Abstract
A new formulation is presented to link continuum damage mechanics with the concept of fabric tensors within the framework of classical elasticity theory. A fourth-rank damage tensor is used and its exact relationship to the fabric tensors is illustrated. A model of damage mechanics for directional data is formulated using fabric tensors. The applications of the new formulation to micro-crack distributions are well illustrated in two solved examples. In the first example, a micro-crack distribution is considered with its data represented by a circular histogram. The values of the fabric tensors and damage tensor are calculated in this case. In the second example, two sets of parallel micro-crack distributions with two different orientations are investigated. In addition, a general hypothesis for damage mechanics is postulated. It is seen that the two available hypotheses of elastic strain equivalence and elastic energy equivalence may be obtained as special cases of the postulated general hypothesis. This general hypothesis is then used to derive the sought relationship between the damage tensor and fabric tensors. Finally, the evolution of the damage tensor is derived in a mathematically consistent manner based on sound thermodynamic principles.
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