Calculation of damage-dependent directional failure indices from the Tsai–Wu static failure criterion

In the Special Issue of Composites Science and Technology on Failure criteria in fibre-reinforced polymer composites (1998), Liu and Tsai proposed an extension of the Tsai–Wu static failure criterion for progressive failure analysis [Comp Sci Tech 1998;58(7):1023–1032]. They defined the strength ratio R as the scaling factor of the loading vector, and the failure index k as the inverse value of R (k=1/R). The current paper outlines a more general approach, where the failure index k is replaced by a set of directional failure indices Σij (associated with the corresponding stresses σij). Further, it will be demonstrated that the failure indices can be made damage-dependent by replacing the nominal stresses σij by the effective stresses View the MathML source in the Tsai–Wu static failure criterion.