The method of asymptotic homogenization is used to develop three comprehensive micromechanical models pertaining to (i) thin smart composite plates reinforced with a network of orthotropic bars that may exhibit piezoelectric behavior;​ (ii) prismatic smart composite structures and (iii) three-dimensional composite structures with an embedded periodic network of isotropic reinforcements, the spatial arrangement of which renders the behavior of the given structures macroscopically anisotropic.

The models developed in this thesis allow the transformation of the original boundary value problems for the regularly non-homogeneous composite structure into simpler ones that are characterized by some effective coefficients. These coefficients are calculated from so-called 'unit cell' or periodicity problems and are shown to depend solely on the geometric and material characteristics of the unit cell and are completely independent of the global formulation of the problem. As such, the effective elastic, piezoelectric and thermal expansion coefficients are universal in nature and can be used to study a wide variety of boundary value problems associated with a structure of a given geometry. The models are illustrated by means of several examples of practical importance and it is shown that the effective properties of a given composite structure can be tailored to meet the requirements of a particular application by changing certain material or geometric parameters such as the type, size and relative orientation of the reinforcements. For models (i) and (ii), if the thermal and piezoelectric behavior of the materials is ignored and if the orthotropic nature of the constituents is reduced to that of isotropy, then the results converge to those of previous models obtained by either asymptotic homogenization, or stress-strain relationships in the reinforcements. For model (iii), if the 3-D arrangement of the reinforcements is reduced to a 2-D one then the model again is shown to converge to previous models.