Mechanics of shear and normal deformable doubly-curved delaminated sandwich shells with soft core

In this work the first- and second-order shear and normal deformation as well as the third-order shear deformation theories are applied to delaminated sandwich shells having constant radii of curvatures. The normal deformation of the first- and second-order models was captured by quadratic functions in the core, while it was ignored in the facesheets. The third-order model was created using cubic displacement functions in the terms of through-thickness coordinate in the core, the facesheets were still captured by second-order shear deformable shell theory. The governing equations were deduced through the virtual work principle, eventually three possible scenarios were considered: core-core, face-core and face-face delamination, respectively. To prove the applicability of the developed shell models several examples were solved including the former three scenarios combined with elliptic and hyperbolic doubly-curved sandwich shell geometries with different facesheet/core material pairs. The traditional simply-supported boundary conditions were assumed involving the Levy-type formulation. Moreover, the state space method was applied to solve the examples. The mechanical fields calculated were compared to results obtained through spatial finite element models. The J-integral was also determined and separated into mode-II and mode-III components making it possible to perform the comparison to energy release rates computed by the virtual crack closure method. The results indicate that the proposed models capture the mechanical fields with high accuracy in the vicinity of points lying along the delamination front. The J are also well the shell models.