A parameterized three-dimensional strength criterion within brittle-ductile domain is proposed in this study. The criterion employs a power function to capture the positive correlation and an elliptic function to capture the negative correlation between deviatoric stress and hydrostatic stress. In addition, a unified deviatoric function framework is developed, enabling smooth transitions between any two deviatoric functions that satisfy the requirements of aspect ratio, curvature, and smoothness. The parameters within deviatoric function are expressed as functions of hydrostatic stress. To validate the proposed strength criterion, three sets of experimental data within the brittle-ductile domain are employed, namely Bentheim sandstone, green sandstone, and Sorcy limestone. The characteristics of three-dimensional failure envelope are analyzed in both meridian and deviatoric planes. At initial yield stage, the deviatoric stress exhibits a negative correlation with Lode angle, while the aspect ratio and curvature of deviatoric plane increase with hydrostatic stress. In contrast, the behavior during compactive yield cap stage follows an opposite trend. Furthermore, the three-dimensional failure envelope is examined in principal stress space to analyze the relationships among the principal stresses. A non-monotonic relationship is observed between the maximum and intermediate principal stresses, resulting from the combined influence of hydrostatic stress and Lode angle on deviatoric stress. • A deviatoric function framework that satisfies the requirements of smoothness, aspect ratio, and convexity requirements is proposed. • A novel parameterization method is developed to derive the analytical expression of three-dimensional strength criterion. • Three sets of strength data within brittle-ductile domain are used to validate the analytical solution of strength criterion. • The relationship between principal stresses on the three-dimensional failure envelope within brittle-ductile domain is discussed.
Liu et al. (Sun,) studied this question.