Semi-layerwise analysis of laminated plates with nonsingular delamination—The theorem of autocontinuity

Abstract The proposed semi-layerwise approach captures the mechanical behavior of delaminated composite plates using four equivalent single layers independently of the lay-up. Two equivalent single layers are applied for both the top and bottom parts of a delaminated plate. The updated version of the system of exact kinematic conditions formulates the continuity of the in-plane displacements between the neighboring layers, the location of the global reference plane of the plate and – as important additions compared to previous papers – the continuity of shear strains, their derivatives and curvatures, respectively. The method is demonstrated using the first-, second- and third-order plate theories. As examples, simply supported delaminated plates are considered.The continuity between the delaminated and undelaminated plate regions is established through the theorem of autocontinuity. The J-integral is calculated along the straight delamination front and compared to the results of the virtual crack closure technique. The results indicate that the first- and third-order plate theories provide the best solutions, and give good approximation even in those cases when the previous models failed, i.e., when the delamination is asymmetrically placed between two layers and it is close to the free surface of the plate.