Effective elastic properties of plane micropolar nano-composites with interface flexural effects

We consider the effective shear and bulk moduli of a micropolar nano-composite in which the interface between individual constituents incorporates intrinsic micropolar elastic properties associated with both extensibility and flexural stiffness. Specifically, we are concerned with the representative problem describing plane deformations of an inhomogeneity-matrix composite in which a circular inhomogeneity is embedded in an infinite micropolar material subjected to arbitrary remote loading. Our main interest lies in the additional contribution of interfacial bending and twisting rigidities to the interface effect and how each influences the mechanical properties of the composite. Using a model of the micropolar interface established in a previous paper by the authors, we present an analytical solution of the problem using two Airy-type stress potentials. This solution is then used to calculate the effective shear and bulk moduli of the corresponding nano-composite with special attention paid to the flexural resistance of the interface and its influence on the size-dependency of the effective moduli. We note also as a check of our results that, in the absence of interfacial flexural rigidity, our solution recovers precisely the results in the literature presented for the effective moduli of a micropolar composite whose interface effect incorporates only membrane type resistance.