Propagation of Wavefronts in Thermoelastic Media

This entry follows section [1] of the present encyclopedia, where the general conditions of propagation and the local balance laws of jump are written for a large class of (nonpolar) material bodies, with no reference to constitutive equations. Here the local conditions for the propagation of discontinuity waves in a deformable and heat-conducting body are developed for certain classes of the above material bodies, that is, linear thermoelastic solids, nonlinear thermoelastic solids, and thermoelastic fluids, with no reference to the constitutive equations of a particular material within each class. The theory of singular surfaces has been constructed as a local theory, but it reveals a nonlocal character. This is connected with the general theory of quasi-linear hyperbolic equations, where characteristic surfaces are surfaces of discontinuity of the derivatives of the solution. In fact, in linear thermoelasticity singular surfaces are characteristic for the field equations. Ref. [1]. Montanaro A (2012) Kinematics of singular surfaces and jump equations of balance. In: Hetnarski R (ed) Encyclopedia of thermal stresses. Springer–Verlag, Berlin/Hiedelberg/New York