Inter-relationships among stiffness matrix components for general laminates with transverse cracks in oblique plies

Abstract

In this paper, nine inter-relationships linking the stiffness matrix components of symmetrical or unsymmetrical laminates having transverse matrix cracks in some of the off-axis plies is presented. The crack closure condition under membrane and bending deformations is established and used to obtain the inter-relationships. The derived crack closure conditions and inter-relationships are validated using a numerical model based on previous work by the authors. These inter-relationships include the eighteen stiffness matrix components and are exact within the assumptions made in the classical lamination theory. When using a two-scale finite element-based model, six loading cases would be needed to obtain the complete stiffness matrix. With the obtained inter-relationships, only four loading cases would be needed, thus saving a third of the total amount of information and computing time.