Showing papers on "Isotropy published in 1986"

Dynamic localization of a charged particle moving under the influence of an electric field.

Abstract: The motion of a charged particle on a discrete lattice under the action of an electric field is studied with the help of explicit calculations of probability propagators and mean-square displacements. Exact results are presented for arbitrary time dependence of the electric field on a one-dimensional lattice. Existing results for the limiting cases of zero frequency and zero field are recovered. A new phenomenon involving the dynamic localization of the moving particle is shown to result in the case of a sinusoidally varying field: The particle is generally delocalized except for the cases when the ratio of the field magnitude and the field frequency is a root of the ordinary Bessel function of order 0. For these special cases it is found to be localized. This localization could be used, in principle, for inducing anisotropy in the transport properties of an ordinarily isotropic material.

High-resolution aluminum-27 NMR of aluminosilicates

Abstract: Recent advances in instrumentation and techniques have made a precise determination of isotropic chemical shifts of quadrupolar nuclei in solids practicable. Aluminum-27 chemical shifts in aluminosilicates closely parallel those of silicon-29 and display a similar dependence upon changes in both the first and second coordination spheres and the Al-O-Si bond angles.

Anisotropy of the inner core inferred from PKIKP travel times

Abstract: Travel-time residuals of the PKIKP phase observed between 170° and 180° show an axisymmetric pattern of degree 2 with an amplitude of about 2 seconds. The effect at shorter distances is much less pronounced and the entire data set cannot be explained by a physically realistic radial distribution of (isotropic) heterogeneity. We propose that, in addition to the general (isotropic) heterogeneity, the inner core is anisotropic with cylindrical symmetry aligned with the earth's rotation axis. Average P-velocity along this axis is about 1 percent faster than in the equatorial plane.

Homogenization and optimal bounds in linear elasticity

Abstract: In their celebrated paper of 1963, HASHIN & SHTRIKMAN [1] addressed the problem of determining optimal bounds for the bulk and shear moduli of a statistically isotropic elastic composite material with arbitrary isotropic phase geometry. They derived a set of bounds for these moduli in the physically meaningful case of three-dimensional elasticity. In the case of a two phase composite, let K 1,/.1 and K 2,/*2 respectively denote the bulk and shear moduli for the first and the second phase, let K,/* denote their analogues for the composite and let 0 stand for the volume fraction of the first phase in the composite. Under the ordering restriction that both

Evidence for inner core anisotropy from free oscillations

Abstract: Previous hypotheses concerning the cause of anomalous splitting in free oscillation spectra have led to models which are difficult to accept from the physical point of view - involving either substantial heterogeneity in the fluid outer core or large topographic variations in the core-mantle boundary and the inner core boundary and heterogeneity of several percent in inner core properties. Furthermore, other seismological evidence, some of it pre-existing and some of it very recently discovered, militates against these models. Within the framework of isotropic earth models there appears to be no acceptable explanation of the modal observations. Here we show that anisotropy in the inner core can produce an effect which is of the correct magnitude and which varies from mode to mode in approximately the observed manner. The data currently available are insufficient to objectively map the anisotropy, but the simple assumption of a constant elastic tensor which is invariant under rotations about the Earth's rotation axis (i.e. is transversely isotropic in the plane of the equator) matches well the gross features of the modal observations. This model does not entirely reconcile the modal data with traveltime observations; it is argued, however, that there exists an anisotropic model which will do so.

Bounding surface plasticity. II: application to isotropic cohesive soils

Abstract: The radial mapping version of the bounding surface plasticity formulation is applied to isotropic cohesive soils. While some aspects of this constitutive model have appeared in the past, a number of important novel features, including closed form analytical relations for certain loadings and the complete analytical formulation, are presented here for the first time. Based on the new aspects a much improved predictive capability is obtained, as shown by successful comparison with experimental data under different loading conditions. The analytical formulation and the significance of the different model constants are carefully investigated in order to have a better understanding of the simulated material response as obtained by numerical methods.

