A variational method for analysis of laminates with parallel arrays of intralaminar cracks

This paper presents a robust variational method for prediction of the effective thermoelastic properties of laminates with parallel, but not necessarily coplanar intralaminar cracks. Arbitrary laminate layup, crack patterns, and any in-plane forces and bending moments, and temperature change can be treated simultaneously. The method is based on the principle of minimum complementary energy. The admissible in-plane stress components are assumed to be linear through the ply thickness. Simple matrix expressions are derived for the effective compliance matrix, thermal expansions and curvatures, and specific heat of a cracked laminate. Predictions for the Young's modulus, Poisson's ratio, shear modulus, flexural rigidity, and thermal expansion as functions of crack density for various laminates of symmetric and nonsymmetric layups demonstrated excellent agreement with experimental results of seven independently published studies. Accuracy and robustness of the method are complemented by the fact that no experimentally fitted parameters are required. It is shown that the same formalism can be applied to analysis of closed intralaminar cracks, as well as nonuniform and nonsymmetrical distributions of cracks.