Effect of imperfect interface on the effective properties of elastic micropolar multi-laminated nanostructures

Abstract

In this paper, the problem of a heterogeneous elastic micropolar nanostructure with a periodic structure subject to imperfect contact conditions is analyzed through the two-scale asymptotic homogenization method (AHM). The imper- fect interface is modeled as a generalization of the well-known spring model; that is, the homogeneous imperfect interface is described by the following con- ditions: tractions and coupled stress are continuous, but displacements and microrotations are discontinuous across the imperfect interface. The jumps in displacements and microrotations are proportional to the interface traction and coupled stress components, respectively. In particular, micropolar multi- laminated nanocomposites with centro-symmetric isotropic constituents and imperfect contact conditions are studied. From AHM, the solutions for the displacement and microrotation fields are found by means of two-scale series expansions depending on a local (microscopic) variable and a global (macro- scopic) variable. The local problem statements and the corresponding effective properties are explicitly described. The formulation depends on the constituent physical properties, the imperfection parameters, the cell length in the 𝑦3- direction, and the phase’s volume fractions. Numerical results are illustrated and discussed. We concluded that the effective moduli are affected by the imperfections and the cell length in the 𝑦3-direction