Mechanisms of viscosity increase for nanocolloidal dispersions

An EMD model for nanocolloidal dispersions considering the interaction between atoms within solid particles is developed for viscosity calculation and studying the effect of the particle size and volume fraction. Strong oscillations are observed in the pressure tensor autocorrelation function. Elimination of this oscillation is achieved by adjusting the potential among atoms of nanoparticles to reduce the acoustic mismatch between particles and liquid. The shear viscosity of nanocolloidal dispersion is found strongly dependent on the particle size, which cannot be predicted by traditional effective medium theory. Through decomposing of the pressure tensor, the viscosity contribution from interactions between liquid-solid atoms and solid-solid atoms are believed to dominate the viscosity increase of colloidal systems. Our model reveals the shear viscosity increase mechanism at the molecular-level and predicts that the shear viscosity of simple colloidal dispersions reaches a plateau value when the particle size becomes large enough.     

On fibre bundle approach to a damage analysis

In this paper the geometric structure of a damaged state in the medium is investigated based on the fibre bundle technique. The damage (a failure) in some region of the medium under loads is regarded as breakdown of the holonomicity in this region. A measure of reduction of load carrying area elements caused by the development of microcracks or microvoids in the damaged medium is identified with the damage tensor. Multiplicative representations of the damage tensor formulated both on the tangent bundle with an affine connection and a fibre bundle with a non-linear connection over the damaged medium are obtained. In the former case the generalization of the damage tensor to the tangent bundle rests on the technique of prolonging the deformation vector to include not only the independent variables and dependent variables appearing in the damage tensor, but also the derivatives of the dependent variables. The so-called lifting technique is used to express the damage tensor by initial, additional and direct (deformation-induced) damages or by direct and transferred ones. In the latter one the higher-order contact geometry approach identified with the Finslerian geometry is employed to analyze the influences of elastic, inelastic, direct, transferred and initial damages on the total damage tensor. Time-dependent relationships of the damage tensor are then presented.     

Stiffness of particulate reinforced metal matrix composites with damaged reinforcements

Abstract

During tensile plastic deformation particulate reinforced metal matrix composites (MMCs) undergo reinforcement damage and a parallel reduction in stiffness. An analytical model is developed to calculate this stiffness reduction using the equivalent inclusion technique proposed by Eshelby. The model considers both damaged and undamaged reinforcement particles as ellipsoidal inclusions but with different stiffness tensors. The effect of the aspect ratio of the reinforcing particles has been accounted for in the model. The model is very flexible and can meet different specific damage situations by designing a suitable stiffness tensor for the damaged reinforcements. Finite element analysis is used to modify a numerical stiffness tensor for cracked reinforcement particles. The model is compared with an earlier model of modulus reduction in MMC materials and with a few experimental measurements made on a 15 vol.-%SiC particulate reinforced aluminium alloy 2618 MMC.     

Immersed molecular electrokinetic finite element method

A unique simulation technique has been developed capable of modeling electric field induced detection of biomolecules such as viruses, at room temperatures where thermal fluctuations must be considered. The proposed immersed molecular electrokinetic finite element method couples electrokinetics with fluctuating hydrodynamics to study the motion and deformation of flexible objects immersed in a suspending medium under an applied electric field. The force induced on an arbitrary object due to an electric field is calculated based on the continuum electromechanics and the Maxwell stress tensor. The thermal fluctuations are included in the Navier–Stokes fluid equations via the stochastic stress tensor. Dielectrophoretic and fluctuating forces acting on the particle are coupled through the fluid–structure interaction force calculated within the surrounding environment. This method was used to perform concentration and retention efficacy analysis of nanoscale biosensors using gold particles of various sizes. The analysis was also applied to a human papillomavirus.     

