This note discusses some basic concepts underlying isotropic material failure criteria under multiaxial loadings. It also describes the shapes and features of the associated failure surfaces in three-dimensional stress space. Failure criteria for ductile materials are first reviewed. They are then generalized so that they may also be applied to brittle materials. The relationships among the various failure criteria, the shapes and characteristics of the associated failure surfaces, and the special features of physically acceptable isotropic failure criteria are then considered.
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