Deformation Due to Mechanical and Thermal Sources in Generalized Thermoelastic Half-Space With Voids

Abstract

The dynamic response of a homogeneous, Isotropic, generalized thermoelastie half-space wirh voids subjected to normal, tangential force and thermal souree is investigated. The displacements, stre.^se.i, temperature distrihution, and change in volume fraction field .so ohtained in the physical domain are computed numerically and illustrated graphically. Thc numerical results of these quantities for magnesium crystal-tike materiat are illustrated to depict the response of various sources in the Lord-Shulman and Green-Lindsay theories for an insulated boundary and temperature gradient boundary.The theory of linear elastic materials with voids is one of the most important generalizations of the classical theory of elasticity. This theory has practical utility for investigating various types of geological and biological materials for which elastic theory is inadequate. This theory is concerned with elastic materials consisting of a distribution of small pores (voids) in which the void volume is included among the kinematic variables and., in the limiting case of volume tending to zero, the theory reduces to the classical theory of elasticity.A nonlinear theory of elastic materials with voids was developed by Nunziato and Cowin [1]. Later, Cowin and Nunziato [2] developed a theory of linear elastic materials with voids for the mathematical study of the mechanical behavior of porous solids. They considered several appiications of the linear theory by investigating the response of the materials to homogeneous deformations, pure bending of beams, and small amplitudes of acoustic waves. Puri and Cowin [3] studied the behavior of plane waves in a linear elastic material with voids. The domain of influence theorem in the linear theory of elastic materials with voids was discussed by Dhaliwal and Wang [4], Scarpetta [5] studied well-posedness theorems for linear elastic materials with voids. Birsan [6] established existence and uniqueness of

Two-temperature dual-phase-lags theory in a thermoelastic solid half-space due to an inclined load

“…The graphically results for the distribution of the real part of the dimensionless field quantities are shown in Figs. 1-7 with F 0 = 1, ω = ω 0 + iξ , ω 0 = 2, ξ = 0.1 and ζ = 2.1 (Kumar and Rani, 2005). All the field quantities are evaluated inside the medium on the z axis as functions of x.…”

“…However, the heat equations for both coupled and uncoupled theories of the diffusion type predict infinite speeds of propagation for heat waves contrary to physical observations. Additional two generalized thermoelasticity theories are presented by Lord and Shulman (1967) and Green and Lindsay (1972) to eliminate the second paradox inherent in the classical uncoupled and coupled theories. They two generalized thermoelasticity theories treat the heat propagation as a wave phenomenon rather than a diffusion phenomenon and predict a finite speed of heat propagation.…”

“…Kumar and Rani (2005) have studied the deformation due to inclined load in thermoelastic half-space with voids. Othman et al (2009) have studied 2-D problems in a half-space possesses cubic symmetry as a result of inclined load.…”

Eigenvalue Approach on Thermoelastic Interactions in an Infinite Elastic Solid with Voids

“…Dhaliwal and Wang [11] developed a heat flux dependent theory of thermoelasticity with voids. Kumar and Rani [12] investigated the temperature and other field variables in a homogeneous isotropic, generalized thermoelastic half space with voids due to normal, tangential force and thermal source.…”

Deformation due to Mechanical and Thermal Sources in a Thermoelastic Body with Voids under Axi-symmetric Distributions

“…Baksi et al [34] explained the eigenvalue approach to study the effect of rotation and relaxation time in two-dimensional problems of generalized thermoelasticity. Kumar and Rani [35] discussed the deformation due to mechanical and thermal sources in a generalized thermoelastic half-space with voids.…”