Stiffness reduction of cracked solids

Abstract A method for the determination of the effective moduli of elastic solids containing a doubly periodic rectangular array of cracks is given. The derivation is based on the analysis of a unit cell in which the displacement vector is expanded to a second order in the distances from centerlines. The equilibrium equations in conjunction with the continuity conditions for the displacements and tractions, give a system of equations for the elastic field variables. The determination of the elastic internal energy provides the requested effective moduli of the cracked body. The method is applied to predict the loss of stiffness of cracked isotropic solids and unidirectional composites, as well as cracked cross-ply laminates.

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