Analytical solution of some delamination scenarios in thick structural sandwich plates

Abstract

The first-, second-and third-order shear deformation plate theories are applied in this work to model thick rectangular sandwich plates with through-width delamination. The models are based on the concept of the four equivalent single layers and the system of exact kinematic conditions. Three different scenarios are considered: the failure of the core, the delamination between the top facesheet and the core, and finally, the case when the delamination takes place in the local midplane of the top facesheet. A general model is derived and applied to sandwich plates with Lévy type boundary conditions. The governing equations are summarized and the state-space model of the system is created. The mechanical fields are calculated and compared to finite element results. The comparison shows that the first-order sandwich plate model is inaccurate, on the other hand, the second-and third-order theories capture very well the mechanical fields compared to finite element results. The J-integral distribution is also calculated along the delamination front and it is concluded that the third-and second-order models give very good approximations of the results by finite element analysis and the virtual crack closure technique.

Higher-order semi-layerwise models for doubly curved delaminated composite shells

“…Moreover, it makes it possible to reduce the number of displacement parameters and the mathematical size of the problem. It should be mentioned that if the mismatch between the shear moduli of adjacent layers is relatively large, as it is in the case of softcore sandwich plates, then this condition should be ignored [21]. The oscillations in the shear strain distribution can be reduced by ensuring continuous shear strain derivatives at interface surfaces 1-2 and 3-4: (1) , ∂γ 2ζ(1) ∂ζ (1) ζ (1)…”

“…Subscript u and v indicates the corresponding direction (ξ 1 or ξ 2 ); finally, w (i) (ξ 1 , ξ 2 ) = w(ξ 1 , ξ 2 ) for each ESLs, i.e., the transverse normal of each ESL is inextensible [14]. Equations (10)-(11) can be obtained by parameter elimination [21]. It is important to note that the size and the elements of ψ depend on the applied theory, the number of ESLs and the number of conditions applied.…”

“…(19) back into Eq. (32) yields [14,21]: where A pq is the extensional, B pq is coupling, D pq is the bending, E pq , F pq , G pq and H pq are higher-order stiffnesses defined as [21]:…”

“…This model is able to provide the sufficient accuracy in most of the cases. If further improvement is required, such as the more accurate description of interlaminar shear or normal stresses, then the second-(SSDT and SST) [20,21] and third-order shear deformation (TSDT and TST) [16,17,22] theories might be taken into consideration, as well as other higher-order theories (HSDT) [23][24][25][26][27][28]. Further developments can be achieved by adding the transverse stretching term to the displacement field [12,[29][30][31][32][33].…”

“…The kinematic continuity of the adjacent layers can be ensured by using the system of exact kinematic conditions (SEKC) developed primarily for the first-order plates [57]. The latter work was followed by the extension of the basic idea to the second-and third-order plates [57] as well as thick sandwich plates [21,32].…”