Abstract
The mathematical modeling of smart composite structures is a rather convoluted task due to the anisotropic nature of the host composite material and the contribution of the integrated sensors and actuators. Therefore special analytical techniques should be developed and applied to the analysis of these structures. In this work, the method of asymptotic homogenization is used to derive micromechanical models pertinent to smart composite materials with a regular structure, and subsequently to determine effective elastic, actuation and thermal expansion coefficients. The actuation coefficients characterize the intrinsic transducer nature of smart materials that can be used to induce strains and stresses in a controlled manner. The general model is applied to a practically important case of a laminated smart material with piezoelectric actuators. Analytical formulae for the effective stiffnesses and piezoelectric coefficients are obtained explicitly. The effectiveness of the derived model is illustrated by means of two-and three-dimensional examples.