Mechanics of low density materials

Abstract: Mechanics analyses are used to derive the effective elastic moduli for low density materials. Both open cell and closed cell geometric models are employed in the case of isotropic media. The five independent effective moduli are derived for a low density transversely isotropic medium. Compressive strength, as defined by elastic stability, is also derived for open cell and closed cell isotropic materials. The theoretical results are compared with some experimental results, and also are assessed with respect to previous work.

Moderate deformations in extension-torsion of incompressible isotropic elastic materials

Abstract: It has been previously shown by anand (1979) that the classical strain energy function of infinitesimal isotropic elasticity is in good agreement with experiment for a wide class of materials for moderately large deformations, provided the infinitesimal strain measure occurring in the strain energy function is replaced by the Hencky or logarithmic measure of finite strain. The basis in Anand's paper for relating Hencky's strain energy function to experiment was data from experiments on metals and rubbers in uniaxial strain, simple tension and compression, and pure shear. Here, to test further the validity of this strain energy function for moderate deformations, its predictions for the twisting moment and the axial force in simple torsion and combined extension-torsion of solid cylinders of incompressible materials are calculated and shown to be in good agreement with data from the classical experiments of R ivlin and S aunders (1951) on vulcanized natural rubber. Indeed, the predictions from Hencky's strain energy function are in better accord with experiment than the predictions from the widely used Mooney (or Mooney-Rivlin) strain energy function.

The Poisson Function of Finite Elasticity

Abstract: The Poisson function is introduced to study in a simple tension test the lateral contractive response of compressible and incompressible, isotropic elastic materials in finite strain. The relation of the Poisson function to the classical Poisson’s ratio and its behavior for certain constrained materials are discussed. Some experimental results for several elastomers, including two natural rubber compounds of the same kind studied in earlier basic experiments by Rivlin and Saunders, are compared with the derived relations. A special class of compressible materials is also considered. It is proved that the only class of compressible hyperelastic materials whose response functions depend on only the third principal invariant of the deformation tensor is the class first introduced in experiments by Blatz and Ko. Poisson functions for the Blatz-Ko polyurethane elastomers are derived; and our experimental data are reviewed in relation to a volume constraint equation used in their experiments.

On material representation and constitutive branching in finite compressible elasticity

Abstract: The mechanical properties of two porous rubbers of different compressibility have been investigated experimentally and represented by aid of a particular isotropic strain-energy function constructed by means of separable distortional and dilatational terms. It is shown that a reduced form of the adopted strain-energy function offers definite advantages for evaluation of experimental data and reproduces well the behaviour of the investigated materials under three different loadings; uniaxial tension, plane strain tension and equibiaxial tension. The possibility of homogeneous branching from fundamental paths of the associated motions is examined and illustrated in detail for axisymmetric loading employing constitutive properties pertinent to the two materials tested.

Bounding Surface Plasticity. III: Application to Anisotropic Cohesive Soils

Abstract: A rate‐independent elasto‐plastic bounding surface constitutive model applicable to anisotropic cohesive soils is presented. It is shown that the theory is capable of realistically accounting for the initial anisotropy and its subsequent evolution in a manner consistent with our current understanding of anisotropy. While retaining the capabilities of the bounding surface theory developed for isotropic cohesive soils, a more general hardening behavior, which includes rotational and shape‐hardening features, is introduced in this anisotropic theory in order to simulate the evolution of material anisotropy. By comparing the predictions with experimental data, the anisotropic theory is shown to provide satisfactory results under stress paths involving strong development of anisotropy.

Vectorial Finite-Element Method Without Any Spurious Solutions for Dielectric Waveguiding Problems Using Transverse Magnetic-Field Component

Abstract: An improved finite-element method for the analysis of dielectric waveguiding problems is formulated rising the transverse magnetic-field component. In this approach, the divergence relation /spl nabla/ · H = 0 is satisfied and the spurious, nonphysical solutions which have been necessarily included in the solutions of earlier vectorial finite-element methods are completely eliminated in the whole region of a propagation diagram. To verify the accuracy of the present method, numerical results for a rectangular metallic waveguide half filled with dielectric are presented and compared with exact and earlier finite-element solutions. Dielectric rectangular waveguides are also analyzed for both isotropic and anisotropic cases.

