Modified G-L thermoelasticity theory for nonlinear longitudinal wave in a porous thermoelastic medium

Abstract

This paper presents a nonlinear analysis of the transient response of a porous medium affected by external traction. The formulation is presented based on a new modified G-L theory of thermoelasticity while temperature and strain rate parameters are included in the governing equations. Based on the finite strain theory (FST), the Lagrangian strain-displacement equation and Second Piola-Kirchhoff stress are applied to express the generalized form of thermoelasticity equations including large deformation. Both mechanical and thermal shocks are applied and finally, the effects of loading rate on transient response are discussed. An updated finite element method and Newmark's numerical time integration method are employed to solve the nonlinear and timedependent equations. It is determined that the modified G-L model is more powerful in predicting the wave propagation phenomenon. Furthermore, the findings indicate that the external surface shock induces compressive stresses, temperature raise, and volume fraction field increase in a porous medium. It is found compared to the classic model, the modified G-L model is superior in capturing the perceived wave propagation phenomenon.

Effect of loading rate on transient response of a nano scale medium based on continuum and thermal conduction nonlocal model

“…u is the components of the displacement vector,  is the nonlocal term, 12 ,  are the relaxation time term, β = (3λ + 2μ)α, α is the coefficient of linear thermal expansion, C is the specific heat, λ, μ are Lamé constants and ρ is the mass density [30][31][32]. In this situation, the stress at a meticulous location of the medium depends on both the strain at that point and its surroundings of other points of the medium.…”

Coupling dynamic response of saturated soil with anisotropic thermal conductivity under fractional order thermoelastic theory

“…Guo et al [ 28 – 30 ] studied two-dimensional thermo-hydro-elastic coupling problems for a series of isotropic, homogeneous, fully saturated, porous elastic and porous viscoelastic half-space subgrades. Shakeriaski et al [ 31 ] studied the transient response of a porous medium affected by external traction using the G-L theory of thermoelasticity. Zhu et al [ 32 ] studied the thermo-hydro-mechanical coupling of saturated porous deep-sea sediments under the action of mine cart vibration, based on the G-L generalized theory of thermoelasticity and Darcy’s law.…”

A thermo-mechanically loaded rotating FGM cylindrical pressure vessels under parabolic changing properties: An analytical and numerical analysis

“…In addition, the phenomenon of wave propagation and reflection resulting from laser-induced effects is being examined [ [24] , [25] , [26] ].They show that, the boundary absorbs the most energy from the laser pulse, leading to the greatest volume fraction variations in that area. Furthermore, Shakeriaski et al [ 27 , 28 ] proposed a nonlinear numerical approach for solving the governing equations of generalized thermoelectricity based on LS and GS theory in a highly deformable elastic medium subjected to thermomechanical shock. However, a large number of analytical and numerical solutions are carried out when the FGM structures are subjected to mechanical load only in the elastic zone under various material inhomogeneities [ [29] , [30] , [31] , [32] , [33] , [34] , [35] , [36] , [37] , [38] ].…”