Nonsingular crack modelling in orthotropic plates by four equivalent single layers

•Delaminated composite plates are modelled by the method of four equivalent single layers.•The system of exact kinematic conditions is updated.•The shear strain control conditions and the theorem of autocontinuity are introduced.•The shear strain controlled second-order plate theory captures accurately the mechanical fields.

In this work the second- and third-order laminated plate theories are applied to model delaminated composite plates with material orthotropy. The method of four equivalent single layers is proposed and a general third-order displacement field is utilized in each layer. The kinematic continuity between the layers is established by the system of exact kinematic conditions. Apart from the continuity of the in-plane displacements between the interfaces of the layers even the continuity of shear strains, their derivatives and curvatures is imposed. As a novelty a so-called shear strain control condition is introduced, which means that the shear strains at two or more points located along the thickness are imposed to be the same. Using the proposed conditions the equilibrium equations are derived for the delaminated and undelaminated regions of the plate. Plates with different boundary conditions are solved as examples and the theorem of autocontinuity is introduced, which is essentially related to the continuity conditions between the delaminated and undelaminated parts. The stress and displacement fields as well as the J-integral are determined in the examples and compared to finite element calculations. The results indicate that the control condition works very well in the case of the second-order plate theory, in contrast it is rather a disadvantage in the case of the third-order approximation.