复合材料的等效弹性性能

用细观力学的分析方法研究了复合材料的宏观等效弹性性能。在严格满足组分相间界面的连续性条件下,正确反映了组分相间的相互作用, 考虑了弹性张量各分量之间的相互关系, 分析了层合介质的宏观等效弹性性能。进一步用统计平均的思想, 得到了总体横观各向同性及总体各向同性复合材料的等效弹性性能的解析表达式。与有关的理论及实验结果比较, 得到了非常满意的结果。      

Computation of green’s tensor and wave propagation in the random granular elastic medium

Abstract

A linear differential operator equation involving randomly variable field parameters, characterising the heterogeneous granular elastic medium is considered. The appropriate Green’s tensor is evaluated for the non-deterministic operator equations in the form of Fourier integrals in the frequency space; the exact evaluation is carried out to obtain the 36 components of Green’s tensor. The problem of wave propagation in the random granular elastic medium is then carried out with the help of the associated Green’s tensor. The effect of random variation of parameters on wave propagation in the granular elastic medium is examined. Dispersion equations have been analysed in details.     

Theoretical aspects of demagnetization tensors

A magnetometric demagnetization tensor is defined for uniformly-magnetized samples of arbitrary geometry. It is shown that this is a real symmetric tensor with non-negative diagonal elements and unit trace. Diagonalization of the magnetometric demagnetization tensor yields the Brown-Morrish equivalent ellipsoid and the conclusion that Stoner-Wohlfarth particles of any surface geometry have only two easy directions of magnetization. Transformation of the tensor, subject to periodicity constraints, leads to the conclusion that uniformly-magnetized samples with rotational periodicity, of ordern geq 3about a single axis, have isotropic behavior perpendicular to that axis. It is also shown that if a sample has spherical periodicity with four or more vertices it does not exhibit shape anisotropy. Various methods for determining the numerical values of the tensor elements are presented.     

A symmetry invariant formulation of the relationship between the elasticity tensor and the fabric tensor

The fabric tensor is employed as a quantitative stereological measure of the structural anisotropy in the pore architecture of a porous medium. Earlier work showed that the fabric tensor can be used additionally to the porosity to describe the anisotropy in the elastic constants of the porous medium. This contribution presents a reformulation of the relationship between fabric tensor and anisotropic elastic constants that is approximation free and symmetry-invariant. From specific data on the elastic constants and the fabric, the parameters in the reformulated relationship can be evaluated individually and efficiently using a simplified method that works independent of the material symmetry. The well-behavedness of the parameters and the accuracy of the method was analyzed using the Mori–Tanaka model for aligned ellipsoidal inclusions and using Buckminster Fuller’s octet-truss lattice. Application of the method to a cancellous bone data set revealed that employing the fabric tensor allowed explaining 75–90% of the total variance. An implementation of the proposed methods was made publicly available.     

A circular inclusion in a finite domain II. The Neumann-Eshelby problem

Summary This is the second paper in a series concerned with the precise characterization of the elastic fields due to inclusions embedded in a finite elastic medium. In this part, an exact and closed form solution is obtained for the elastic fields of a circular inclusion embedded in a finite circular representative volume element (RVE), which is subjected to the traction (Neumann) boundary condition. The disturbance strain field due to the presence of an inclusion is related to the uniform eigenstrain field inside the inclusion by the so-called Neumann-Eshelby tensor. Remarkably, an elementary, closed form expression for the Neumann-Eshelby tensor of a circular RVE is obtained in terms of the volume fraction of the inclusion. The newly derived Neumann-Eshelby tensor is complementary to the Dirichlet-Eshelby tensor obtained in the first part of this work. Applications of the Neumann-Eshelby tensor are discussed briefly.     

Variational estimate of the effective generalized conductivity tensor of a two-phase medium with an anisotropic distribution of phases

An inequality is found for the effective generalized conductivity tensor of a two-phase medium with an anisotropic distribution of phases.     

