Generalized Matsuoka–Nakai criterion considering hydrostatic pressure dependence in the brittle–ductile region

Abstract

A generalized Matsuoka–Nakai criterion is proposed in this study, taking the form of a polynomial function, incorporating two parameters to characterize the evolution of the failure envelope within the deviatoric plane. These two parameters exhibit an inverse correlation with both the aspect ratio and curvature. Besides, the first parameter $\alpha$ primarily affects the curvature around the triaxial compression state, while the second parameter $\beta$ predominantly influences the curvature around the triaxial extension state. Three sets of strength data under true triaxial stress states were selected to evaluate the generalized strength criterion. These sets include three types: hydrostatic pressure independent within the brittle region (HPI-B), hydrostatic pressure dependent within the brittle region (HPD-B), and hydrostatic pressure dependent within the brittle–ductile region (HPD-BD). In the case of HPI, the failure envelope within the deviatoric plane remains constant and is accurately described by two fixed deviatoric parameters. In contrast, for the HPD type, the shape of the failure envelope varies with hydrostatic pressure, and this variation is precisely captured using two deviatoric parameters. The experimental data are distributed around the edges of the three-dimensional failure envelope. Additionally, a comparison with existing criteria further validates the accuracy of the proposed criterion.