Variational models for shear modulus of symmetric and balanced laminates with cracks in 90-layer

• A model is developed to predict shear modulus reduction in cracked laminates.
• The developed model is based on the minimization of complementary energy.
• Simulations are compared to analytical models, FEM and experimental results.

Three 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.