Propagation of Thermoelastic Waves in Micropolar Mixture of Porous Media

The theory of coupled thermoelasticity for a micropolar mixture of porous media (Eringen AC, J Appl Phys 94:909, 2003) is generalized in the context of Lord and Shulman and Green and Lindsay theories of generalized thermoelasticity. The governing equations of generalized thermoelasticity of a micropolar mixture of porous media are solved to show the existence of three coupled longitudinal displacement waves, two coupled longitudinal microrotational waves, and six coupled transverse waves, which attenuate and are dispersive in nature.     

Transient Response in a Micropolar Mixture of Porous Media During Thermal Shock

In this article, the micropolar mixture theory for porous media is generalized in the context of generalized L-S theory and classical C-T theory of thermoelasticity. The thermoelastic problem for a micropolar mixture of porous media is investigated in the context of the generalized micropolar mixture theory for porous media. The surface of a semi-infinite porous media is subjected to a zonal time-dependent thermal shock. The problem is solved by using the finite element method. The results, including the temperature, stresses, displacements, and microrotation are presented graphically. Comparisons are made between the results obtained by using two theories. The fluid constituting the mixture has a significant influence on the microrotation but a very slight influence on other responses.     

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.     

Free convection boundary layer flow of a micropolar fluid past slender bodies

The transverse curvature effects on axisymmetric free convection boundary layer flow of a micropolar fluid past vertical cylinders are investigated using the theory of micropolar fluids formulated by Eringen. The governing equations for momentum, angular momentum and energy have been solved numerically. Missing values of the velocity, angular velocity and thermal functions are tabulated for a wide range of the material parameters, transverse curvature parameter and Prandtl number of the fluid. A comparison has been made with the corresponding results for Newtonian fluids. Micropolar fluids display drag reduction and reduced surface heat transfer rate as compared with Newtonian fluids.     

Reflection and transmission of waves from a plane interface between two microstretch solid half-spaces

In this paper, we have investigated the wave propagation and their reflection and transmission from a plane interface between two different microstretch elastic solid half-spaces in perfect contact. It is shown that there exist five waves in a linear homogeneous isotropic microstretch elastic solid, one of them travel independently, while other waves are two sets of two coupled waves. It is also shown that these waves travel with different velocities, three of which disappear below a critical frequency. Amplitude ratios and energy ratios of various reflected and transmitted waves are presented when a set of coupled longitudinal waves and a set of coupled transverse waves is made incident. It is found that the amplitude ratios of reflected and transmitted waves are functions of angle of incidence, frequency and are affected by the elastic properties of the media. Some special cases have been reduced from the present formulation.     

The propagation of plane waves in bilevel anisotropic elastic solids with nonlocal polar constitution

In analyzing problems involving material behavior from the standpoint of generalized continuum mechanics, one is often faced with different forms of anisotropy at different levels of microscopic and macroscopic aggregates within the same material. In this article, a continuum theory incorporating nonlocal effects within the microstructure of anisotropic solids is developed. In order to illustrate the mathematical development of the theory in practical applications, the theory is applied to the case of materials possessing orthotropy on the nonlocal micropolar level and transverse isotropy on the local micropolar level. This case may apply to materials such as wood and wood composites. The resulting field equations are solved for the propagation of plane waves in a bilevel, anisotropic, nonlocal, micropolar elastic solid.     

Propagation and decay of acceleration waves in thermoconsolidating media

Summary The propagation of acceleration waves in a fluid-saturated porous medium is considered. The two-phase medium is the system consisting of a porous elastic solid skeleton, filled with a viscous compressible fluid. Two types of the media are taken into account: the medium composed of definite conductors and the medium composed of non-conductors. The method of singular surfaces has been used in these considerations. The acceleration waves in the medium consisting of non-conductors are not homentropic, in general. In this paper the conditions are determined which must be fulfilled to satisfy the acceleration waves to be homentropic.The propagation conditions of the waves are formulated and analysed. As usual in such a two-phase medium two longitudinal waves and one transverse wave are propagated. The growth equations of homothermal and homentropic waves are derived, and their solutions are analysed.     

Hygrothermomechanical evaluation of porous media under finite deformation. Part I - finite element formulations

The coupled thermomechanical responses of fluid-saturated porous continua subjected to finite deformation are investigated. Field equations governing the transient response of the media are derived from a continuum thermodynamics mixture theory based on mass balance, momentum balance and energy balance laws as well as the Clausius-Duhem inequality. Finite element procedures for the two-dimensional response, employing updated Lagrangian formulations for the solid skeleton deformation and the weak formulations for fluid and thermal transport equations, are implemented in a fully implicit form. Temperature-dependent mechanical properties for the non-linear solid matrix, characterized by Perzyna's viscoplastic model, are assumed. An iterative scheme based on the full Newton-Raphson method is presented for simultaneously solving the coupled non-linear equations.     

