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1.
An energy approach is proposed to derive the physical constitutive equations of nonlinear thermomechanics for inertial elastic
systems. A potential of local inertial thermodynamic state and a potential of thermoelastic energy dissipation are introduced.
The variational formulation of nonlinear boundary problems of thermoelasticity is implemented on the basis of the Hamiltonian
energy functional. Sufficient conditions for the convexity of the functional are formulated
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Translated from Prikladnaya Mekhanika, Vol. 41, No. 9, pp. 52–59, September 2005. 相似文献
2.
We present the theory of space–time elasticity and demonstrate that it is the extended reversible thermodynamics and gives the coupled model of thermoelasticity and heat conductivity and involves traditional thermoelasticity. We formulate the generally covariant variational model’s dynamic thermoelasticity and heat conductivity in which the basic kinematic and static variables are unified tensor objects (subject, matter). Variation statement defines the whole set of the initial-boundary problems for the 4D vector governing equation (Euler equation), the spatial projections of which define motion equations and the time projection gives the heat conductivity equation. We show that space–time elasticity directly implies the Fourier and the Maxwell–Cattaneo laws of heat conduction. However, space–time elasticity is richer than classical thermoelasticity, and it advocates its own equations of motion for coupled thermoelasticity. Moreover, we establish that the Maxwell–Cattaneo law and Fourier law can be defined for the reversible processes as compatibility equations without introducing dissipation. We argue that the present framework of space–time elasticity should prove adequate to describe the thermoelastic phenomena at low temperatures for interpreting the results of molecular simulations of heat conduction in solids and for the optimal heat and stress management in the microelectronic components and the thermoelectric devices. 相似文献
3.
In the early 1990s, Green and Naghdi introduced a theory attracting interest as heat propagates as thermal waves at finite
speed and does not necessarily involve energy dissipation. Another outstanding property of the so-called theory of type II
is the fact that the entropy flux vector is determined by means of the same potential as the mechanical stress tensor. Motivated
by the procedure of [9, 15], we formulate a variational formulation within the incremental framework for coupled thermoelasticity for type I mimicing
type II. The entropy flux of type II is determined via the free energy acting as a potential. This is not possible for the
classical Fourier case in the continuous setting. Therefore, we target a derivation of an incremental entropy flux following
Fourier’s law by means of incremental potentials similar to the spirit of the theory of the non-dissipative Green–Naghdi-type
II. Subsequently, we show that the resulting update algorithm is a convenient fully coupled finite element formulation of
the proposed thermoelastic problem. 相似文献
4.
Coupled nonlinear constitutive models for rarefied and microscale gas flows: subtle interplay of kinematics and dissipation effects 总被引:1,自引:0,他引:1
R. S. Myong 《Continuum Mechanics and Thermodynamics》2009,21(5):389-399
The constitutive relations of gases in a thermal nonequilibrium (rarefied and microscale) can be derived by applying the moment
method to the Boltzmann equation. In this work, a model constitutive relation determined on the basis of the moment method
is developed and applied to some challenging problems in which classical hydrodynamic theories including the Navier–Stokes–Fourier
theory are shown to predict qualitatively wrong results. Analysis of coupled nonlinear constitutive models enables the fundamentals
of gas flows in thermal nonequilibrium to be identified: namely, nonlinear, asymmetric, and coupled relations between stresses
and the shear rate; and effect of the bulk viscosity. In addition, the new theory explains the central minimum of the temperature
profile in a force-driven Poiseuille gas flow, which is a well-known problem that renders the classical hydrodynamic theory
a global failure. 相似文献
5.
Reza Mirzaeifar Reginald DesRoches Arash Yavari 《Continuum Mechanics and Thermodynamics》2011,23(4):363-385
In this paper, the coupled thermo-mechanical response of shape memory alloy (SMA) bars and wires in tension is studied. By
using the Gibbs free energy as the thermodynamic potential and choosing appropriate internal state variables, a three-dimensional
phenomenological macroscopic constitutive model for polycrystalline SMAs is derived. Taking into account the effect of generated
(absorbed) latent heat during the forward (inverse) martensitic phase transformation, the local form of the first law of thermodynamics
is used to obtain the energy balance relation. The three-dimensional coupled relations for the energy balance in the presence
of the internal heat flux and the constitutive equations are reduced to a one-dimensional problem. An explicit finite difference
scheme is used to discretize the governing initial-boundary-value problem of bars and wires with circular cross-sections in
tension. Considering several case studies for SMA wires and bars with different diameters, the effect of loading–unloading
rate and different boundary conditions imposed by free and forced convections at the surface are studied. It is shown that
the accuracy of assuming adiabatic or isothermal conditions in the tensile response of SMA bars strongly depends on the size
and the ambient condition in addition to the rate dependency that has been known in the literature. The data of three experimental
tests are used for validating the numerical results of the present formulation in predicting the stress–strain and temperature
distribution for SMA bars and wires subjected to axial loading–unloading. 相似文献
6.
