A Constitutive Formulation for the Linear Thermoelastic Behavior of Arbitrary Fiber-Reinforced Composites

Melek Usal

doi:10.1155/2010/404398

Abstract

The linear thermoelastic behavior of a composite material reinforced by two independent and inextensible fiber families has been analyzed theoretically. The composite material is assumed to be anisotropic, compressible, dependent on temperature gradient, and showing linear elastic behavior. Basic principles and axioms of modern continuum mechanics and equations belonging to kinematics and deformation geometries of fibers have provided guidance and have been determining in the process of this study. The matrix material is supposed to be made of elastic material involving an artificial anisotropy due to fibers reinforcing by arbitrary distributions. As a result of thermodynamic constraints, it has been determined that the free energy function is dependent on a symmetric tensor and two vectors whereas the heat flux vector function is dependent on a symmetric tensor and three vectors. The free energy and heat flux vector functions have been represented by a power series expansion, and the type and the number of terms taken into consideration in this series expansion have determined the linearity 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.

Highlights

Composite materials are separated into natural composites and artificial composites
The type and the number of terms taken in the series expansion have been determined based on the assumption that mechanical interactions and temperature changes are linear
Since the matrix material has to remain insensitive to directional changes along fibers, even-numbered exterior products of vector fields representing fiber distributions have been considered

Summary

Introduction

Composite materials are separated into natural composites and artificial composites. In our study 5 , it has been assumed that a viscoelastic medium with two different inextensible fiber families does not have a discontinuity surface. Constitutive equations have been obtained that indicate the stress and heat distribution determining the thermoelastic behavior of a composite material reinforced by two arbitrary independent and inextensible fiber families. Fiber-reinforced composite materials belong to a very important class of materials which are often employed in a wide variety of industrial applications These composite materials consist of a fabric structure where the fibers are continuously arranged in a matrix material, and, at the macroscopic level, these composite materials exhibit strong directional dependencies. In a class of engineered fiber composites for structural load-bearing components in civil or aerospace applications, an assumption of linear elastic behavior is suitable and this class of composites belongs to a compressible material response

Kinematics of Fibers Deformation

Thermomechanic Balance Equations

Thermodynamic Constraints and Modeling Constitutive Equations

Determination of Stress Constitutive Equation in Linear Thermoelasticity

Determination of Field Equations

Conclusions