Asymptotic homogenization model for generally orthotropic reinforcing networks in smart composite plates

Abstract

A general three-dimensional micromechanical model pertaining to smart composite layers with wavy boundaries is applied to the case of thin smart plates reinforced with a network of generally orthotropic bars that may also exhibit piezoelectric behavior. The method used for the development of the structural model is that of asymptotic homogenization, which reduces the original boundary value problem into a set of three decoupled problems, each problem being characterized by two differential equations. These three sets of differential equations, referred to as 'unit cell problems', deal, independently, with the elastic, piezoelectric, and thermal expansion behavior of the network-reinforced smart composite plates. The solution of the unit cell problems yields expressions for effective elastic, piezoelectric and thermal expansion coefficients which, as a consequence of their universal nature, can be used to study a wide variety of boundary value problems associated with a smart structure of a given geometry. The model can be used to customize the effective properties of a smart structure by changing some material or geometric parameters such as the size or nature of the reinforcements. The developed general methodology is applied to smart network-reinforced composite structures with generally orthotropic reinforcements and actuators. As particular examples, spatial rectangular, triangular, and rhombic smart network plates are analyzed. The general orthotropy of materials is very important from the practical viewpoint and this orthotropy makes micromechanical modeling significantly more complex. In the limiting case of isotropic reinforcements and absence of actuators, the above general orthotropic micromechanical model converges to results that are consistent with those of previous models obtained by either asymptotic homogenization, or stress-strain relationships in the isotropic reinforcements.