A unified theory of thermomechanical materials

Abstract The present paper is an attempt to organize and unify the mechanics, thermodynamics and constitutive equations of nonpolar materials subject to thermal effects and mechanical forces. The approach is that of continuum theory. The philosophy is new in that it unifies and extends all known theories under certain common fundamental axioms, some of which are introduced here for the first time. All theories of simple solids and fluids turn out to be special cases of this theory. Several theorems are given on the inexistence of certain classes of non-simple thermo-solids and the restricted forms of the constitutive equations of other thermomechanical materials. A general class of non-simple thermofluids is studied and the specific form of the constitutive equations of second order Stokesian thermo-fluids are obtained.