Evaluation of the Micropolar elasticity constants for honeycombs

Summary The Micropolar and Lamè constants for a circular cell polycarbonate honeycomb are calculated using a finite element representation of the honeycomb microstructure. A hexagonally packed, circular cell, honeycomb sheet with a rigid circular inclusion was numerically analyzed under uniaxial tension. Micropolar Elasticity was found to be the best continuum representation of the discrete honeycomb. This conclusion was arrived at by matching the strain field in the discrete honeycomb with that predicted by a micropolar elastic continuum representation of the honeycomb. The minimum ratio of inclusion radius a to cell diameter d, for the honeycomb to be approximated accurately as a continuum was between 16 and 20. A radius of 20d and 32d showed a near perfect approximation to a continuum.     

A note on energy flux in micropolar elastic waves

The expressions for the time average power per unit area, the kinetic energy per unit volume, strain energy per unit volume and velocity of energy flux are derived for the case of a plane time harmonic micropolar elastic waves and it has been shown that the time-average energy density is equally divided between the time-averages of the kinetic and strain energy densities. The energy ratios of reflected micropolar elastic waves with the angle of emergence of incident longitudinal displacement wave have been shown graphically.     

On the bending of micropolar viscoelastic plates

The theory of micropolar elastic plates has been established by [A.C. Eringen, Linear theory of micropolar viscoelasticity, Int. J. Engng. Sci. 5 (1967) 191–204]. The present paper is concerned with the bending of micropolar viscoelastic plates within the dynamic theory. First, the basic equations of the bending theory of viscoelastic thin plates are presented. Then, a variational characterization of solutions and a minimum principle of Reiss type are established.     

Wave Propagation in a Green–Naghdi Thermoelastic Solid with Diffusion

The Green and Naghdi theory of thermoelasticity is applied to study plane-wave propagation in an elastic solid with thermo-diffusion. The governing equations of an elastic solid with generalized thermo-diffusion are solved to show the existence of three coupled longitudinal waves and a shear vertical (SV) wave in a two-dimensional model of the solid with thermo-diffusion. The reflection of plane waves from a thermally insulated stress-free surface of an elastic solid with thermo-diffusion is also studied. A non-homogeneous system of four equations in reflection coefficients is obtained. The speeds of the plane waves are computed numerically and plotted against frequency for a particular range. The complex absolute values of the reflection coefficients of all reflected waves are computed numerically and plotted against the angle of incidence of the striking wave at the free surface. The effects of diffusion parameters are shown graphically for speeds and reflection coefficients of plane waves.     

Mechanics of porous elastic materials containing multiphase fluid

A continuum theory of mixtures for a porous elastic solid saturated by immiscible viscous fluids is presented. The theory includes micro-inertial effects for the local fluctuation in volume fractions of the solid and fluid constituents. Gradients of volume fraction of both the elastic solid and fluid constituents are included in the constitutive variables. Equations governing the macroscopic motion are developed and show that the present theory contains both Biot's equations and multiphase Darcy flow through porous media as special cases.     

A macroscopic description of the quasi-static behavior of granular materials based on the theory of porous media

Granular materials fall into the class of porous media. But in contrast to materials like foams and sponges their structure is discontinous on a microscopic level. For this reason the particles may undergo independent displacements and rotations. This is the classical kinematics which may be captured by a micropolar or Cosserat theory on the macroscopic level. The goal of this paper is to combine the theory of porous media as a macroscopic theory dealing with multi-phase systems and the micropolar theory describing extended kinematics and taking care of the discountinous structure of granular media on the micro scale. The resulting micropolar theory of porous media may be used to describe the quasistatic behavior of granular materials. In the present contribution thermodynamically consistent constitutive relations for the elastic response of a dense granular matrix material saturated by a viscous pore fluid are given and applied to some boundary value problems which demonstrate the physical relevance of the proposed model. Received: 9 June 1999     

Reflection and Refraction of Micropolar Magneto-thermoviscoelastic Waves at the Interface between Two Micropolar Viscoelastic Media

Using micropolar generalized thermoviscoelastic theories, problems of reflection and refraction of magneto-thermoeviscoelastic waves at the interface between two viscoelastic media are studied when a uniform magnetic field permeates the media. Coefficient ratios of reflection and refraction are obtained using continuous boundary conditions. Some special cases are considered, i.e., the absence of micropolar and viscous effects. By numerical calculations, variations of the amplitude ratios of reflection and refraction coefficients with the angle of incidence are shown graphically for incident rotational and dilatational waves at the interface between two media (one medium is aluminium-epoxy micropolar iscoelastic material, and the other is magnesium crystal micropolar viscoelastic material). Comparing the generalized thermoelastic theories developed by Lord and Shulman (LS) and by Green and Lindsay (GL) in this paper to conventional dynamics (CD) theory the effects of a magnetic field and viscosity are shown numerically in this paper.     

