On the plane strain in a generalized theory of thermoelasticity

This paper is concerned with the plane strain in the linear theory of generalized thermoelasticity, proposed by Green and Lindsay[1]. Using the associated matrices method[2], a representation of Galerkin type, is given. This representation is used to derive the solution of the vibration problem corresponding to concentrated body forces and concentrated heat source in an infinite medium.     

On isovector fields and similarity solutions of generalized dynamic thermoelasticity

The purpose of the present work is the investigation of the isovector fields as well as the similarity solutions of the PDEs describing the generalized dynamic thermoelasticity. The adopted methodology and solution techniques belong totally to the analytical realm, while special treatment of the reduced differential equations resulting from similarity solution adoption has been realized.     

A generalized linear thermoelasticity theory for piezoelectric media

Summary A theory of thermoelasticity for piezoelectric materials which includes heat-flux among the independent constitutive variables is formulated. It is found that the linearized version of the theory admits a finite speed for thermal signals. An equation of energy balance and a theorem on the uniqueness of solution are obtained.     

On fractional order generalized thermoelasticity with micromodeling

This paper presents the theory of fractional order generalized thermoelasticity with microstructure modeling for porous elastic bodies and synthetic materials containing microscopic components and microcracks. Built upon the micromorphic theory, the theory of fractional order generalized micromorphic thermoelasticity (FOGTE_mm) is firstly established by introducing the fractional integral operator. To generalize the FOGTE_mm theory, the general forms of the extended thermoelasticity, temperature rate dependent thermoelasticity, thermoelasticity without energy dissipation, thermoelasticity with energy dissipation, and dual-phase-lag thermoelasticity are introduced during the formulation. Secondly, the uniqueness theorem for FOGTE_mm is established. Finally, a generalized variational principle of FOGTE_mm is developed by using the semi-inverse method. For reference, the theories of fractional order generalized micropolar thermoelasticity (FOGTE_mp) and microstretch thermoelasticity (FOGTE_ms) and the corresponding generalized variational theorems are also presented.     

On dual-phase-lag thermoelasticity theory with memory-dependent derivative

A new mathematical model of generalized thermoelasticity with memory-dependent derivatives for the dual-phase-lag heat conduction law is constructed. The governing equations of the new model are applied to a half-space subjected to ramp-type heating. Laplace transforms technique is used. The solution is obtained for different types of functions representing the thermal shock and for different values of the parameter of the time fraction derivative of the model. The effects of time-delay and arbitrary kernel function on elastic material are studied and represented graphically. The predictions of the theory are discussed and compared with dynamic classical coupled theory.     

On conservation laws in generalized dynamic thermoelasticity

The differential equations of generalized dynamic thermoelasticity constitute a coupled non-self-adjoint system of PDEs, which in its variational form does not admit a Lagrangian. However following exterior calculus methodology, we augment the space of dependent variables, accompanying the initial differential equations with suitable adjoint equations and additional auxiliary “fields”. So the construction of a Lagrangian is now possible along with the realization of Noether's theory for finding conservation laws. Finally, in our case, it is possible to characterize the additional dependent variables in terms of the physical fields themselves and obtain then conservation laws expressed via the original known thermoelastic fields.     

On a mixed problem for the temperature equation in generalized thermoelasticity

Summary In the context of the generalized thermoelasticity theory, a mixed problem for the temperature equation is constructed by starting with a mixed problem for the coupled governing equations for the displacement and temperature fields. The uniqueness of solution of the former problem is established. A method of deducing a solution of the latter problem from that of the former problem is presented.     

A generalized theory of thermoelasticity based on thermomass and its uniqueness theorem

In this paper, a new theory of generalized thermoelasticity has been proposed by taking into account the general heat conduction law, which depends on the motion of the thermomass defined as the equivalent mass of phonon gas in dielectrics according to Einstein’s mass–energy relation and involves the inertia effect on the time and space of the heat flux and temperature. The formulations are derived and given for anisotropic heterogeneous and isotropic homogenous materials. The uniqueness theorem of equations for the isotropic homogenous materials is proved. By comparison with the other theories of generalized thermoelasticity, the theory based on the motion of thermomass is more reasonable to predict the propagation of thermal and elastic waves in the microscale heat conduction conditions.     

