Failure Criteria and Compliance Variation of Anisotropically Damaged Materials

Abstract

The damage state is usually described by introducing damage tensor of the second or fourth order. An alternative approach would be based on damage distribution function specifying the damage state on any physical plane. This approach is assumed in the paper. First, the limit state failure condition for a material element is specified by assuming crack density distribution on physical planes. The critical plane approach is next used and the limit condition is obtained in the parametric form with the plane orientation vector to be determined from the maximization of the failure function. The resulting failure condition is applied to the analysis of directional strength evolution of uniaxially compressed specimens with varying orientation of principal stress and damage tensor axes. The damage evolution in a stressed element can also be described by postulating the damage state on the physical plane and its growth due to increasing stress or strain. The damage growth function is assumed and the resulting damage distribution is specified. The associated compliance variation is next determined by accounting for the effect of frictional slip at compressed crack interfaces and opening modes for crack under tensile tractions.