Micromechanical modeling of smart composite structures

Abstract

Effective elastic, actuation, thermal expansion and hygroscopic expansion coefficients for periodic smart composite structures are derived through the application of asymptotic homogenization models. The actuation coefficients characterize the intrinsic transducer nature of active smart materials that can be used induce strains and stresses in a controlled manner. The pertinent mathematical framework is that of asymptotic homogenization. Differential equations with rapidly oscillating coefficients which govern the behavior of a general anisotropic (composite) material with a regular array of reinforcements and/or actuators are transformed into simpler ones that are characterized by some effective coefficients; it is implicit, of course, that the physical problem based on these effective coefficients should give predictions differing as little as possible from those of the original problem. The governing equations pertaining to a generalized model of a smart structure with non-homogeneous boundary conditions are derived and are shown to differ from those of a corresponding problem with homogeneous boundary conditions by what amounts to a boundary layer solution. The effective properties are determined by means of so-called 'unit cell' problems and calculated for the case of periodic laminates. The use of these effective coefficients is illustrated by means of two- and three-dimensional examples.