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Mathematical modeling of temperature stresses in a nonlocal thermoviscoelastic continuous medium

The improvement of the properties of structural and functional materials is associated with the synthesis of materials from structures with limiting values of properties (for example, extremely strong, refractory, thermostable, etc.). Such materials have an inhomogeneous structure, justified by the technological features of their preparation. In recent years, such materials have come to be called “structure–sensitive,” and the study of their thermomechanical characteristics has become possible within the framework of generalized mechanics of a continuous medium. Mathematical models describing such materials belong to the class of non-local models proposed by A. K. Ehringen. Now, there are few works on the use of nonlocal viscoelasticity, while many materials exhibit viscoelastic properties, even nonlocal viscoelastic properties, for example, solid propellants, composite materials, etc. The paper considers a mathematical model of a nonlocal thermoviscoelastic continuous medium. Using the finite element method, the temperature stress distributions are found for high-intensity pulsed heating of a nonlocal half-space.