Three fundamentally different failure theories for homogeneous and isotropic materials are examined in both the ductile and brittle ranges of behavior. All three theories are calibrated by just two independent failure properties. These three are the Coulomb-Mohr form, the Drucker-Prager form, and a recently derived theory involving a quadratic representation along with a fracture restriction. The three theories are given a detailed comparison and evaluation. The Coulomb-Mohr form and the Drucker-Prager form are found to predict physically unrealistic behavior in some important cases. The present form meets the consistency requirements.

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