Influence of boundary conditions on the response of multilayered plates with cohesive interfaces and delaminations using a homogenized approach

Abstract

Stress and displacement fields in multilayered composites with interfacial imperfections, such as imperfect bonding of the layers or delaminations, or where the plies are separated by thin interlayers allowing relative motion, have large variations in the thickness, with characteristic zigzag patterns and jumps at the layer interfaces. These effects are well captured by a model recently formulated by the author for multilayered plates with imperfect interfaces and affine interfacial traction laws (Massabò & Campi, Meccanica, 2014, in press; Compos Struct, 2014, 116, 311-324). The model defines a homogenized displacement field, which satisfies interfacial continuity, and uses a variational technique to derive equilibrium equations depending on only six generalized displacement functions, for any arbitrary numbers of layers and interfaces. The model accurately predicts stresses and displacements in simply supported, highly anisotropic, thick plates with continuous, sliding interfaces. In this paper the model is applied to wide plates with clamped edges and some inconsistencies, which have been noted in the literature for models based on similar approaches and have limited their utilization, are explained. A generalized transverse shear force is introduced as the gross stress resultant which is directly related to the bending moment in the equilibrium equations of multilayered structures with imperfect interfaces and substitutes for the shear force of single-layer theory. An application to a delaminated wide plate highlights the potential and limitations of the proposed model for the solution of fracture mechanics problem

Local zigzag effects and brittle delamination fracture of n-layered beams using a structural theory with three displacement variables

“…This implies that continuity is not satisfied at the local level and displacements and force sub-resultants within the single layers may differ. This typically occurs near the crack tip and clamped ends, within boundary regions whose size depends on the mismatch of the elastic constants of the layers and on the stiffness of the interfaces and is very small when the mismatch is small and the interfacial stiffness is very large or very small [20,22]. The model and analyses presented here are limited to mode II dominated problems, were transverse extensibility of the layers and interfacial openings may be neglected.…”

“…The local fields are accurately captured also in very thick beams and wide plates. Predictions are less accurate near clamped edges, due to the presence of boundary regions which will be discussed later [19,20,22]. The diagrams in Fig.…”

Refined zigzag theory for homogeneous, laminated composite, and sandwich beams derived from Reissner’s mixed variational principle

“…[42]. Recent investigations [37,45,46] provide further insight into the transverseshear consistency issues associated with clamped boundary conditions, and highlight accuracy deficiencies of Murakami-type zigzag and stress functions, particularly when applied to highly heterogeneous and multi-layered laminates.…”

“…By replacing the transverseshear strain measures with the bending rotation variables in the displacement assumptions, modifications of Di Sciuva theory have been proposed in Refs. [34] and [37]. The formulation in Ref.…”

“…[34] ensures that C 0 -continuous functions can be used in finite element approximations, whereas Ref. [37], by a particular interpretation of the transverse-shear stress resultants, helps in understanding the transverse-shear inconsistencies along clamped boundary conditions. Moreover, in Ref.…”