Micromechanical modeling of smart composite materials with a periodic structure

Abstract

Comprehensive micromechanical models for smart composite materials with a periodic structure are derived and effective elastic, actuation, thermal expansion and hygroscopic expansion coefficients pertaining to these structures are obtained. The actuation coefficients characterize the intrinsic nature of adaptive structures that can be used to induce strains and stresses in a controlled manner. The effective coefficients replace the rapidly oscillating coefficients inherent to the differential equations that govern the behavior of smart anisotropic materials with a regular array of reinforcements and actuators. The mathematical framework employed is that of asymptotic homogenization that permits the determination of the effective coefficients through solution of unit cell problems. The unit cell problems are shown to be independent of the global boundary value problem. It is implicit of course that the physical model based on these coefficients should give predictions differing as little as possible from those of the original problem. Once determined, the effective coefficients can be utilized in studying different types of boundary value problems associated with a given structure. The effectiveness of the derived models and the use of the effective coefficients is illustrated by means of various two- and three-dimensional examples associated with periodic laminates.