About finite energy solutions in thermoelasticity of micropolar bodies with voids

Abstract

Our study is dedicated to the problem with initial and boundary conditions in the theory of thermoelasticity for micropolar materials with pores. We obtain some results regarding the existence and uniqueness of a finite energy solution of this mixed problem by generalizing the corresponding results obtained by Dafermos in the context of classical elasticity. In some specific conditions we prove some properties regarding the possibility to control the finite energy solution.

Analysis of a Poro-Thermo-Viscoelastic Model of Type III

“…The corresponding linear system can be expressed in terms of a product variable x n and the resulting symmetric linear system is solved by using the well-known Cholesky method. Finally, the displacement field u hk n , the volume fraction ϕ hk n and the thermal displacement ψ hk n are updated using (18).…”

“…Since the first works by Nunziato and Cowin [1,2], many research papers have been published involving the theory of elasticity of voids (see, for instance, [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] and also the monographs [21,22]). The main idea of such a theory is the assumption that the mass at each material point is found as the product of the mass density by the volume fraction, adding a new variable in the constitutive equations.…”

Finite Element Analysis of Nonlinear Bioheat Model in Skin Tissue Due to External Thermal Sources

“…Alzahrani and Abbas [16] investigated the analytical solution of thermal damage in living tissue due to laser irradiations. In considering the study of real phenomenon regarding thermal transfers in finite mediums, the linear/nonlinear models of heat transfers have been expanded, and their numerical or analytical solutions have been solved by several authors [17][18][19][20][21][22][23][24][25][26][27][28][29]. This work explores the numerical solutions of the thermal injury of biological tissue using a nonlinear bioheat theory in the living tissue.…”

Effect of hall current on propagation of plane wave in transversely isotropic thermoelastic medium with two temperature and fractional order heat transfer

“…Alesemi [21] demonstrated the efficiency of the thermal relaxation time depending upon LS theory, Coriolis and Centrifugal Forces on plane wave's reflection coefficients in an anisotropic MT rotating medium. Despite of this several researchers worked on different theory of thermoelasticity Marin [22][23][24][25], Marin and Baleanu [26], Ezzat et al [27], Marin [28,29] Ezzat et al [30], Ezzat et al [31], Marin and Stan [32], Marin and Nicaise [33], Ezzat and El-Bary [34], Othman and Marin [35], Chauthale et al [36], Marin [37], Kumar et al [38], Marin et al [39], Lata and Kaur [40][41][42] and Lata and Kaur [43,44]. Inspite of these, not much work has been carried out in study of the plane wave propagation with combined effect of hall current, fractional order TPL heat transfer and two temperature.…”