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A synergistic damage mechanics approach, i.e., a combined continuum damage mechanics (CDM) and micromechanics approach, is developed to characterize the viscoelastic response of cross-ply laminates with transverse cracks. The approach relies upon a second-order tensor-based description of damage wherein the crack opening displacement appears as an explicit function. The time variation of this function is calculated by micromechanics and is inserted into the continuum damage formulation. The relaxation moduli calculated for fixed states of damage (transverse crack density) by this approach agree well with independently calculated values by a CDM approach and finite element model.

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a b s t r a c tThree analytical models with increasing complexity, all based on minimization of complementary energy, are compared in their ability to predict shear modulus reduction of laminates with intralaminar cracks in 90-layer. The very elegant and simple (and the less accurate) model by Hashin assumes linear out-of-plane shear stress distribution across the ply in all layers. The second model assumes exponential shape of these stresses in the constraint layer keeping linear assumption in the cracked layer. The model developed in the present paper accounts for nonlinear out-of-plane shear stress thickness distribution in all layers described by shape functions determined in the procedure of minimization. Increasing the complexity of the model the predicted shear modulus of the damaged laminate increases approaching to value obtained using finite elements (FE). Results show that for laminates with relatively thick cracked layers the stress state description in the cracked layer should be refined whereas for laminates with constraint layer thicker than the cracked layer more accurate stress description in the constraint layer is necessary. More accurate solutions could be derived using the described methodology, but the involved complexity and the numerical routines required for their application diminish their value comparing with direct FE solution.