ABSTRACT
In this chapter, we consider ordered rate constitutive theories for isotropic, homogeneous, compressible and incompressible thermoviscoelastic solids with memory under finite deformation in Lagrangian description. The rate constitutive theories are derived using the entropy inequality expressed in terms of Helmholtz free energy density Φ as well as Gibbs potential Ψ. Section 11.2 presents details of the rate constitutive theories derived using Helmholtz free energy density Φ. Rate constitutive theories using Gibbs potential Ψ are given in Section 11.3. Thermoviscoelastic solids contain thermal and elastic effects. In addition, such solids also contain (i) mechanism of dissipation of mechanical energy, i.e. some part of the external mechanical energy applied to the matter is converted into entropy which results in heat and (ii) memory, i.e. relaxation behavior or rheology. Derivations of the constitutive theories for such solid matter are considered in this chapter.
