Uniqueness and reciprocity theorems in generalized linear micropolar thermoviscoelasticity

Abstract

A model of the equations of generalized linear micropolar thermoviscoelasticity is given. The formulation is applied to the coupled theory as well as to five generalizations, the Lord–Shulman theory with one relaxation time, the Green–Lindsay theory with two relaxation times, the Green–Naghdi theories of type II (without energy dissipation) and of type III, and the Chandrasekharaiah–Tzou theory with dual-phase-lag. Using Laplace transforms, a uniqueness theorem for this model is proved, restrictions on relaxation functions are deduced and the dynamic reciprocity theorem is derived. The cases of generalized linear micropolar thermoviscoelasticity of Kelvin–Voigt model, generalized linear micropolar thermoelasticity, generalized thermoviscoelasticity and generalized thermoelasticity can be obtained from the given general model.