Damage related material constants in continuum damage mechanics for unidirectional composites with matrix cracks

Application of a continuum damage mechanics formulation rests on the ease with which the material constants involved in the formulation can be determined. For an initially linear elastic material, the changes in elastic constants induced by damage depend on certain damage related material constants that are commonly determined by experiments in addition to those required to determine the initial properties. This additional experimental task can render the continuum damage mechanics theory less attractive. The present paper will only deal with those associated with damage representation. We propose here a procedure for analytically determining seven out of eight damage related material constants for unidirectional composites assumed initially transversely isotropic and containing a parallel array of matrix cracks along fibres. The remaining constant can be determined experimentally or by a numerical experiment proposed here for the purpose. The analytical expressions derived are in terms of initial elasticity constants of a unidirectional composite and are verified for their accuracy by numerical experiments. Since a unidirectional composite forms a building block in composite laminates, the results obtained here can be naturally used for damage in laminates.