Thermoelastic Fields Research Articles

Study on the Temperature Distribution Law of Thermoelastic Coupling Field in Concrete Pavement under Tunnel Fire

Much research work about tunnel fire focused on a single temperature field of tunnel lining structures, and ignored the thermoelastic coupling effects in concrete pavement. Normally, the simplified heating curve sush as the environment temperature curve was adopted, therefore, a mathematical model of the thermoelastic coupling field was established based on finite element method, and the solving algorithm using finite difference method was proposed to analyze tunnel fire problem. Moreover, the results by the above method was also compared to those without considering thermoelastic coupling effects. In addition, the influences of material parameters, such as heat conductivity coefficient, specific heat capacity, elastic modulus and so on, were studied respectively to give the sensitivity of the problem. Through this research, the following conclusions were obtained: the thermoelastic coupling has a certain impact on the temperature field, and it appears the hysteresis phenomenon along the depth direction. Furthermore, when considering the thermoelastic coupling, the temperature of tunnel pavement under fire decreases with the increment of each material parameter respectively, i.e. all the material parameters have similar effects on the temperature field.

Partial closure of a curved crack in a plane using an induced thermoelastic stress field

On the basis of the methods of thermoelasticity, a mathematical description of the model of partial closure of a curved crack in a plane with the help of an induced temperature field was carried out. The determination of unknown contact stresses and the sizes of the contact zones in each approximation is reduced to the solution of a singular integral equation. Normal and tangential contact stresses and the values of the size of the tip zones where the faces of a curved crack close are found.

Decagonal quasicrystalline elliptical inclusions under thermomechanical loading

In this work, an elegant method is proposed to derive the thermoelastic field induced by thermomechanical loadings in a decagonal quasicrystalline composite composed of an infinite matrix reinforced by an elliptical inclusion. The thermomechanical loadings include a uniform temperature change, remote uniform in-plane heat fluxes and remote uniform in-plane stresses. The corresponding boundary value problem is ultimately reduced to the solution of two independent sets of four coupled linear algebraic equations, each of which involves four complex constants characterizing the internal stress field. The solution demonstrates that a uniform temperature change and remote uniform stresses will induce an internal uniform stress field, and that uniform heat fluxes will result in a linearly distributed internal stress field within the elliptical inclusion. The induced uniform rigid body rotation within the inclusion is given explicitly.

Exact solution for an interface crack between dissimilar anisotropic thermoelastic solids under uniform heat flow

Abstract An interface crack between dissimilar anisotropic thermoelastic solids subjected to uniform heat flow at infinity and no mechanical loading on its boundary is analyzed. Generalized two-dimensional deformations such as plane stress and plane strain deformations are considered. The exact solution for the thermoelastic fields is obtained on the basis of the thermoelastic formalism with the transformed function representations. The closed-form solutions of the stress intensity factor and energy release rate are obtained, and the explicit exact expressions for the stress intensity factor and energy release rate are derived for both orthotropic and isotropic bimaterials. Numerical computations are performed using the finite element method to verify the exact solutions. Close agreement is observed between the exact solution and the numerical solution.

Study on the coated isotropic thermoelastic material based on the three-dimensional Green’s function for a point heat source

Abstract Three-dimensional Green׳s function for a point heat source acting on the surface of a coated isotropic thermoelastic material is investigated in this paper to improve our understanding about the interface mechanisms of coating/substrate system. Based on the general solution of isotropic thermoelastic materials expressed by harmonic functions, the corresponding harmonic functions with undetermined constants for coating layer and semi-infinite substrate are constructed by the trial-and-error method, respectively. The thermoelastic field can be obtained by substituting the harmonic functions into the general solution. The constants can be determined by the boundary conditions of the surface and the continuous conditions of the interface between the coating layer with the semi-infinite substrate. Numerical results are exhibited in form of contours and some valuable conclusions for interface effect, interface debonding and stress field distortion are presented.

