Potential of a simple variational analysis in predicting shear modulus of laminates with cracks in 90-layers

The potential of accurate modelling of the shear modulus reduction of laminates with cracked 90-layers using models based on the minimization of the complementary energy with improved stress description in the constraint layers is evaluated.

This group of models refine Hashin’s model by introducing shape functions with unknown parameters to represent the out-of-plane shear stress distribution across the constraint layer thickness. The Hashin’s model becomes a particular case of the presented when the shape parameter approaches to zero. The most accurate shape parameters are found in the result of minimization. Three models are compared: the present variational model, Hashin’s model and the shear lag model introduced by Soutis which assumes linear out-of-plane shear stress distribution over an unknown part of the layer. It is shown in this paper that the size of this part may be determined by minimization of the complementary energy. The present model is the most accurate amongst the three, whereas Soutis’ model is more accurate than the Hashin’s model for laminates with constraint layer, thicker than the cracked layer. The comparison with finite element method results shows reasonable agreement. Agreement can be improved developing models with better description of the stress state in the cracked layer.