The thermodynamic driving force for bone growth and remodelling: a hypothesis

The Eshelby stress (static energy momentum) tensor is derived for bone modelled as an inhomogeneous piezoelectric and piezomagnetic Cosserat (micropolar) medium. The divergence of this tensor is the configurational force felt by material gradients and defects in the medium. Just as in inhomogeneous elastic media, this force is identified with the thermodynamic force for phase transformations, in bone it is the thermodynamic cause of structural transformations, i.e. remodelling and growth. The thermodynamic approach shows that some terms of driving force are proportional to the stress, and some acting on material inhomogeneities are quadratic in the stress-the latter outweigh by far the former. Since inertial forces due to acceleration enter the energy-momentum tensor, it follows that the rate of loading matters and that both tension and compression stimulate growth, which is favoured at heterogeneities.     

Theoretical rheology of suspensions of ferromagnetic rod-like particles

We extend the linear response-like derivation of the generalized Navier-Stokes equation to non-Newtonian flows with rate of strain-dependent transport coefficients. We derive a time correlation function expression for the viscosity tensor and point out possible ambiguities in the operational definitions of viscosity coefficients. Our analysis is specific to a suspension of polar, rod-like ferromagnetic particles. A commentary is included about the approximations that lead from the time correlation function and the molecular definition of the viscosity tensor to the standard, Brownian dynamics model used in the theoretical rheology of suspensions. Some theoretical difficulties and logical inconsistencies are pointed out. Preliminary results for the transport coefficients of dilute suspension of magnetic rod-like particles are presented.Paper presented at the Tenth Symposium on Thermophysical Properties, June 20–23, 1988, Gaithersburg, Maryland, U.S.A.     

Equations for the Momentum and Energy of an X-ray Wave Field in a Crystal

A new approach for describing the interaction of X rays with a crystalline medium is proposed. General relations for a change in the electromagnetic-field momentum and energy have been derived for a nonmagnetic medium with variable permittivity. A special local coordinate system for an inhomogeneous medium is introduced, in which the Maxwell tension tensor has a canonical form determined by the energy and momentum densities. Main relations for changes in the energy and momentum densities have been obtained in the coordinate system related to the propagation direction of a plane electromagnetic wave pulse in a homogeneous medium.     

About the numerical simulation of the dynamics of granular media and the definition of the mean stress tensor

To define the stresses in a granular medium considered as a continuum, Weber has calculated a tensor at a point by averaging the contact forces in the vicinity. However this tensor is not symmetric. Besides, the Weber formula neglects the body forces, which does not allow it to describe dynamical problems. In the present work, it is proposed to use a general expression of the mean stress tensor based not only on the contact reactions but also on the body forces. It is proved that this tensor is automatically symmetric and invariant by translation. Next, the pertinence of this approach is illustrated by an analytical example. It can be clearly ascertained that accounting for the contribution of the gravity and inertia effects is essential to ensure the symmetry of the stress tensor, according to Cauchy theory. We then propose to extend this definition of the mean stress tensor to a space–time analysis. An average in time as well appears to be pertinent. Finally, numerical simulations with a large number of grains are performed using the software ‘MULTICOR' developed in our laboratories and based on the contact dynamics and the bipotential approach. The attention is particularly focused on the motion of ensiled matters.     

Influence of Heterogeneous Magnetism on Magneto-Optical Properties

The influence of inhomogeneity on magnetic materials is considered; in particular, we examine how it affects the magneto-optical (MO) response of films and multilayers. From ab initio calculations of the band structure, the optical conductivity tensor is derived, providing the basis for computing the MO spectra. The presence of magnetic nanoprecipitates is taken into account by modeling the system as an effective medium or as an infinitely thin layered structure. A possible depth concentration distribution of the magnetic species is also accounted for, by considering the structure as a sequence of layers. This formalism is applied to some real systems constituted by magnetic particles dispersed in a hosting nonmagnetic matrix. The agreement between theoretical and measured MO Kerr effect spectra supports the validity of the model and establishes its predictive power, suggesting that the analysis of experimental MO spectra can provide information not only on the magnetic, but also on the structural properties of heterogeneous magnetic systems.     