Application of the Staggered Cell-Vertex Finite Volume Method to Thermoelastic Analysis in Heterogeneous Materials

The two-dimensional (2D) staggered cell vertex finite volume method (CV-FVM) has been developed for unsteady thermoelastic problems in heterogeneous materials. The staggered grid technique is employed to incorporate property variation into the course of solution. The capabilities of methods for vibration analysis, unsteady thermoelastic analysis and elastic analysis with orthotropic materials have been validated. The applications of the method to functionally graded materials (FGMs), multi-phase materials with inclusions, and a thermal barrier coating (TBC) with a gradual FGMs layer or a graded microstructure layer have been accessed. The developed method provides accurate thermoelastic fields and avoids artificial discontinuous stress predictions in heterogeneous materials.

Numerical and experimental investigation of the influence of tumor size on laser-induced ultrasonics in soft tissue

The generation and propagation of laser-induced ultrasonic waves in soft tissue systems are investigated using the finite element method. Taking into account the effects of thermal diffusion, optical penetration, tumor elastic modulus and finite laser pulse duration, the transient temperature distribution is obtained. Using this temperature field as thermal loading in structural analysis, the thermoelastic stress field and laser-induced ultrasound waves in soft tissues are obtained. The results show that the intensity of the positive peak in the ultrasound wave increases and the arrival of the longitudinal wave takes place sooner as the tumor size becomes larger. It is also found that the duration of the laser ultrasound signal becomes shorter as the size of the tumor decreases. Meanwhile, the percentage of the received ultrasonic signal in the high-frequency region increases as the size of the tumor decreases, as has been proved by the experimental results.

Finite Difference Solution to Thermoelastic Field in a Thin Circular FGM Disk with a Concentric Hole

This study pays attention to the analysis of thermoelastic filed in a thin circular functionally graded material (FGM) disk with a concentric hole subjected to thermal loads. The material distribution in the disk is assumed to vary in the radial direction only. The mechanical and thermal properties of the FGM disk are simulated by the power function and exponential variation with the radius of the disk. As the range of variation of Poisson's ratio is small and its effect on the thermoelastic characteristics is negligible, it is reasonably assumed to be constant throughout the disk. Based on the two dimensional thermoelastic theories, the problem is reduced to the solution of a second order differential equation which is converted to a system of algebraic linear equations with the help of finite difference discretization. Solution of these equations is obtained by Gauss elimination method for an Al2O3/Al FGM disk. Numerical results of different components of stress and displacement are presented and analyzed. The analysis of the results reveals that the thermoelastic characteristics of an FGM disk are substantially dependant on material distribution as well as difference of temperatures at the inner and outer surfaces of the disk.

Modeling of Mechanical Influence of Double-Beam Laser on Single-Crystalline Silicon

Abstract The results of finite-element modeling of controlled laser thermosplitting of crystalline silicon are presented. The case of treatment by two laser beam with wavelengths, namely 0.808 μm and 1.06 μm is studied. Calculations of the thermoelastic fields formed in a single-crystalline silicon wafer as a result of consecutive two-beam laser heating and action of coolant were performed for silicon crystalline orientations: (100), (110), (111). Modeling was performed for circular and U-shaped laser beams. The results received in the presented work, can be used for the process optimization concerning the precise separation of silicon wafers by laser cutting.

A coupled cohesive zone model for transient analysis of thermoelastic interface debonding

A coupled cohesive zone model based on an analogy between fracture and contact mechanics is proposed to investigate debonding phenomena at imperfect interfaces due to thermomechanical loading and thermal fields in bodies with cohesive cracks. Traction-displacement and heat flux–temperature relations are theoretically derived and numerically implemented in the finite element method. In the proposed formulation, the interface conductivity is a function of the normal gap, generalizing the Kapitza constant resistance model to partial decohesion effects. The case of a centered interface in a bimaterial component subjected to thermal loads is used as a test problem. The analysis focuses on the time evolution of the displacement and temperature fields during the transient regime before debonding, an issue not yet investigated in the literature. The solution of the nonlinear numerical problem is gained via an implicit scheme both in space and in time. The proposed model is finally applied to a case study in photovoltaics where the evolution of the thermoelastic fields inside a defective solar cell is predicted.

