The system of exact kinematic conditions and application to delaminated first-order shear deformable composite plates

• We derive the system of exact kinematic conditions.
• The displacement field is based on the interface constraints.
• The delamination causes sudden changes in the stresses.
• First order plate theory is useful if the delamination is close to the midplane.

In this work the analysis of unsymmetrically delaminated composite plates with straight crack front is presented. It is shown that in the undelaminated region of laminated plates the problem can be captured by applying a double-plate system. The displacement continuity between the top and bottom plates requires five conditions, three of them are known in the literature, however further two are necessary to define the reference plane of the undelaminated region. This so-called system of exact kinematic conditions can be applied to any plate theory to satisfy the requirements against the displacement field. The first-order shear deformable plate theory is applied to demonstrate the applicability of the system of exact kinematic conditions. The key step of the formulation is that the in-plane displacement and the rotation parameters are not independent of each other, therefore the size of the problem can be significantly reduced. Laminated simply supported plates are analyzed by varying the position of the delamination in the thickness direction. The energy release rates and the mode mixity are calculated by using the J-integral. It is shown based on the comparison of the analytical results to those by finite element solution that if the delamination is close to the midplane of the plate, then good agreement can be obtained. In contrast, if the delamination is close to the top or bottom plate surfaces, then the first-order plate theory is not appropriate to estimate the fracture mechanics parameters of the plates.