On the equivalence of stress- and strain-based failure criteria in Elastic Media *

Conditions for which strain-based and stress-based failure criteria are mathematically equivalent in elastic media are explored by expressing the criteria in the spectral eigenspace of the elasticity tensor. For scalar-valued quadratic criteria that are homogeneous functions of degree one, stressbased and strain-based criteria are most likely to be mathematically equivalent when the criteria’s operators are linear combinations of the elasticity’s spectral eigenbasis tensors. For the commonly employed fiber-direction strain-based and fiber-direction stress-based “composite” failure criteria, the equivalence conditions are explicitly examined for orthotropic and transversely isotropic material symmetry. The difference between the two criteria decreases as the degree of extensional anisotropy increases but, in general, is unbounded for arbitrary deformation states. Over a moderate, but restricted, range of loading conditions, the difference between the criteria is small for high-modulus fiber-reinforced uni-directional lamina, often less than the uncertainties in either the elastic coefficients or failure values, and the two criteria appear interchangeable.  Elsevier, Paris failure criteria / fiber direction