Alexander Vatulyan Sergey Nesterov Rostislav Nedin 《Continuum Mechanics and Thermodynamics》2020,32(4):1173-1186
In present research, we investigate dynamic coupled thermoelasticity problem for a “coating-substrate” system. We present a number of models of thermoelastic deformation of the “coating-substrate” system with thermomechanical characteristics which may vary both continuously and discontinuously. To solve these problems, we use the variational principle of coupled thermoelasticity in the Laplace transforms space and hypotheses on a distribution of temperature and displacements transforms. The transforms inversion is realized according to the Durbin method. The calculations were carried out based on both proposed simplified models and FEM. 相似文献
7.
Ibrahim A. Abbas 《Archive of Applied Mechanics (Ingenieur Archiv)》2009,79(1):41-50
In this paper, we constructed the equations of generalized magneto-thermoelasticity in a perfectly conducting medium. The
formulation is applied to generalizations, the Lord–Shulman theory with one relaxation time, and the Green–Lindsay theory
with two relaxation times, as well as to the coupled theory. The material of the cylinder is supposed to be nonhomogeneous
isotropic both mechanically and thermally. The problem has been solved numerically using a finite element method. Numerical
results for the temperature distribution, displacement, radial stress, and hoop stress are represented graphically. The results
indicate that the effects of nonhomogeneity, magnetic field, and thermal relaxation times are very pronounced. In the absence
of the magnetic field or relaxation times, our results reduce to those of generalized thermoelasticity and/or classical dynamical
thermoelasticity, respectively. Results carried out in this paper can be used to design various nonhomogeneous magneto-thermoelastic
elements under magnetothermal load to meet special engineering requirements.
An erratum to this article can be found at 相似文献
8.
We prove the global existence of solutions for a shape-memory alloys constitutive model at finite strains. The model has been
presented in Evangelista et al. (Int J Numer Methods Eng 81(6):761–785, 2010) and corresponds to a suitable finite-strain version of the celebrated Souza–Auricchio model for SMAs (Auricchio and Petrini
in Int J Numer Methods Eng 55:1255–1284, 2002; Souza et al. in J Mech A Solids 17:789–806, 1998). We reformulate the model in purely variational fashion under the form of a rate-independent process. Existence of suitably
weak (energetic) solutions to the model is obtained by passing to the limit within a constructive time-discretization procedure. 相似文献
9.
L. P. Khoroshun 《International Applied Mechanics》2008,44(2):121-133
Thermodynamic and statistical methods for setting up the constitutive equations describing the viscoelastoplastic deformation
and hardening of materials are proposed. The thermodynamic method is based on the law of conservation of energy, the equations
of entropy balance and entropy production in the presence of self-balanced internal microstresses characterized by conjugate
hardening parameters. The general constitutive equations include the relationships between the thermodynamic flows and forces,
which follow from nonnegative entropy production and satisfy the generalized Onsager’s principle, and the thermoelastic relations
and the expression for entropy, which follow from the law of conservation of energy. Specific constitutive equations are derived
by representing the dissipation rate as a sum of two terms responsible for kinematic and isotropic hardening and approximated
by power and hyperbolic-sinus functions. The constitutive equations describing viscoelastoplastic deformation and hardening
are derived based on stochastic microstructural concepts and on the linear thermoelasticity model and nonlinear Maxwell model
for the spherical and deviatoric components of microstresses and microstrains, respectively. The problem of determining the
effective properties and stress-strain state of a three-component material found using the Voigt-Reuss scheme leads to constitutive
equations similar in form to those produced by the thermodynamic method
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Translated from Prikladnaya Mekhanika, Vol. 44, No. 2, pp. 3–18, February 2008. 相似文献
10.
