Showing papers on "Isotropy published in 1982"
TL;DR: In this article, the connection between microstructure and absolute limits to the allowed values of the dielectric response of two-phase composites is reviewed and a solution of the Clausius-Mossotti problem is developed from basic principles.
1,433 citations
TL;DR: In this article, the existence of singular solutions to the nonlinear elastostatics problem with respect to radial motion has been studied for a class of strongly elliptic materials by means of the direct method of the calculus of variations, and it has been shown that the only radial equilibrium solutions without cavities are homogeneous.
Abstract: A study is made of a class of singular solutions to the equations of nonlinear elastostatics in which a spherical cavity forms at the centre of a ball of isotropic material placed in tension by means of given surface tractions or displacements. The existence of such solutions depends on the growth properties of the stored-energy function W for large strains and is consistent with strong ellipticity of W . Under appropriate hypotheses it is shown that a singular solution bifurcates from a trivial (homogeneous) solution at a critical value of the surface traction or displacement, at which the trivial solution becomes unstable. For incompressible materials both the singular solution and the critical surface traction are given explicitly, and the stability of all solutions with respect to radial motion is determined. For compressible materials the existence of singular solutions is proved for a class of strongly elliptic materials by means of the direct method of the calculus of variations, an important step in the analysis being to show that the only radial equilibrium solutions without cavities are homogeneous. Work of Gent & Lindley (1958) shows that the critical surface tractions obtained agree with those observed in the internal rupture of rubber.
660 citations
TL;DR: In this paper, a unique measure called fabric tensor Fij is introduced to embody the fabric concept without loss of generality, which is important as an index measure to evaluate the crack intensity which is related to the number and dimension of cracks.
300 citations
TL;DR: In this article, an exact solution of the one-dimensional isotropic Heisenberg chain with arbitrary spins S is obtained, and on the basis of the exact solution the thermodynamic properties of the model with antiferromagnetic interaction are investigated.
292 citations
TL;DR: In this article, the overall elastic moduli of a composite with an isotropic elastic matrix containing periodically distributed (anisotropic) inclusions or voids, can be expressed in terms of several infinite series which only depend on the geometry of the inclusions and voids.
268 citations
TL;DR: In this paper, a new method was developed for calculating effective elastic parameters of a medium containing oblate spheroidal cracks having parallel planes, free from the restrictions of isotropic matrix material and low crack density.
Abstract: A new method was developed for calculating effective elastic parameters of a medium containing oblate spheroidal cracks having parallel planes. This new method is free from the restrictions of isotropic matrix material and low crack density. Velocity anisotropy was calculated for the case of oriented cracks filled with fluid. Effects of crack aspect ratio, fluid bulk modulus, and crack volume on velocity anisotropy were investigated. The present results showed smaller anisotropy than that given by ANDERSON et al. (1974) for a medium containing oriented spheroidal cracks. The relation between velocity and crack density parameter (ratio of porosity to aspect ratio of cracks divided by 4π/3) was investigated using these results.
207 citations
TL;DR: In this article, simple relations are established between isotropic functions and anisotropic functions through some vectors or tensors which characterized the anisotropy group, and the results enable us to obtain representations of anisoustropy functions using the much well-known tables for representations of isotropics.
181 citations
TL;DR: In this article, the authors show how the McCoy bounds on the effective shear modulus of a statistically isotropic composite can be simplified and expressed in terms of the volume fraction, f 1, and two geometric parameters.
Abstract: W e show in detail how the McCoy bounds on the effective shear modulus of a statistically isotropic composite, can be simplified and expressed in terms of the volume fraction, f 1 , and two geometric parameters. ζ 1 and η 1 . We simplify Silnutzer's bounds on the effective elastic moduli of fibre-reinforced composites and find they can be expressed in terms f 1 and two geometric parameters, ζ' 1 and η' 1 . The parameter ζ' 1 also determines bounds on the transport and optical constants of such composites. Also, the Elsayed-McCoy bounds on the transport properties of fibre-reinforced, symmetric-cell materials are shown to depend on three geometric parameters.
