element implicit and explicit algorithms. Finally, the accuracy of the proposed method is validated using rock true triaxial test data and semi-analytical solutions for stresses and displacement around a circular opening under the GZZ criterion.