New model representations of dynamic thermoviscoelasticity in the problem of heat shock

Abstract

Investigation of heat shock is a central problem in thermomechanics because this phenomenon is used in powerful energy sources and different technological processes. The solution of the indicated problem with the use of dynamic and quasi-static thermoelasticity models made it possible to investigate the physical mechanisms of the heat-stressed state of isotropic and anisotropic elastic bodies on the basis of the classical Fourier and Maxwell–Cattaneo–Lykov phenomenologies of the finite velocity of heat propagation in solid bodies, to develop the generalized theory of conjugation of thermomechanical fields with different physical (electric, magnetic) fields, to formulate the main relations of the linearized theory with account for the heat memory of solids, and to determine the relation between the macroscopic behavior of a continuous medium, the internal parameters of its state, and the rate of their change with time. A systematization of the results obtained in this field of thermomechanics is given in the reviews of the author of this work [1, 2] and in his monograph [3, 4]. The problem being considered was investigated mainly for technologically important materials obeying Hooke’s law. In the corresponding mathematical models defining the dynamic, quasi-static, and static thermoelasticity parameters of materials, isotropic materials with constant temperature-independent thermomechanical coefficients, small temperature differences not larger than any limiting value determined by the properties of a material, and stresses lower than the yield point of the material are considered. It is believed [3] that at relatively low temperatures and stresses, the behavior of a wide class of materials is well defined by the thermoelasticity theory. However, at higher temperatures and larger stresses, the notion of elastic body becomes insufficient because in all the materials a viscous flow is present. A real body exhibits elastic and viscous properties and, therefore, it is properly termed the viscoelastic body. The problem on the heat shock of such a body is solved by generalization of the relations between its stresses and deformations. Alfrey, Hilton, and Shternberg [5] concluded that the behavior of a viscoelastic body under the conditions of extremal temperature and chemical actions can be defined in the context of a purely thermoelastic problem