A model of the equations of a generalized thermoelasticity (GT) with relaxation times for a saturated porous medium is given
in this article. The formulation can be applied to the GT theories: Lord–Shulman theory, Green–Lindsay theory, and Coupled
theory for the porous medium. A two-dimensional thermoelastic problem that is subjected to a time-dependent thermal/mechanical
source is investigated with the model of the generalized porous thermoelasticity. By using the Laplace transform and the Fourier
transform technique, solutions for the displacement, temperature, pore pressure, and stresses are obtained with a semi-analytical
approach in the transform domain. Numerical results are also performed for portraying the nature of variations of the field
variables. In addition, comparisons are presented with the corresponding four theories. 相似文献
11.
The normality structure proposed by [Rice, J.R., 1971. Inelastic constitutive relations for solids: an integral variable theory and its application to metal plasticity. J. Mech. Phys. Solids 19, 433–455.] provides a minimal framework of multiscale thermodynamics. As shown in this paper, Rice’s multiscale thermodynamic formalism is exactly consistent with Ziegler’s essential notion [Ziegler, H., 1977. An Introduction to Thermomechanics, North-Holland, Amsterdam.] that the entire constitutive response is determined by the knowledge of two scalar potential functions: an energy function and a dissipation function. In Rice’s multiscale thermodynamic formulation, the variational equation relating macroscale and microscale thermodynamic fluxes and forces plays a central role and ensures the equality between microscale and macroscale dissipation rate. The variational equation can be further reformulated into a principle of maximum equivalent dissipation. Based on the variation equation, the transformation from microscale to macroscale is characterized by two linear transformations with the same corresponding matrix. 相似文献
12.
The goal of this paper is to present a flexible multibody formulation for Euler-Bernoulli beams involving large displacements. This method is based on a discretisation of internal and kinetic energies. The beam is represented by its line of centroids and each section is oriented by a frame defined by three Euler angles. We apply a finite element formulation to describe the evolution of these angles along the neutral fibre and describe the internal energy. The kinetic energy is approximated as the one of two rigid bars tangent to the neutral fibre at the ends of the beam. We derive the equations of motion from a Lagrange formulation. These equations are solved using the Newmark method or/and the Newton-Raphson technique. We solve some very classic problems taken from the literature as the curved beam presented by Simo [Simo, J. C., ‘A three-dimensional finite-strain rod model. the three-dimensional dynamic problem. Part I’, Comput. Meths. Appl. Mech. Engrg.
49, 1985, 55–70; Simo, J. C. and Vu-Quoc, L., ‘A three-dimensional finite-strain rod model, Part II: Computationals aspects’, Comput. Meths. Appl. Mech. Engrg.
58, 1988, 79–116] and Lee [Lee, Kisu, ‘Analysis of large displacements and large rotations of three-dimensional beams by using small strains and unit vectors’, Commun. Numer. Meth. Engrg.
13, 1997, 987–997] or the rotational rod presented by Avello [Avello, A., Garcia de Jalon, J., and Bayo, E., ‘Dynamics of flexible multibody systems using cartesian co-ordinates and large displacement theory’, Int. J. Num. Methods in Engineering
32, 1991, 1543–1563] and Simo [Simo, J. C. and Vu-Quoc, L., ‘On the dynamics of flexible beams under large overall motions – the planar case. Part I’ Jour. of Appl. Mech.
53, 1986, 849–854; Simo, J. C. and Vu-Quoc, L., ‘On the dynamics of flexible beams under large overall motions – the planar case. Part II’, Jour. of Appl. Mech.
53, 1986, 855–863]. 相似文献
13.
In Part I Moyne and Murad [Transport in Porous Media 62, (2006), 333–380] a two-scale model of coupled electro-chemo-mechanical phenomena in swelling porous media was derived by
a formal asymptotic homogenization analysis. The microscopic portrait of the model consists of a two-phase system composed
of an electrolyte solution and colloidal clay particles. The movement of the liquid at the microscale is ruled by the modified
Stokes problem; the advection, diffusion and electro-migration of monovalent ions Na+ and Cl− are governed by the Nernst–Planck equations and the local electric potential distribution is dictated by the Poisson problem.
The microscopic governing equations in the fluid domain are coupled with the elasticity problem for the clay particles through
boundary conditions on the solid–fluid interface. The up-scaling procedure led to a macroscopic model based on Onsager’s reciprocity
relations coupled with a modified form of Terzaghi’s effective stress principle including an additional swelling stress component.