On 2D Green's functions for 1D hexagonal quasi-crystals

This paper cokncerns itself with two-dimensional fundamental solutions for infinite and semi-infinite planes, subjected to point heat sources, of one-dimensional hexagonal quasi-crystals. From the basic equations for plane problem in the context of thermo-elasticity of QCs, the rigors operator theory and generalized Almansi's theorem are employed to derive the general solutions in terms of four quasi-harmonic functions. In the framework of the present general solutions, three concreted examples are investigated. Appropriate potentials are set by the trail-and-error technique, and corresponding fundamental thermo-elastic fields are obtained in a complete and exact fashion. Since the fundamental solutions are all in elementary functions, the present solutions not only bear theoretical merits, but also can serve as benchmarks to clarify various approximate methods.

Three-Dimensional Steady-State General Solution for Isotropic Thermoelastic Materials with Applications II: Green's Functions for Two-Phase Infinite Body

Green's function for isotropic thermoelastic two-phase infinite body under a point heat source is established in this paper. By virtue of the compact general solution compact which is expressed in harmonic functions, six new suitable harmonic functions with undetermined constants are constructed for the two semi-infinite bodies of two-phase infinite body. The corresponding thermoelastic field can be obtained by substituting these harmonic functions into the general solutions. And the undetermined constants can be obtained by the equilibrium conditions and compatibility conditions for both perfectly bonded interface and smooth contact interface. Numerical results are given graphically by contours.

Transformed function representations of plane solutions for anisotropic elasticity and thermoelasticity

Abstract A generalized two-dimensional deformation of an anisotropic elastic solid is considered. The transformed function method is employed to remove the breakdown limitation of the Stroh formalism for a degenerate anisotropic solid with multiple characteristic roots. The anisotropic elastic formalism for a general solution of elastic fields does not breakdown, and the closed form expressions of elastic fields for the degenerate anisotropic materials are obtained. A general solution of the thermoelastic fields in an anisotropic material under steady-state heat conduction is also derived. The thermoelastic formalism is shown to be valid for an anisotropic solid with distinct thermoelastic characteristic roots and a degenerate anisotropic solid with multiple thermoelastic characteristic roots.

Two-dimensional steady-state general solution for isotropic thermoelastic materials with applications. II. Green’s function for two-phase infinite plane

Green’s function for isotropic thermoelastic two-phase infinite plane under a line heat source is established in this paper. By virtue of the fourth compact general solutions in Part I which is expressed in three harmonic functions, six new suitable harmonic functions with undetermined constants are constructed for the two semi-infinite planes of the two-phase infinite plane, respectively. The corresponding thermoelastic field can be obtained by substituting these harmonic functions into the general solution, and the undetermined constants can be determined by compatibility conditions and the equilibrium conditions. Numerical results are given graphically by contours.

Thermally conducting collinear cracks engulfed by thermomechanical field in a material with orthotropy

The problem of two collinear cracks in an orthotropic solid is investigated under applied mechanical and uniform heat flow loadings. The thermal medium crack model is applied to address the effects of the medium inside cracks. Applying the Fourier transform technique, the boundary-valve problem is reduced to solving triple integral equations, then to solving singular integral equations with the Cauchy kernel. The crack-tip thermoelastic fields involving of the strain energy density (SED) factors, the stress intensity factors, the jumps of temperature and elastic displacements across the cracks are given in closed forms. Numerical results are carried out to show the influences of applied mechanical loading and thermal conductivity of crack interior on the thermal stress intensity factors, the temperature change across crack faces and the strain energy density factors. The results reveal that the crack-tip thermoelastic fields are dependent on applied thermo-mechanical loadings and the thermophysical properties of crack interior. The crack-face thermal property is important and it should not be disregarded in analyzing thermoelastic problems of a cracked solid under a thermal loading.