Isotropic Stochastic Flows

Abstract: We consider isotropic stochastic flows in a Euclidean space of $d$ dimensions, $d \geq 2$. The tendency of two-point distances and of tangent vectors to shrink or expand is related to the dimension and the proportion of the flow that is solenoidal or potential. Tangent vectors from the same point tend to become aligned in the same or opposite directions. The purely potential flows are characterized by an analogue of the curl-free property. Liapounov exponents are treated briefly. The rate of increase or decrease of the length of an arc of small diameter is related to the shape of the arc. In the case $d = 2$ a sufficient condition is given under which the length of a short arc has a high probability of approaching 0.

Exact estimates of the conductivity of a binary mixture of isotropic materials

Abstract: This paper describes the set GmU of effective conductivity tensors of mixtures generated by two isotropic materials taken in prescribed proportions m1 and m2 We describe microstructures which realise any point of GmU for n-dimensional space.

Assessment of local isotropy using measurements in a turbulent plane jet

Abstract: Following a review of the difficulties associated with the measurement and interpretation of statistics of the small-scale motion, the evidence for and against local isotropy is assessed in the light of measurements in a turbulent plane jet at moderate values of the Reynolds and Peclet numbers. These measurements include spatial derivatives with respect to different spatial directions of the longitudinal velocity fluctuation and of the temperature fluctuation. Relations between mean-square values of these derivatives suggest strong departures from local isotropy for both velocity and temperature. In contrast, the locally isotropic forms of the vorticity and temperature dissipation budgets are approximately satisfied. Possible contamination of the fine-scale measurements by the anisotropic large-scale motion is assessed in the context of the measured structure functions of temperature and of the measured skewness of the streamwise derivative of temperature. Structure functions are, within the framework of local isotropy, consistent with the average frequency and amplitude of temperature signatures that characterize the quasi-organized large-scale motion. Conditional averages associated with this motion account, in an approximate way, for the skewness of the temperature derivative but make negligible contributions to the skewness of velocity derivatives. The degree of spatial organization of the fine structure is inferred from conditional statistics of temperature derivatives.

Field fluctuations in multicomponent mixtures

Abstract: F luctuations of electrostatic and elastostatic fields in a random phase mixture may be characterized by mean values and square means of the fields in each component. Exact relations between the square means and the analytical properties of the effective moduli are established for isotropic mixtures. Moreover, a modified effective medium procedure for calculating the field fluctuations in mixtures with aggregate topology is proposed. Explicit results are given for mixtures of isotropic components and spherical grain shapes. Particularly strong fluctuations occur in strongly heterogeneous media near the percolation threshold.

Existence of needle crystals in local models of solidification.

Abstract: The way in which surface tension acts as a singular perturbation to destroy the continuous family of needle-crystal solutions of the steady-state growth equations is analyzed in detail for two local models of solidification. All calculations are performed in the limit of small surface tension or, equivalently, small velocity. The basic mathematical ideas are introduced in connection with a quasilinear, isotropic version of the geometrical model of Brower et al., in which case the continuous family of solutions disappears completely. The formalism is then applied to a simplified boundary-layer model with an anisotropic kinetic attachment coefficient. In the latter case, the solvability condition for the existence of needle crystals can be satisfied whenever the coefficient of anisotropy is arbitrarily small but nonzero.