Brillouin Diagrams for Optical Wave Propagation in Twisted Dielectric Media

Light propagation in an inhomogeneous, anisotropic medium is discussed. The medium shows the most general anisotropy (optically biaxial) and a special kind of inhomogeneity: rotation of a principal axis of the dielectric tensor about the z-axis. Since the analytic treatment is very troublesome, we use group theory to deduce qualitative statements on frequency splitting in the Brillouin diagram. As in all periodic anisotropic media, where two different group velocities exist, an infinite number of stop bands is produced by a splitting into maximally three stop bands at each point of interaction. Two special cases for the dielectric tensor are treated also: optically biaxial media with one axis in the z -direction and optically uniaxial media with an oblique optical axis. The group theory required is similar to the theory of crystallographic double space groups.     

各向同性弹性介质非线性本构方程

从张量函数出发,围绕共轭应力、应变变量,研究了各向同性非线性弹性介质各种形式的本构方程以及各种形式方程之间的关系。推导出用张量不变量,标量不变量表示的两种形式非线性Green弹性介质本构方程。证明了方程是完备的,不可约的。作为应用举例,研究了橡胶材料的工程应用问题。     

Homogenization with uncertainty in Poisson ratio for polymers with rubber particles

The main aim of this work is dual computer analysis of probabilistic coefficients for the homogenized tensor of the polymer filled with the rubber particles having randomized Poisson ratios of both constituents. The major issue is to verify an influence of a randomness in rubber Poisson ratio close to the compressibility limit on the uncertainty of the effective tensor probabilistic characteristics. Probabilistic analysis presented here is carried out using mainly the stochastic perturbation technique provided by the common application of the traditional FEM commercial code ABAQUS and the symbolic computations package MAPLE. This FEM-based technique employs polynomial response function of the optimum order recovered from the weighted least squares method and following a set of deterministic solutions obtained for various values of the randomized input parameter. Optimization procedure is released entirely into a symbolic environment, where maximization of the correlation factor together with minimization of the fitting variance and approximation error are applied. Homogenization technique consists in equating of deformation energies for the real composite and the artificial one characterized by the effective elasticity tensor with uncertainty.     

Relations between the critical angles and the optical tensor of a biaxial material

The behavior of the critical angles between a high-index isotropic medium and a biaxial crystal with arbitrary orientation of the optical tensor has been theoretically analyzed and numerically modeled. The results indicate that, as the biaxial crystal is rotated around an axis perpendicular to the interface, two critical angles appear, corresponding to the excitation of two eigen modes, which periodically vary with a period of pi. An optical procedure for fully characterizing the optical tensor of a biaxial crystal is suggested on the basis of the twist-angle dependence of these critical angle. This procedure simply requires the measurement of the p- to s-conversion reflectivity against the sample rotation angle, with just one polished surface of a biaxial crystal.     

On Bhattacharyya relative entropy in a homogenization of composite materials

The main idea of this work is an application of relative entropy in the numerical analysis of probabilistic divergence between original material tensors of the composite constituents and its effective tensor in the presence of material uncertainties. The homogenization method is based upon the deformation energy of the representative volume elements for the fiber-reinforced and particulate composites and uncertainty propagation begins with elastic moduli of the fibers, particles, and composite matrices. Relative entropy follows a mathematical model originating from Bhattacharyya probabilistic divergence and has been applied here for Gaussian distributions. The semi-analytical probabilistic method based on analytical integration of polynomial bases obtained via the least squares method fittings enables for determination of the basic probabilistic characteristics of the effective tensor and the relative entropies. The methodology invented in this work may be extended toward other probability distributions and relative entropies, for homogenization of nonlinear composites and also accounting for some structural interface defects.