Generalized Thermoelastic Interaction in a Half-Space under a Nonlocal Thermoelastic Model

Abstract

In the current article, the nonlocal thermoelastic theory is used to discuss the wave propagation in unbounded thermoelastic materials. Due to the inclusion of relaxation time in thermal conduction formulation and the equations of motion, this model was developed using Lord and Shulman’s generalized thermoelastic model. The theory of the nonlocal continuum proposed by Eringen is used to obtain this model. The integral transforms of the Laplace transform methods used to generate an analytical solution for physical variables are utilized to produce the analytical solutions for the thermal stress, displacement, and temperature distribution. The effects of nonlocal parameters and relaxation time on the wave propagation distributions of physical fields for material are visually shown and explored.

A non‐local fractional two‐phase delay thermoelastic model for a solid half‐space whose properties change with temperature and affected by hydrostatic pressure

“…To verify the validity of the results and the proposed model, the results were compared. The results were compared with those of Sur et al [62] and Luo et al [63], where the differential derivatives with fractional orders were ignored, as well as the comparison with Abbas et al [64] in the case of ignoring the non-locality and fractional operators. The comparison shows the effect of the non-local thermal parameter and the fractional differential operators on the different physical distributions.…”

The Effect of a Nonlocal Thermoelastic Model on a Thermoelastic Material under Fractional Time Derivatives

“…where Now, the suggested eigenvalues techniques may be applied to obtain the solutions of coupled differential Equations ( 25) and (26) as in [45][46][47][48]:…”

“…Sheoran et al [25] studied the thermomechanical interaction in nonlocal transversely isotropic materials with rotations. Abbas et al [26] studied the generalized thermoelastic interactions in a plane under a nonlocal thermoelastic model. Hobiny et al [27] studied the analytical solution of nonlocal thermoelastic interactions on a thermoelastic medium with ramp-type heating.…”

The Effect of Nonlocal on Poro-thermoelastic Solid with Dependent Properties on Refrence Temperature via the Three-phase-lag Model

“…Luo et al [11] introduced the nonlocal thermoelastic model to predict the thermoelastic behavior of nanostructures under extreme environments. Abbas et al [12] displayed the analytical solutions for the nonlocal thermoelastic problem using Laplace transforms and the eigenvalue method. Lata and Singh [13] studied of the axisymmetric deformations in a two-dimensional non-local homogeneous isotropic thermoelastic solid without energy dissipation.…”