An additive theory for finite elastic–plastic deformations of the micropolar continuous media

In this paper, the method of additive plasticity at finite deformations is generalized to the micropolar continuous media. It is shown that the non-symmetric rate of deformation tensor and gradient of gyration vector could be decomposed into elastic and plastic parts. For the finite elastic deformation, the micropolar hypo-elastic constitutive equations for isotropic micropolar materials are considered. Concerning the additive decomposition and the micropolar hypo-elasticity as the basic tools, an elastic–plastic formulation consisting of an arbitrary number of internal variables and arbitrary form of plastic flow rule is derived. The localization conditions for the micropolar material obeying the developed elastic–plastic constitutive equations are investigated. It is shown that in the proposed formulation, the rate of skew-symmetric part of the stress tensor does not exhibit any jump across the singular surface. As an example, a generalization of the Drucker–Prager yield criterion to the micropolar continuum through a generalized form of the J ₂-flow theory incorporating isotropic and kinematic hardenings is introduced.     

Theory and FE-analysis for structures with large deformation under magnetic loading

We introduce and discuss a reduced micropolar continuum theory to simulate structures with large deformations under magnetic loading. Three numerical examples show the motivation of this model and its use in practical applications. The question of how to choose the micropolar material parameters is addressed. We use that a finite strain micropolar model would reduce to classical elasticity in the absence of curvature effects and body couples and for certain parameter ranges. This gives us information about a proper choice of material parameters. Thus, we introduce in fact a nearly classical model, but with the feature to cover large deformations and non-classical types of loading. As in shell theories, our continuum theory treats angular momentum as an explicit complementary principle. Thus, net couples—the typical loading of magnetized bodies in a magnetic field—can be modelled. Note that, in this case, the possibility for nonsymmetric Cauchy stresses is required for equilibrium, unlike classical shell theories. Micropolar theories are not commonly used, by comparison to the Boltzmann continuum. One reason may be that micropolar theories often require greater modelling effort without significant advantage. However, the simplicity of introducing physical effects like magnetic loading compensates those efforts.     

Point defects as sources of micropolar effects in elastic continua

It is shown in this paper that point defects in an elastic continuum can cause micropolar effects. Using micropolar elasticity transversal microrotation and displacement wave fields are derived which arise from the interaction of point defects with a longitudinal wave. It is shown that the microrotation wave can exist even in a classical elastic continuim.     

Thermo elastic waves with thermal relaxation in isotropic micropolar plate

In the present investigation, we have discussed about the features of waves in different modes of wave propagation in an infinitely long thermoelastic, isotropic micropolar plate, when the generalized theory of Lord–Shulman (L–S) is considered. A more general dispersion equation is obtained. The different analytic expressions in symmetric and anti-symmetric vibration for short as well as long waves are obtained in different regions of phase velocities. It is found that results agree with that of the existing results predicted by Sharma and Eringen in the context of various theories of classical as well as micropolar thermoelasticity.     

饱和多孔介质中动力渗流耦合分析的Biot-Cosserat连续体模型与应变局部化有限元模拟

提出了适用于饱和多孔介质中应变局部化分析及动力渗流耦合分析的Biot-Cosserat连续体模型。基于饱和多孔介质动力渗流耦合分析的Biot理论,将固体骨架看作Cosserat连续体,并考虑旋转惯性,建立了饱和多孔介质动力渗流耦合分析的Biot-Cosserat连续体模型。基于Galerkin加权余量法,对所发展的模型推导了以固体骨架广义位移(包含旋转)及孔隙水压力为基本未知量的有限元公式。利用所发展的数值模型,对包含压力相关弹塑性固体骨架材料的饱和多孔介质进行了动力渗流耦合分析与应变局部化有限元模拟,结果表明,所发展的两相饱和多孔介质动力渗流耦合分析的Biot-Cosserat连续体模型能保持饱和两相介质应变局部化问题的适定性及模拟饱和多孔介质中由应变软化引起的应变局部化现象的有效性。