Fracture mechanical finite element analysis for delaminated composite plates applying the first-order shear deformation plate theory

In this paper, we are concerning the finite element discretization of delaminated polymer composite plates from the point of view of fracture mechanical analysis. The current study applies the first-order shear deformation plate theory with the conception of two equivalent single layers. For the finite element analysis, three distinct element types shall be defined: an intact and a delaminated element for the corresponding regions, and a so-called transition element that provides the coupling between the aforementioned regions. Here, delaminated plates are analysed that include only one delamination front. This analysis is limited to linear elastic but orthotropic material behaviour, therefore, the energy release rate along the crack front can be determined by the J-integral in the cross-section of the transition element. Usually, simply supported plates are used mostly for model verifications in the literature by applying Levy's semi-analytical solution. However, this solution depends on the continuity conditions between the intact and delaminated regions. There are more physically possible continuity conditions, thus several possible solutions exist. Besides, the employed boundary conditions usually are not the same in the semi-analytical and finite element approaches. Since both kinds of boundary conditions can be applied to this plate finite element model the differences that are derived from the boundary conditions are discussed, too.