Size-dependent generalized thermoelasticity model for Timoshenko microbeams

A size-dependent, explicit formulation for coupled thermoelasticity addressing a Timoshenko microbeam is derived in this study. This novel model combines modified couple stresses and non-Fourier heat conduction to capture size effects in the microscale. To this purpose, a length-scale parameter as square root of the ratio of curvature modulus to shear modulus and a thermal relaxation time as the phase lag of heat flux vector are considered for predicting the thermomechanical behavior in a microscale device accurately. Governing equations and boundary conditions of motion are obtained simultaneously through variational formulation based on Hamilton’s principle. As for case study, the model is utilized for simply supported microbeams subjected to a constant impulsive force per unit length. A comparison of the results with those obtained by the classical elasticity and Fourier heat conduction theories is carried out. Findings indicate that simultaneous considering the length-scale parameter and thermal relaxation time has strong influence on the thermoelastic behavior of microbeams. In dynamic thermoelastic analysis of the microbeam, while the non-Fourier heat conduction model is employed, the modified couple stress theory predicts larger deflection compared with the classical theory.     

On the propagation of waves in layered anisotropic media in generalized thermoelasticity

In view of the increased usage of anisotropic materials in the development of advanced engineering materials such as fibers and composite and other multilayered, propagation of thermoelastic waves in arbitrary anisotropic layered plate is investigated in the context of the generalized theory of thermoelasticity. Beginning with a formal analysis of waves in a heat-conducting N-layered plate of an arbitrary anisotropic media, the dispersion relations of thermoelastic waves are obtained by invoking continuity at the interface and boundary conditions on the surfaces of layered plate. The calculation is then carried forward for more specialized case of a monoclinic layered plate. The obtained solutions which can be used for material systems of higher symmetry (orthotropic, transversely isotropic, cubic, and isotropic) are contained implicitly in our analysis. The case of normal incidence is also considered separately. Some special cases have also been deduced and discussed. We also demonstrate that the particle motions for SH modes decouple from rest of the motion, and are not influenced by thermal variations if the propagation occurs along an in-plane axis of symmetry. The results of the strain energy distribution in generalized thermoelasticity are useful in determining the arrangements of the layer in thermal environment.     

Dynamic response of a generalized piezoelectric-thermoelastic problem under fractional order theory of thermoelasticity

The dynamic response of a piezoelectric-thermoelastic rod made of piezoelectric ceramics (PZT-4) subjected to a moving heat source is dealt with in the context of the fractional order theory of thermoelasticity. The piezoelectric-thermoelastic governing equations for the problem are formulated and then solved by means of Laplace transform together with its numerical inversion. The distributions of the considered nondimensional temperature, displacement, stress, and electric potential are obtained and illustrated graphically. The effects of fractional order parameter and the velocity of heat source on the variations of the considered variables are investigated, and the results show that they have significant influence on the variations of the considered variables. The present investigation could be helpful for better understanding the multi-field coupling effect of mechanical, electric, and thermal fields in real piezoelectric ceramics structures, and provide some guidelines in the optimal design of actuators or sensors made of piezoelectric ceramics serving in a thermoelastic environment.     

Memory-dependent derivatives for photothermal semiconducting medium in generalized thermoelasticity with two-temperature

In this work, a novel generalized model of photothermal theory with two-temperature thermoelasticity theory based on memory-dependent derivative (MDD) theory is performed. A one-dimensional problem for an elastic semiconductor material with isotropic and homogeneous properties has been considered. The problem is solved with a new model (MDD) under the influence of a mechanical force with a photothermal excitation. The Laplace transform technique is used to remove the time-dependent terms in the governing equations. Moreover, the general solutions of some physical fields are obtained. The surface taken into consideration is free of traction and subjected to a time-dependent thermal shock. The numerical Laplace inversion is used to obtain the numerical results of the physical quantities of the problem. Finally, the obtained results are presented and discussed graphically.     

