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Stress-heat flux characterization of linear dynamic coupled thermoelasticity for an inhomogeneous isotropic infinite cylinder under plane strain conditions and zero heat-flux normal to the plane is presented. It is shown that for a bounded cross-section of the cylinder, a 3D stress-heat flux process is generated by a 2D one, and a uniqueness theorem for the associated 2D initial-boundary value problem is established. In addition, an asymptotic approach to the 2D stress-heat flux initial-boundary value problem, in the form of a power series with respect to a small thermoelastic coupling field, is proposed. Also, Green' s formulas for time-periodic complex-valued solutions to 2D stress-heat flux field equations are obtained; and the existence of a globally constrained real-valued periodic and attenuated on the time-axis stress-heat flux mode satisfying homogeneous natural boundary conditions is proved. The stress-heat flux characterization covers a large class of FGM's with physical properties smoothly distributed over the cross-section of the infinite cylinder. The results obtained are complementary to those of linear dynamic coupled thermoelasticity published up to date and should prove useful for a number of researchers in the field. [ABSTRACT FROM AUTHOR]

A nonlinear rigid heat conductor obeying the first and second laws of thermodynamics, Cattaneo's law, and a generalized energy-entropy relation in which both the energy and entropy are parabolic functions of the heat flux, is revisited. For a one-dimensional Cauchy problem in which both the temperature and heat flux are time-dependent only, a solution in terms of elementary functions is obtained. Also, for a one-dimensional traveling wave problem, a solution in terms of elementary functions is presented. Graphs illustrating the solutions are included. [ABSTRACT FROM AUTHOR]

The second law of thermodynamics asserts that heat will always flow “downhill”, i.e., from an object having a higher temperature to one having a lower temperature. For a parabolic rigid heat conductor with a single temperature T and a single heat-flux q this amounts to the statement that the inner product of q and ∇T must be non-positive for every point x of the conductor and for every non-negative time t. For a homogeneous and isotropic body in which classical Fourier law with a heat conductivity coefficient k is postulated, the second law is satisfied if k is a positive parameter. For ultra-fast pulse-laser heating on metal films, a parabolic two-temperature model coupling an electron temperature T e with a metal lattice temperature T l has been proposed by several authors. For such a model, at a given point of space x and a given time t there are two different temperatures T e and T l as well as two different heat-fluxes q e and q l related to the gradients of T e and T l , respectively, through classical Fourier law. As a result, for a homogeneous and isotropic model the positive definiteness of the heat conductivity coefficients k e and k l corresponding to T e and T l , respectively, implies that the second law of thermodynamics is satisfied for each of the pairs (T e , q e ) and (T l , q l ), separately. Also, the positive definiteness of k e and k l , and of the corresponding heat capacities c e and c l as well as of a coupling factor G imply that a temperature initial-boundary value problem for the two-temperature model has unique solution. In the present paper, an alternative form of the second law of thermodynamics for the two-temperature model with k l = 0 and q l = 0 is obtained from which it follows that in a one-dimensional case the electron heat-flux q e (x, t) has direction that is opposite not only to that of ∂̸T e (x, t)/∂̸x but also to that of ∂̸T l (x, t + τ T )/∂̸x, where τ T is an intrinsic small time of the model. Also, for a general two-temperature rigid heat conductor in which k e , k l , c e , c l , and G are positive, an inequality of the second law of thermodynamics type involving a pair (T e - T l , q e - q l ) is postulated to prove that a two-heat-flux initial-boundary value problem of the two-temperature model has a unique solution. For a one-dimensional case, the semi-infinite sectors of the plane ( q l , q e ) over which uniqueness does not hold true are also revealed. [ABSTRACT FROM AUTHOR]

In previous work a one-dimensional averaged theory of thermoelastic waves in a microperiodic layered infinite solid was proposed in which an eighth-order-in-time partial differential equation involving a high intrinsic mechanical frequency ΩM and a high intrinsic thermal frequency ΩT is a central equation. Also, the existence of two harmonic thermoelastic waves of a given frequency ω propagating in a positive direction normal to the layering was previously established when &OHgr;M&ThickSpace;→&ThickSpace;∞ and &OHgr;T&ThickSpace;<&ThickSpace;∞, or &OHgr;M&ThickSpace;<&ThickSpace;∞ and &OHgr;T&ThickSpace;→&ThickSpace;∞. The existence of two harmonic thermoelastic waves of a given frequency &ohgr; propagating in the positive direction normal to the layering is proved when &OHgr;M&ThickSpace;<&ThickSpace;∞ and &OHgr;T&ThickSpace;<&ThickSpace;∞. Also, a closed form of the associated velocities and attenuation coefficients is obtained. Numerical results illustrating propagation of the two waves in a particular microperiodic layered thermoelastic solid are included. [ABSTRACT FROM AUTHOR]

A Saint-Venant's principle associated with a one-dimensional dynamic coupled thermoelastic effective modulus theory (EMT) for a microperiodic layered semispace was presented in J. Thermal Stresses, vol. 23, pp. 1–14, 2000. It was shown there that a thermoelastic energy associated with a solution to an initial boundary value problem of the theory decays exponentially as a distance x from the thermomechanical load region goes to infinity and that its decay length depends on the time t, an effective velocity , an effective time unit , and an effective thermoelastic coupling parameter <ε*>. In the present article the Saint-Venant's principle is extended to include a refined averaged theory (RAT) for a microperiodic layered thermoelastic semispace in which a microstructural length is taken into account (see [IFTR Report #25, pp. 1–158, 1995]). It is shown that for such an extended theory, a similar exponential decay estimate for a thermoelastic energy holds true. In the refined estimate the thermoelastic energy depends on a number of microstructural parameters while its decay length is independent of these parameters; and the decay length for small (large) times is comparable to that of a pure thermal (elastic) energy for a rigid (elastic) semispace for every time t > 0 . [ABSTRACT FROM AUTHOR]