Effective Material Properties of Damaged Elastic Solids
By using a continuum modeling approach based on the equivalent elliptical crack representation of a local damage and the strain energy equivalence principle, the effective elastic compliances and the effective engineering constants are derived in closed forms in terms of the virgin (undamaged) elastic properties and a scalar damage variable for damaged two- and threedimensional isotropic solids. It is shown that the effective Young’s modulus in the direction normal to the crack surfaces is always smaller than its intact value.
M.H. Aliabadi, Qingfen Li, Li Li and F.-G. Buchholz
U. Lee and D. Youn, "Effective Material Properties of Damaged Elastic Solids", Key Engineering Materials, Vols. 324-325, pp. 1185-1188, 2006