Thermal stresses in micropolar elastic cylinders

Summary The present paper is concerned with the static problem in the linear theory of micropolar thermoelasticity for homogeneous and isotropic cylinders. The problem is solved using some results established in [1]–[5].

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Wärmespannungen in mikropolaren elastischen Zylindern

Zusammenfassung Die vorliegende Arbeit beschäftigt sich mit dem statischen Problem der linearen Theorie der mikropolaren Thermoelastizität für homogene und isotrope Zylinder. Das Problem wird mit Hilfe einiger in [1]–[5] enthaltenen Ergebnisse gelöst.

     

Overall elastoplastic property for micropolar composites with randomly oriented ellipsoidal inclusions

Overall linear and non-linear properties for micropolar composites containing 3D and in-plane randomly oriented inclusions are examined with an analytical micromechanical method. This method is based on Eshelby solution for a general ellipsoidal inclusion in a micropolar media and secant moduli method. The influence of inclusion’s shape, size and orientation on the classical effective moduli, yielding surface and non-linear stress and strain relation are examined. The results show that the effective moduli and non-linear stress–strain curves are always higher for micropolar composites than the corresponding classical composites. When the inclusion’s size is sufficiently large, the classical results can be recovered.     

Saint-Venant's problem for a micropolar elastic circular cylinder

In the present paper Saint-Venant's problem in the linear theory of micropolar elasticity is solved for a circular cylinder. Expressions for the macrodisplacement vector and microrotation vector are obtained.     

Almansi's problem in micropolar elasticity

The present paper is concerned with Almansi's problem in the linear theory of micropolar elasticity. The problem is solved using the results from [8], [10–13].     

Stability of periodic flow in a micropolar fluid

The stability of unidirectional periodic flow in a micropolar fluid is treated. An analytic expression is found for the critical Reynolds number of stability loss.Translated from Inzhenerno-fizicheskii Zhurnal, Vol. 60, No. 4, pp. 670–679, April, 1991.     

Numerical solution of thermal instability of a rotating micropolar fluid layer

In this paper, we have considered the thermal instability of a rotating, heat conducting, micropolar fluid layer heated from below and confined between two rigid boundaries. The onset of thermal instability is governed by a linear eigenvalue problem. The solution of the eigenvalue problem is obtained by using finite difference method and Wilkinson's iteration technique. The effects of rotation and micropolar parameters on the critical Rayleigh number and the wave number at the threshold of instability are discussed in detail.     

Boundary layer of a microstructural fluid on a plate

A numerical solution of the self-similar problem of the boundary layer of a micropolar model fluid on a semiinfinite plate is obtained.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 36, No. 1, pp. 121–126, January, 1979.     

Some applications of micropolar mechanics to earthquake problems

In this paper the theory of micropolar continua has been used to study some earthquake problems. In the first part of the paper the changes in the Earth's inertia tensor due to earthquake faulting are calculated by using a reciprocal relation. The case of a homogeneous and isotropic elastic Earth model is analyzed. The result is compared to that of the classical theory. In the second part of the paper the problem of body loadings equivalent to a seismic dislocation, in the framework of the linear theory of micropolar thermoelasticity, is studied.     

Three-dimensional linearized steady-state problems for micropolar viscous liquid media

Linearized steady-state boundary-value problems are posed within the micropolar (asymmetric) theory of liquid media, and analysis of their uniqueness is carried out.Belarusian State University, Minsk, Belarus. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 66, No. 5, pp. 617–621, May, 1994.     

Bernoulli theorem generalized to rheologically complex viscous fluid flow

The Bernoulli theorem is generalized to two-dimensional and axisymmetric micropolar incompressible fluid flows. It is shown that the approach developed is also applicable to magnetohydrodynamic flows of a viscous Newtonian fluid.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 63, No. 2, pp. 220–222, August, 1992.     

Heating of a micropolar liquid due to viscous energy dissipation in channels. II. Couette flow

The heating of a micropolar liquid due to viscous energy dissipation as it flows in a plane channel when one of the plates moves at a constant velocity relative to the other is investigated.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 46, No. 3, pp. 393–398, March, 1984.     

Decrease of resistance in a micropolar liquid

Modified equations of motion of a micropolar liquid are derived. It is shown that, in nonlinear problems, a lower resistance is possible in comparison with an ordinary liquid, even in the case of laminar flow.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 57, No. 2, pp. 213–219, August, 1987.     

Unsteady heat transfer in a micropolar fluid flowing in a plane channel

Heat transfer in a micropolar fluid flowing in a plane channel following an abrupt change in the wall temperature is investigated. The obtained results indicate that in several cases the fluid microstructure has a considerable effect on the main heat-transfer characteristics.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 37, No. 6, pp. 994–999, December, 1979.     