Effect of Fiber Anisotropy on Thermal Stresses in Fibrous Composites

Abstract: An elasticity solution is utilized to analyze an orthotropic fiber in an isotropic matrix under uniform thermal load. The analysis reveals that stress distributions in the fiber are singular in the radial coordinate when the radial fiber stiffness (C-rr) is greater than the hoop stiffness (C-theta-theta). Conversely, if C-rr is less than C-theta-theta the maximum stress in the composite is finite and occurs at the fiber-matrix interface. In both cases the stress distributions are radically different than those predicted assuming the fiber to be transversely isotropic (C-rr = C-theta-theta). It is also shown that fiber volume fraction greatly influences the stress distribution for transversely isotropic fibers, but has little effect on the distribution if the fibers are transversely orthotropic.

Dynamic response of 3-D embedded foundations by the boundary element method

Abstract: The dynamic response of three-dimensional rigid embedded foundations of arbitrary shape, resting on a linear elastic, homogeneous, and isotropic half-space is numerically obtained. The foundations are subjected either to externally applied forces or to obliquely incident seismic body or surface waves of arbitrary time variation. The time domain boundary element method (BEM) is utilized to simulate the soil medium with the aid of Stokes' fundamental solutions. The dynamic response of the foundation-soil system is obtained in a step-by-step time-marching solution. Use of this time domain BEM requires a minimum amount of surface discretization only and provides the basis for an extension to nonlinear soil-structure interaction (SSI) problems.

Dynamic response of rigid strip‐foundations by a time‐domain boundary element method

Abstract: SUMMARY The dynamic response of rigid strip-foundations placed on or embedded in a homogeneous, isotropic, hear elastic half-space under conditions of plane strain to either external forces or obliquely incident seismic waves of arbitrary time variation is numerically obtained. The above mixed boundary-value problems are treated by the time domain boundary element method which is used in a step-by-step timewise fashion to provide the foundation response to a rectangular impulse. Numerical examples are presented in detail to demonstrate the use and importance of the proposed method. The method appears to be more advantageous than frequency domain techniques, because it provides the transient foundation response in a natural and direct way and can form the basis for extension to the non-linear case.

Molecular theory for freezing of a system of hard ellipsoids: Properties of isotropic-plastic and isotropic-nematic transitions.

Abstract: The theory for isotropic-nematic transition at constant pressure described in an earlier paper is extended to include isotropic-plastic transition. The transition is located from the structural information about the liquid using the first-principles order-parameter theory of freezing. This theory makes the role of the structure of the medium explicit and the role of the intermolecular interaction implicit. For the plastic phase, order parameters are the coefficients of a Fourier expansion of the spatially varying single-particle density \ensuremath{\rho}(r,\ensuremath{\Omega}) in terms of the reciprocal lattice of the plastic. For the nematic phase, order parameters are the coefficients of a spherical harmonic expansion of an orientational singlet distribution. The theory predicts that the equilibrium positional freezing (plastic) on fcc lattice takes place for the value of c\ifmmode\bar\else\textasciimacron\fi{}${^}_{0}$,${0}^{1}$ [=1-1/S(\ensuremath{\Vert}${\mathrm{G}}_{m}$\ensuremath{\Vert}), where S(\ensuremath{\Vert}${\mathrm{G}}_{m}$\ensuremath{\Vert}) is the first peak in the structure factor of the center of mass] \ensuremath{\simeq}0.67 [or S(\ensuremath{\Vert}${\mathrm{G}}_{m}$\ensuremath{\Vert})\ensuremath{\simeq}3.07]. The equilibrium orientational freezing (nematic) takes place when the orientational correlation c\ifmmode\bar\else\textasciimacron\fi{}${^}_{2}$,${2}^{0}$\ensuremath{\simeq}4.45. For a simple model of hard ellipsoids of revolution parametrized by length-to-width ratio ${X}_{0}$, we find that the plastic phase stabilizes first for 0.57\ensuremath{\lesssim}${X}_{0}$\ensuremath{\lesssim}1.75 and the nematic phase for ${X}_{0}$0.57 and ${X}_{0}$g1.75. These values are in reasonable agreement with the computer-simulation results. We also find, in agreement with computer simulation, a remarkable symmetry between the systems with inverse length-to-width ratios.