## 1 Introduction  
A composite material is a combination of two or more materials with different physical and (or) chemical properties. A composite material usually has characteristics that do not correspond to those of its isolated components [1]. Thermoelastic composites constitute an important class of materials with a wide variety of applications ranging from aerospace structures and electronic printed circuit boards to recreational and commercial equipment. Some of the most important and useful properties of these composites are lightweight, high strength and stiffness, excellent frictional properties, good resistance to fatigue and retention of these properties at high temperatures [2]. The effective thermo-mechanical properties of the composite depend on properties of the constituents and the fiber volume fraction. Previous knowledge of physical properties of composite materials is one of the problems that science faces. Success in practical applications of composites largely depends on the possibility to predict their properties and behavior through the development of appropriate models. Numerous studies and investigations have been carried out to obtain the properties of composite materials [3; 4; 5; 6]. The prediction of global homogenized properties based on knowledge of the composite constituents provides a useful tool for the design of composite materials. Homogenization methods have proven to be powerful techniques for the study of heterogeneous media. Among the homogenization methods, one of the most used methods is the Asymptotic Homogenization Method (AHM). The AHM can provide overall material constants which describe the global behavior of the composite structure. First, the periodic cell is identified; then, by means of the AHM [7; 8; 9; 10; 11; 12], the original constitutive relations with rapidly oscillating material coefficients are transformed in two setsof mathematical problems. The first set has new physical relations over the periodic cell with constant coefficients which represent the properties of an equivalent homogeneous medium and they are called the effective coefficients of the composite under study. The second set allows the calculation of some functions which are solutions of the so-called local problems. The local problems are solved over the periodic cell. A state-of-the-art review where the AHM is applied to composites is provided in ref. [13]. A variety of existing homogenization methods are presented with their advantages and disadvantages. Previous research has been performed for the estimation of the effective properties in composite materials. The elastic properties of carbon nanotube/polymer composites are computed in ref. [14]. A combination of the Finite Element Method (FEM) and the Strain Energy Method was used to obtain the effective elastic constants. The nanotubes are assumed to follow a helical path along the length of the array. The finite element software ANSYS 7.1 was used for the analysis. A review on the application of the FEM in the analysis of composite materials is performed in ref. [15]. A numerical homogenization approach to calculate the effective properties of fiber and particle reinforced materials including smart and multifunctional materials with a focus on piezoelectric fiber composites applied to control vibration and noise radiation of structures was presented in ref. [16]. The authors employ the FEM based on homogenization to optimize the material distribution at the micro-scale by applying an evolutionary approach to receive a desired global behavior of a structure at the macro-scale level. The FEM based on the homogenization of a fiber-reinforced composite has also been applied in ref. [17] by using MAPLE symbolic calculations. Improved versions of the Stochastic perturbation-based Boundary Element Method (SBEM) have been formulated and implemented in ref. [18]. The new approach is compared with a previous version of the SBEM in both isotropic and composite cantilever panels.