Effect of internal state variables in thermoelasticity of microstretch bodies

First, we formulate the mixed initial boundary value problem in the theory of thermoelastic microstretch bodies having certain internal state variables. Then by using some approachable computing techniques and the known Gronwall’s inequality we will prove that the presence of internal state variables do not influence the uniqueness of solution of the mixed problem. The purpose of the theory of thermo-microstretch elastic solids is to eliminate discrepancies between classical elasticity and experiments. This is a theory of thermoelasticity with microstructure that include intrinsic rotations and microstructural expansion and contractions. The classical elasticity failed to present acceptable results when the effects of material microstructure were known to contribute significantly to the body’s overall deformations, for example, in the case of granular bodies with large molecules (e.g. polymers), graphite or human bones. These cases are becoming increasingly important in the design and manufacture of modern day advanced materials, as small-scale effects become paramount in the prediction of the overall mechanical behaviour of these materials.