The MFS–MPS for two-dimensional steady-state thermoelasticity problems

Abstract We consider the numerical approximation of the boundary and internal thermoelastic fields in the case of two-dimensional isotropic linear thermoelastic solids by combining the method of fundamental solutions (MFS) with the method of particular solutions (MPS). A particular solution of the non-homogeneous equations of equilibrium associated with a planar isotropic linear thermoelastic material is derived from the MFS approximation of the boundary value problem for the heat conduction equation. Moreover, such a particular solution enables one to easily develop analytical solutions corresponding to any two-dimensional domain occupied by an isotropic linear thermoelastic solid. The accuracy and convergence of the proposed MFS–MPS procedure are validated by considering three numerical examples.

Thermoelastic in-plane fields in a linear anisotropic solid

Linear anisotropic thermoelastic in-plane problems are considered. A new formalism for general solutions of in-plane thermoelastic fields that satisfy the equilibrium equation and the steady state heat conduction equation is obtained in terms of analytic functions. The anisotropic thermoelastic formalism does not break down for a degenerate anisotropic thermoelastic solid with multiple characteristic roots, in contrast to the known solutions. An orthotropy rescaling technique is developed to determine the dependence of thermoelastic fields on the one dimensionless orthotropy parameter. The complete thermoelastic fields for the original problem can be evaluated from the solutions of the transformed problem by linear transformation with orthotropy rescaling. Thermal stresses in a simply connected anisotropic thermoelastic solid are investigated. Thermal stresses for the case of no mechanical loading anywhere on the boundary are expressed in terms of two dimensionless functions. The two dimensionless functions are shown to depend on only six dimensionless material parameters.

The conductivity, dielectric permittivity, and electric module of erbium formate crystallohydrate at frequencies of 0.07 Hz-1 MHz

The influence of heating after sharp cooling to −60°C on the low-frequency dielectric response of erbium formate crystallohydrate is investigated. Such research has been performed previously for objects of different chemical natures and structural organizations (in colemanite, diglycinenitrate, triglycinetellurate crystals, and several polymers with water). There is one structural fragment in these substances, viz., a weak hydrogen bond O...H-O that is 0.26–0.29 nm in length. A common feature of these measurements is a sharp increase of dielectric permittivity of the orders at frequencies of 0.1–4 Hz close to 0°C, upon heating after sharp cooling, and decay in the region of 40°C. To explain similar phenomena one can use the deformation model of the double minimum potential in the field of the thermoelastic stresses and other molecular fields.

Numerical Modelling of Microcracking in PV Modules Induced by Thermo-mechanical Loads

Micro-cracking in polycrystalline Silicon is a serious concern for the durability of photovoltaic (PV) modules due to the resulting electrical power-loss. In this contribution, a thermo-mechanical cohesive zone model is proposed to predict the evolution of micro-cracks under the action of mechanical and thermal loads. The classical nonlinear cohesive zone approach, used in fracture mechanics to depict the phenomenon of cracking as a result of progressive breakage of atomic bonds, is extended to thermo-elastic fields. The additional thermal resistance of micro-cracks due to imperfect bonding is estimated according to an analogy with a contact mechanics formulation, where the dependency on the crack opening is suitably accounted for. A numerical example shows the applicability of the proposed approach to practical problems.

Two-dimensional Green’s functions for semi-infinite isotropic thermoelastic plane

Based on the two-dimensional steady-state governing equations of isotropic thermoelastic material and the compact general solution expressed in three harmonic functions, the corresponding three harmonic functions contain nine undetermined constants are constructed for a line heat source applied in the interior of a semi-infinite thermoelastic plane. All components of thermoelastic field in the semi-infinite plane can be derived by substituting the harmonic functions into the general solution. And the undetermined constants can be obtained by the compatibility conditions, equilibrium conditions and the different boundary conditions for extended Mindlin problem and extended Lorentz problem. Thus, the Green’s functions in above two cases are obtained, and the numerical results are given graphically by contours.