A failure criterion for isotropic materials based on Mohr's failure plane theory

A failure criterion for isotropic materials is developed in the present study. The fundamental hypotheses of the Mohr-Coulomb criterion are re-examined and re-evaluated. The failure function of Mohr's envelope is firstly expanded into a polynomial in terms of the stress components (σn, τn) on the failure plane, then truncated at the second order due to the fine curve-fitting results of quadratic functions with experimental data. The parameters of the nonlinear failure functions are calibrated by the three basic mechanical properties-the uniaxial tensile and compressive strengths, T and C, as well as the pure shear strength, S. Theoretical and experimental evaluation for various isotropic materials demonstrates that the present failure criterion provides no worse results for ductile materials and far better results for brittle materials compared with the linear Mohr-Coulomb criterion. The strength theory shows good agreement with physical reality and has a wide range of applicability.