Mathematical Models of Thermal Reaction of Viscoelastic Bodies

This paper examines mathematical models of the thermal response of viscoelastic bodies under intense heating of the solid boundary (temperature heating; thermal heating; heating by the environment). The proposed theory is based on the linear rheological models of Maxwell and Kelvin, introducing stress and strain deviators. A generalized model is considered, incorporating three coordinate systems simultaneously: Cartesian coordinates – a massive body bounded by a flat surface; spherical coordinates – a massive body with an internal spherical cavity; and cylindrical coordinates – a massive body with an internal cylindrical cavity. Numerical experiments are presented, and the influence of the domain topology on the magnitude of the corresponding thermal stresses is revealed; the properties of Maxwell and Kelvin viscoelastic media are described.