Minimization of complementary energy to predict shear modulus of laminates with intralaminar cracks

The most common damage mode and the one examined in this work is the formation of intralaminar cracks in layers of laminates. These cracks can occur when the composite structure is subjected to mechanical and/or thermal loading and eventually lead to degradation of thermo-elastic properties. In the present work, the shear modulus reduction due to cracking is studied. Mathematical models exist in literature for the simple case of cross-ply laminates. The in-plane shear modulus of a damaged laminate is only considered in a few studies. In the current work, the shear modulus reduction in cross-plies will be analysed based on the principle of minimization of complementary energy. Hashin investigated the in-plane shear modulus reduction of cross-ply laminates with cracks in inside 90-layer using this variational approach and assuming that the in-plane shear stress in layers does not depend on the thickness coordinate. In the present study, a more detailed and accurate approach for stress estimation is followed using shape functions for this dependence with parameters obtained by minimization. The results for complementary energy are then compared with the respective from literature and finally an expression for shear modulus degradation is derived.