Reinforced materials with thermo-mechanical constraints

Abstract This paper contains a class of exact (controllable) solutions for materials subjected to thermomechanical constraints. The constraints are intended to model materials reinforced with cords. The thermomechanical constraints examined consist of the natural extensions of the purely mechanical constraints of incompressibility and inextensibility to thermo-mechanical problems along with a purely thermal constraint on the temperature gradient. The solutions found are controllable in that they can be sustained in every isotropie homogeneous simple material by surface tractions and heat fluxes alone. The solutions are independent of all the response functions of the material except those appearing in the constraint equations.