A notable consequence of the two-scale framework are the new closure problems derived for the macroscopic electro-chemo-mechanical
parameters. Such local representation bridge the gap between the macroscopic Thermodynamics of Irreversible Processes and
microscopic Electro-Hydrodynamics by establishing a direct correlation between the magnitude of the effective properties and
the electrical double layer potential, whose local distribution is governed by a microscale Poisson–Boltzmann equation. The
purpose of this paper is to validate computationally the two-scale model and to introduce new concepts inherent to the problem
considering a particular form of microstructure wherein the clay fabric is composed of parallel particles of face-to-face
contact. By discretizing the local Poisson–Boltzmann equation and solving numerically the closure problems, the constitutive
behavior of the diffusion coefficients of cations and anions, chemico-osmotic and electro-osmotic conductivities in Darcy’s
law, Onsager’s parameters, swelling pressure, electro-chemical compressibility, surface tension, primary/secondary electroviscous
effects and the reflection coefficient are computed for a range particle distances and sat concentrations. 相似文献
14.
A. V. Yasinskii 《International Applied Mechanics》2008,44(1):34-40
The problem of identifying the law of time variation in the temperature of one boundary surface of a two-layer cylinder and
its thermal and thermostressed state from the temperature and radial displacement of the other surface is formulated and solved.
The inverse problem of thermoelasticity to which the problem posed is reduced is analyzed for well-posedness. The solution
of the direct problem of thermoelasticity is used to numerically test the technique of solving the inverse problem
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Translated from Prikladnaya Mekhanika, Vol. 44, No. 1, pp. 40–47, January 2008. 相似文献
15.
16.
A variational formulation of the coupled thermo-mechanical boundary-value problem for general dissipative solids 总被引:2,自引:0,他引:2
A variational formulation of the coupled thermo-mechanical boundary-value problem for general dissipative solids is presented. The coupled thermo-mechanical boundary-value problem under consideration consists of the equilibrium problem for a deformable, inelastic and dissipative solid with the heat conduction problem appended in addition. The variational formulation allows for general dissipative solids, including finite elastic and plastic deformations, non-Newtonian viscosity, rate sensitivity, arbitrary flow and hardening rules, as well as heat conduction. We show that a joint potential function exists such that both the conservation of energy and the balance of linear momentum equations follow as Euler-Lagrange equations. The identification of the joint potential requires a careful distinction between equilibrium and external temperatures, which are equal at equilibrium. The variational framework predicts the fraction of dissipated energy that is converted to heat. A comparison of this prediction and experimental data suggests that α-titanium and Al2024-T conform to the variational framework. 相似文献
17.
M. B. Babenkov 《Journal of Applied Mechanics and Technical Physics》2011,52(6):941-949
Dispersion relations for a coupled thermoelasticity problem including a hyperbolic heat conduction equation are derived, and their asymptotic analysis is performed. Dependences of the wave number and characteristics of the vibration damping rate on frequency are obtained and compared with similar diagrams in the classical model. 相似文献
18.
19.
A boundary-value problem of coupled thermoelasticity for a half-layer with a hole and mixed boundary conditions is solved.
The problem is reduced to a system of four singular integral equations. It is solved numerically using the mechanical-quadrature
method. A numerical experiment is conducted to study the dynamic stress concentration around cavities of different cross sections.
The effect of the coupled thermal and elastic fields on the wave processes in the body is established
Translated from Prikladnaya Mekhanika, Vol. 44, No. 10, pp. 28–36, October 2008. 相似文献
20.
We consider a series of problems with a short laser impact on a thin metal layer accounting various boundary conditions of the first and second kind. The behavior of the material is modeled by the hyperbolic thermoelasticity of Lord–Shulman type. We obtain analytical solutions of the problems in the semi-coupled formulation and numerical solutions in the coupled formulation. Numerical solutions are compared with the analytical ones. The analytical solutions of the semi-coupled problems and numerical solutions of the coupled problems show qualitative match. The solutions of hyperbolic thermoelasticity problems are compared with those obtained in the frame of the classical thermoelasticity. It was determined that the most prominent difference between the classical and hyperbolic solutions arises in the problem with fixed boundaries and constant temperature on them. The smallest differences were observed in the problem with unconstrained, thermally insulated edges. It was shown that a cooling zone is observed if the boundary conditions of the first kind are given for the temperature. Analytical expressions for the velocities of the quasiacoustic and quasithermal fronts as well as the critical value for the attenuation coefficient of the excitation impulse are verified numerically. 相似文献