On constitutive equations for thermoelastic analysis of fiber-reinforced composites with isotropic matrix material

This paper is concerned with developing constitutive equations for the thermoelastic analysis of composites consisting of an isotropic matrix reinforced by independent and inextensible two families of fibers having an arbitrary distribution. The composite medium is assumed to be incompressible, dependent on temperature gradient, and showing linear elastic behavior. The reaction of the composite material subject to external loads is expressed in stress tensor and heat flux vector. The matrix material made of elastic material involving an artificial anisotropy due to fibers reinforcing by arbitrary distributions has been assumed as an isotropic medium. The theory is formulated within the scope of continuum mechanics. As a result of thermodynamic constraints, it has been determined that the stress potential function is dependent on the deformation tensor, the fiber fields vectors and the temperature, while the heat flux vector function is dependent on the deformation tensor, the fiber fields vectors, the temperature and temperature gradient. To determine arguments of the constitutive functionals, findings relating to the theory of invariants have been used as a method because of that isotropy constraint is imposed on the material. The constitutive equations of stress and heat flux vector have been written in terms of different coordinate descriptions.