Variational theorem of generalized Cosserat-medium thermoelasticity

An equation which represents the content of the variational theorem of generalized Cosserat-medium elasticity is introduced. It is shown that, on the basis of this theorem, the basic energy equation of this medium may be obtained.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 40, No. 1, pp. 139–142, January, 1981.     

A heat-flux dependent theory of thermoelasticity with voids

Summary A thermoelasticity theory for elastic materials with voids is formulated. This theory includes the heat-flux among the constitutive variables and assumes an evolution equation for the heat-flux. A class of mixed initial boundary value problems is defined and the uniqueness is established.     

Equations of generalized thermoelasticity of cosserat medium

Dynamic equations of generalized thermoelasticity are derived for the Cosserat continuum, the theorem of uniqueness of solution of the problem is proved, and an expression is derived which represents the content of a theorem analogous to the reciprocal theorem.Notation absolute temperature - d surface element - Euler radius vector of a point - r Lagrange radius vector of a point - n vector of the external normal to the surface - E unit tensor - s entropy per unit volume - q vector of heat flux - w density of volumetric heat release - =(–_o) _o ¹ relative deviation of temperature from the initial value - _o initial absolute temperature of the medium - asymmetric strain tensor - tensor of flexure and torsion - _o constant characterizing the rate of heat propagation - k coefficient of thermal conductivity - A mechanical power of external surface forces - L mechanical power of external body forces - W kinetic energy of strain - potential energy of strain - X dissipation function - temperature potential - U thermal analog of the power of internal sources - Q thermal analog of the power of the surface of sources Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, Wo. 4, pp. 716–723, October, 1980.     

Response of frequency domain in generalized thermoelasticity with two temperatures

The paper is concerned with the time-harmonic deformation in a homogeneous, isotropic, generalized thermoelastic medium with two temperatures. The Hankel transform is employed to solve the boundary-value problem in the frequency domain in the context of two generalized theories of thermoelasticity (Lord and Shulman, Green and Lindsay). The inverse transform integral is evaluated by using the Romberg integration in order to obtain the results in the physical domain. The components of the stresses as well as the temperature and conductive temperature obtained in this manner are computed numerically. The effects of two temperatures are presented graphically.     

A unified generalized thermoelasticity solution for the transient thermal shock problem

A unified generalized thermoelasticity solution for the transient thermal shock problem in the context of three different generalized theories of the coupled thermoelasticity, namely: the extended thermoelasticity, the temperature-rate-dependent thermoelasticity and the thermoelasticity without energy dissipation is proposed in this paper. First, a unified form of the governing equations is presented by introducing the unifier parameters. Second, the unified equations are derived for the thermoelastic problem of the isotropic and homogeneous materials subjected to a transient thermal shock. The Laplace transform and inverse transform are used to solve these equations, and the unified analytical solutions in the transform domain and the short-time approximated solutions in the time domain of displacement, temperature and stresses are obtained. Finally, the numerical results for copper material are displayed in graphical forms to compare the characteristic features of the above three generalized theories for dealing with the transient thermal shock problem.     

On the micromorphic thermoelasticity

The linear dynamic theory of micromorphic thermoelasticity is considered. Following [Rev. Roum. Sci. Technol. Méc. Appl. 34 (1989) 101] we establish a reciprocity relation which involves thermoelastic processes at different instants. Then we show that this relation can be used to obtain a uniqueness theorem and a reciprocal theorem. The uniqueness result is derived with no definiteness assumption on elastic constitutive coefficients. The reciprocal theorem avoids both the use of the Laplace transform and the incorporation of initial conditions into the equations of motion. A uniqueness result which avoids the positive definiteness of the conductivity tensor is also established. Then, the existence of a generalized solution is studied.