A homogenized structural model for shear deformable composites with compliant interlayers

Abstract

Cylindrical bending of multilayered plates with thin compliant interlayers is studied through a homogenized structural model. The layers are homogeneous and orthotropic with principal material axes parallel and normal to the plane of bending and the interlayers are represented as sliding interfaces controlled by interfacial tractions which depend linearly on the relative displacements of the adjacent layers. The formulation is based on the zigzag theory formulated in Tessler et al. (J Compos Mater 43:1051–1081, https://doi.org/10.1177/0021998308097730 , 2009) for fully bonded beams and the multiscale strategy in Massabo and Campi (Compos Struct 116:311–324, https://doi.org/10.1016/j.compstruct.2014.04.009 , 2014), which is used to include the imperfect interfaces in the homogenized description of the problem. The kinematic variables are independent of the number of layers or imperfect interfaces and equal to four. The problem is solved in closed form on varying the interfacial stiffness between zero and infinite, which are the limiting values used to describe unbonded layers (traction-free interfacial sliding) and fully bonded layers (no sliding). The model accurately predicts global and local fields in highly anisotropic, simply supported, thick plates; some limitations are observed and discussed in the presence of in-plane material discontinuities and clamped supports. The model is applicable to study the elastic response of layered composites with adhesives interlayers or composite assemblies fastened by uniformly distributed mechanical connectors.