Thermodynamic effects of linear dissipative small deformations

This paper presents a phenomenological model of dissipative losses manifested as heat transfer effects in small linear deformations of solid continua. The impetus is the need for a unified theory characterizing heat transfer effects (called "stretching calorimetry" in the literature) on the mechanics of deformations from a macroscopic point of view, overcoming the fragmentary description of these thermodynamic effects in the available literature. The model is based on derivation of mathematical expressions that quantify the contribution of the heat transfer effects and of the mechanical work in small linear deformations. The formulation has been developed by considering the Gibbs' free energy and the entropy functions of the body under deformation and applying the energy balance to the continuum. The model has been compared to available experimental data of measurements of such heat effects in linear deformations ("stretching calorimetry") of a broad range of materials. Results are presented by illustrating force-elongation values under the Hooke's law, the proposed model, and the experimental data. The calculated model results show excellent agreement with the reported experimental data, for all the different classes of materials considered.