Modelling of Damaged Laminated and Sandwich Shell Structures by means of Higher-order Shear Deformation Theories

The main aim of the current research is the development of a mathematical formulation for the modelling of damage in laminated and sandwich composite shells. For this purpose, the damage of some areas of the structures can be seen as concentrated decays of the mechanical properties of the elastic constituents. In general, several kinds of damage can affect the mechanical behavior of a generic laminated structure, such as microcracking, debonding, fiber ruptures, and transverse matrix cracking, as specified in [1]. Without investigating the causes of the damage, the current approach suggests to introduce peculiar functions that multiply directly the mechanical properties of the elastic media, expressed in terms of engineering constants. To this aim, the Gaussian function and an ellipse shaped law are used to model a quick variation of the mechanical properties within the whole structural domain. By setting properly the parameters that characterize these distributions, it is possible to control the intensity of the deterioration and the width of the damaged areas, as well as the point of applications. The present approach is employed to characterize the damage in some doubly-curved shells characterized by different radii of curvature. The difficulties related to the description of these curved surfaces are overcome by means of an analytical formulation based on differential geometry [2]. As far as the mechanical properties are concerned, several constituents are considered and combined. The theoretical framework is based on a formulation that allows to develop easily different kinematic models and expansions in a unified manner. Thus, several Higher-order Shear Deformation Theories, which can include also the zig-zag effect, are employed. In fact, it has been proven that peculiar mechanical configurations require an enriched structural model, since lower-order theories could be inadequate to capture the effective mechanical behavior. Finally, a numerical technique able to solve the strong form of the governing equations is used. For this purpose, the partial derivatives that appear in the fundamental system are directly approximated through the Generalized Differential Quadrature method due to its accuracy [3]. References [1] Tornabene, F., Fantuzzi, N., Bacciocchi, M., “Linear Static Behavior of Damaged Laminated Composite Plates and Shells”, Materials, 10, 811, 1-52 (2017). [2] Tornabene, F., Fantuzzi, N., Bacciocchi, M., and E. Viola, Laminated Composite Doubly-Curved Shell Structures. Differential Geometry. Higher-order Structural Theories, Esculapio, Bologna (2016). [3] Tornabene, F., Fantuzzi, N., Ubertini, F., Viola, E., “Strong Formulation Finite Element Method Based on Differential Quadrature: A Survey”, Applied Mechanics Reviews, 67, 020801-1-55.