Micromechanical modeling of smart compositestructures

Abstract

Effective elastic, actuation, thermal expansion andhygroscopic expansion coefficients for periodic smart compositestructures are derived through the application of asymptotichomogenization models. The actuation coefficients characterizethe intrinsic transducer nature of active smart materials that can be used to induce strains and stresses in a controlledmanner. The pertinent mathematical framework is that ofasymptotic homogenization. Differential equations with rapidlyoscillating coefficients which govern the behavior of a generalanisotropic (composite) material with a regular array ofreinforcements and/or actuators are transformed into simplerones that are characterized by some effective coefficients; itis implicit, of course, that the physical problem based onthese effective coefficients should give predictions differingas little as possible from those of the original problem. Thegoverning equations pertaining to a generalized model of asmart structure with non-homogeneous boundary conditions arederived and are shown to differ from those of a correspondingproblem with homogeneous boundary conditions by what amounts toa boundary layer solution. The effective properties aredetermined by means of so-called `unit cell' problems andcalculated for the case of periodic laminates. The use of theseeffective coefficients is illustrated by means of two- and three-dimensional examples.