Problem of axisymmetric plane strain of generalized thermoelastic materials with variable thermal properties

• Generalized thermoelastic problem with variable material properties is studied.
• Explicit expressions for propagation of waves induced by thermal shock are derived.
• Asymptotic solutions for each physical field induced by thermal shock are derived.
• Effect of variable material properties on thermoelastic response is estimated.

This paper is concerned with asymptotic solutions for the axisymmetric plane strain problem with variable material properties in the context of different generalized models of thermoelasticity. The unified forms of the governing equations for axisymmetric plane strain problem, involving the generalized theory with one thermal relaxation time (L-S theory), the generalized theory with two thermal relaxation time (G-L theory) and the generalized theory without energy dissipation (G-N theory), are presented by introducing the unifier parameters. The Laplace transform techniques and the Kirchhoff’s transformation are used to obtain the general solutions for any set of boundary conditions in the physical domain. The asymptotic solutions for a specific problem of an infinite cylinder, formed of an isotropic homogeneous material with variable thermal material properties, whose boundary is subjected to a sudden temperature rise, are derived by means of the limit theorem of Laplace transform. In the context of these asymptotic solutions, some generalized thermoelastic phenomena are obtained and illustrated, especially the jumps at the wavefronts, induced by the propagation of heat signal with a finite speed, are also observed clearly. By the comparison with the results obtained from the case of constant material properties, the effect of variable thermal material properties on the thermoelastic behavior is also discussed.