Layerwise mixed element with sublaminates approximation and 3D zig-zag field, for analysis of local effects in laminated and sandwich composites

The analysis of damaged sandwich composites and thick laminates remains a still challenging task, owing to their intricate distributions of displacements and stresses across the thickness. The arduous task is capturing these distributions with an affordable computational effort. The use of sublaminate zig-zag models appears promising since they allow to group several physical layers into a sublaminate without violating the continuity of interlaminar stresses. To contribute to research in this field, a mixed, sublaminate element is developed in which displacements and stresses are approximated by two independent zig-zag models. Like for any zig-zag model, the interfacial contact conditions are fulfilled a priori suitably choosing the continuity functions and constants. In addition to the contact conditions on interlaminar shears, here those on the transverse normal stress and stress gradient are also fulfilled, as required by the elasticity theory. This uncustomary feature implies the presence of unwise terms which need C2 continuous shape functions. To overcome this drawback, C1 and C2 terms are eliminated from the displacement field, as allowed by the mixed approach, then the interlaminar stresses obtained by the C0-made displacement model are cast into a separate zig-zag representation which restores their continuity at the interfaces. As nodal d.o.f. the three displacements and the three interlaminar stresses at the upper and lower faces are assumed, in order to fulfil the contact conditions assembling the sublaminates. Standard, C0, serendipity interpolation polynomials are used to represent both internal displacements and stress fields. As a consequence of this choice, the intra-element stress equilibria are fulfilled in an approximate integral form. This makes easier the development of the element, but does not compromise its accuracy and convergence rate, as shown by former applications. A postprocessing procedure is developed which improves the estimation of interlaminar stresses and helps to reduce the number of sublaminates. The result is that the analysis can be carried out using a single computational layer across the thickness and a reasonably fine in-plane discretization, even with distinctly different material properties of layers and in presence of damage. The overall computational time is reduced to an half of that required by a conventional sublaminate model, like present one deprived of zig-zag terms and postprocessing procedure.