Abstract
This paper discusses the interaction between the stress and temperature field of the viscoelastic solids described by the fractional calculus constitutive model. The infinitesimal deformation of the solids is assumed. The theory is based on the first and the second thermodynamics laws. The governing equations were derived in which the fractional calculus constitutive relations are incorporated into the formulation. For the theoretical and qualitative analysis one dimensional problems are studied in details, the coupling effects of the temperature change and the thermal stress in the solids are emphasized. The results show that the mechanical and thermal behaviors of the viscoelastic materials modeled by the fractional calculus constitutive law illustrate their features and are evidently different from those of the materials described by the traditional integer-operator constitutive laws.
