## A MATHEMATICAL MODEL FOR THE LINEAR CONSTITUTIVE EQUATIONS OF A THERMOELASTIC COMPOSITE CONTINUUM REINFORCED BY SINGLE FAMILY OF ARBITRARILY FIBER

JOURNAL OF THE FACULTY OF ENGINEERING AND ARCHITECTURE OF GAZI UNIVERSITY, vol.26, no.2, pp.315-324, 2011 (SCI-Expanded)

#### Abstract

Main objective of this study is to construct a mathematical model belonging to constitutive equations which represent linear thermoelastic behavior of a composite material, where the material was reinforced by single family of arbitrarily fiber. General thermodynamic balance equations, Clausius-Duhem inequality, constitutive theory axioms, equations dealing with to kinematic and deformation geometry of fiber have been determining in the process of this study. It has been assumed that material attains a strong anisotropy due to the fiber distribution. Because the matrix material remains insensitive to change of direction along the fiber, a symmetric tensor which outer products of fiber vector has been defined. Considering incompressibility of the medium and inextensibility of the fiber family, these assumptipons are fairly meaningful for the practical applications, constitutive equations of the stress and heat flux vector have been obtained. As a result of thermodynamic constraints, it has been shown that the stress potential function is dependent on two symmetric tensors whereas the heat flux vector function is dependent on two symmetric tensors and a vector. In this study, the matrix material has been considered as an anisotropic medium. In the scope of this approach, constitutive equations of stress and heat flux vector has been revealed representing by a power series expansion according to arguments of constitutive functions. The type and number of terms taken into consideration in this series expansion has been determined based on the linearity condition of the medium. The linear constitutive equations of the stress and heat flux vector are substituted in the Cauchy equation of motion and in the equation of conservation of energy to obtain the field equations.