Effective moduli and characteristic lengths of micropolar media with dense periodic distribution of ellipsoidal nano-/micro-inhomogeneities

Abstract

Nanoscopic elastic behavior of the field quantities in the vicinities of nanosize defects and nano-inhomogeneities cannot be properly described within the size independent classical theory. As a remedy to this type of dilemmas and enhancement of the accuracy of the solution, polar or gradient continuum theories may be utilized. The current work is concerned with composites consisting of micropolar matrix and micropolar ellipsoidal particles with periodic distribution throughout the three dimensional space. In particular, the analytical determinations of the effective micropolar elastic moduli tensor, effective micropolar couple stress moduli tensor, and effective micropolar characteristic lengths are of interest. To this end, in addition to the classical eigenstrain field the concept of eigencurvature field, too, is introduced into micropolar theory. Moreover, the classical Eshelby equivalent inclusion method is extended to mathematical framework of micropolar theory of elasticity. The effects of the size and the volume fraction of the particles on the overall properties of the nano-/micro-composites of concern are addressed. An important feature of the current theory, in addition to its size dependency, is valid for high volume fraction of particles.