Thermal shock problem of a generalized thermoelastic solid sphere affected by mechanical damage and thermal diffusion

Abstract

A mathematical model was created in this article, which consists of a thermoelastic, unified, and isotropic rigid sphere subjected to thermal diffusion. Thermal and chemical potential shocks of a diffusive substance have loaded the sphere's bounding structure. The governing equations were established in the form of a theory of generalized thermoelastic diffusion with mechanical damage taken into account. The temperature increment, concentration, pressure, displacement, stress, and chemical potential numerical effects have been expressed in figures with different values of the mechanical damage parameter, thermal relaxation time, and diffusional relaxation time. All the studied functions are significantly affected by the mechanical damage parameter, radial distance, time, thermal, and diffusional relaxation times. In the Lord-Shulman model, heat, diffusion, and mechanical waves spread at finite speeds on the thermoelastic solid sphere.

Generalized Thermoelastic Infinite Annular Cylinder under the Hyperbolic Two-Temperature Fractional-Order Strain Theory

“…Here we obtain the numerical findings and present them graphically to demonstrate the impact of the investigated factors on the propagation of thermal and mechanical waves in thermoelastic media. So, copper was utilized as the thermoelastic material, and the following physical constants were included in the calculations [25,39]:…”

The vibration analysis of a nanobeam due to a ramp-type heating under Moore-Gibson-Thompson theory of thermoelasticity

“…where 𝑖 is an imaginary number unit and Re is the real part. For faster convergence, many numerical experiments have concluded that the value 𝜅 satisfies the relation 𝜅𝑡 ≈ 4.7 Tzou [22,23].…”