A variational criterion for micropolar fluids

A variational criterion for the study of micropolar continuous media in which dissipative phenomena occur is proposed. This criterion is an extension of Lebon-Lambermont's, which is recovered when the spin becomes zero (structureless media). The Euler-Lagrange equations obtained from the variational principle are the balance equations for a micropolar medium with microisotropy. As application of the criterion, one treats numerically the Poiseuille flow of a micropolar medium.     

Uniqueness and reciprocity theorems in generalized linear micropolar thermoviscoelasticity

A model of the equations of generalized linear micropolar thermoviscoelasticity is given. The formulation is applied to the coupled theory as well as to five generalizations, the Lord-Shulman theory with one relaxation time, the Green-Lindsay theory with two relaxation times, the Green-Naghdi theories of type II (without energy dissipation) and of type III, and the Chandrasekharaiah-Tzou theory with dual-phase-lag. Using Laplace transforms, a uniqueness theorem for this model is proved, restrictions on relaxation functions are deduced and the dynamic reciprocity theorem is derived. The cases of generalized linear micropolar thermoviscoelasticity of Kelvin-Voigt model, generalized linear micropolar thermoelasticity, generalized thermoviscoelasticity and generalized thermoelasticity can be obtained from the given general model.     

Influence of precipitations on elastic–plastic properties of Al alloys

The elastic–plastic behaviour of rapidly solidified Al-based Fe-enriched alloys containing intermetallic phase, subjected to densification is considered. The size of the intermetallic phase is taken into account through Cosserat matrix model combined with Cauchy inclusions model. The approach is based on the secant moduli method, modified for micropolar media and on density-dependent models for porous materials. The effect of the intermetallic phase volume fraction and its average diameter on densification and hardening behaviour of powder based aluminium alloy is investigated. The model is implemented as user defined subroutines into the FE code MARC.     

Some uniqueness and continuous dependence results in the micropolar mixture theory of porous media

The present paper studies the uniqueness and continuous data dependence of solutions of the initial-boundary value problem associated with the micropolar mixture linear theory of porous media. For a binary homogeneous mixture of an isotropic micropolar elastic solid with an incompressible micropolar viscous fluid, an uniqueness result is established. Then we deduce some estimates for describing the continuous dependence of solution with respect to the changes in the body force and body couple and in the initial-boundary given data. Thus, it is shown that the general approach of a binary homogeneous mixture of an isotropic micropolar elastic solid with an incompressible micropolar viscous fluid is well posed.     

Linear micropolar elastic crack-tip fields under mixed mode loading conditions

Micropolar elasticity laws provide a possibility to describe constitutive properties of materials for which internal length scales may become important. They are characterized by the presence of couple stresses and nonsymmetric Cauchy stress tensor. Beyond the classical displacement field, the kinematical variables are augmented by a so-called microrotation field and its gradient, the latter introducing an internal length scale in the theory. For an isotropic, linear micropolar elastic material, the near-tip asymptotic field solutions for mode I and mode II cracks are derived. It is shown that these solutions behave similar to those according to the so-called couple stress theory, which has been investigated by Huang et al. (1997a), or similar to those derived for cellular materials by Chen et al. (1998). In particular, the singular fields have an order of singularity r ^–1/2 and are governed by some amplitude factors, having the meaning of stress intensity factors as in the classical linear elastic theory. The effect of material parameters on the stress intensity factors is studied by applying the finite element method to calculate the values of the stress intensity factors for an edge-cracked specimen of finite width.     

Stability of linear micropolar elastic media

The theory of elastic stability of linear micropolar elastic media is examined. A functional is constructed which is suitable for the study of the stability of motion of linear micropolar elastic media. An example of stability of undeformed state is solved to show the applicability of the method. The uniqueness criteria are also discussed.     

Effect of rotation on a layer of micropolar ferromagnetic fluid heated from below saturating a porous medium

This paper deals with the theoretical investigation of the effect of rotation on a layer of micropolar ferromagnetic fluid heated from below saturating a porous medium subjected to a transverse uniform magnetic field. For a flat fluid layer contained between two free boundaries, an exact solution is obtained using a linear stability analysis theory and normal mode analysis method. For the case of stationary convection, the effect of various parameters like medium permeability, rotation, non-buoyancy magnetization, coupling parameter, spin diffusion parameter and micropolar heat conduction has been analyzed. The critical magnetic thermal Rayleigh number for the onset of instability are also determined numerically for sufficiently large values of magnetic parameter M₁ and results are depicted graphically. The principle of exchange of stabilities is found to hold true for the micropolar ferromagnetic fluid saturating a porous medium heated from below in the absence of micropolar viscous effect, microinertia and rotation. The oscillatory modes are introduced due to the presence of the micropolar viscous effect, microinertia and rotation, which were non-existent in their absence. The sufficient conditions for the non-existence of overstability are also obtained.