178 citations
TL;DR: In this article, the authors considered noncentrosymmetry in a micropolar elastic solid and derived three new elastic constants in addition to the six considered in the fully isotropic micropolastic solid.
176 citations
TL;DR: In this article, high-frequency fluctuations of temperature and of longitudinal and vertical velocity components have been measured with high-resolution probes in order to test the localisotropy assumption.
Abstract: High-frequency fluctuations of temperature and of longitudinal and vertical velocity components have been measured with high-resolution probes in order to test the local-isotropy assumption. The simultaneous measurements of u’, w’, θ’ and the measurements in two space points with various separations in either the longitudinal or transverse directions were made in the large boundary layer (Rλ = 616) of the I.M.S.T. Air-Sea Interaction Simulation Tunnel. There is consistent evidence that the local-isotropy assumption is satisfied by the velocity field at all scales smaller than twenty times the Kolmogorov microscale (η ≈ 0.27 × 10−3 m), i.e. in the dissipative range of scales but not in the expected inertial subrange. The direct comparisons of the lateral and longitudinal temperature autocorrelation and structure functions show that the temperature field does not verify the isotropy assumption at all scales greater thanor equal to 37 and presumably at even smaller scales. This is confirmed by the study of the temperature-increment skewness and flatness factors. The spectral distribution -of the non-zero derivative skewness (S(θ) = +0.9) shows that it is essentially contributed by those scales for which the dynamic field satisfies isotropy.
171 citations
TL;DR: Moreovet as discussed by the authors proposed a modification of the form of the singular integral equation for the problem of a plane crack of arbitrary shape in a three-dimensional isotropic elastic medium.
Abstract: A modification of the form of the singular integral equation for the problem of a plane crack of arbitrary shape in a three-dimensional isotropic elastic medium is proposed. This modification consists in the incorporation of the Laplace operator δ into the integrand. The integral must now be interpreted as a finite-part integral. The new singular integral equation is equivalent to the original one, but simpler in form. Moreovet, its form suggests a new approach for its numerical solution, based on quadrature rules for one-dimensional finite part integrals with a singularity of order two. A very simple application to the problem of a penny-shaped crack under constant pressure is also made. Moreover, the case of straight crack problems in plane isotropic elasticity is also considered in detail and the corresponding results for this special case are also derived.
TL;DR: In this article, normal mode partial derivatives for a transversely isotropic earth model with a radial axis of symmetry are calculated for the upper 200km of the upper mantle and two shear-type moduli are determined from the toroidal modes.
Abstract: Isotropic earth models are unable to provide uniform fits to the gross Earth normal mode data set or, in many cases, to regional Love-and Rayleigh-wave data. Anisotropic inversion provides a good fit to the data and indicates that the upper 200km of the mantle is anisotropic. The nature and magnitude of the required anisotropy, moreover, is similar to that found in body wave studies and in studies of ultramafic samples from the upper mantle. Pronounced upper mantle low-velocity zones are characteristic of models resulting from isotropic inversion of global or regional data sets. Anisotropic models have more nearly constant velocities in the upper mantle.
Normal mode partial (Frediet) derivatives are calculated for a transversely isotropic earth model with a radial axis of symmetry. For this type of anisotropy there are five elastic constant. The two shear-type moduli can be determined from the toroidal modes. Spheroidal and Rayleigh modes are sensitive to all five elastic constants but are mainly controlled by the two compressional-type moduli, one of the shear-type moduli and the remaining, mixed-mode, modulus. The lack of sensitivity of Rayleigh waves to compressional wave velocities is a characteristic only of the isotropic case. The partial derivatives of the horizontal and vertical components of the compressional velocity are nearly equal and opposite in the region of the mantle where the shear velocity sensitivity is the greatest. The net compressional wave partial derivative, at depth, is therefore very small for isotropic perturbations. Compressional wave anisotropy, however, has a significant effect on Rayleigh-wave dispersion. Once it has been established that transverse anisotropy is important it is necessary to invert for all five elastic constants. If the azimuthal effect has not been averaged out a more general anisotropy may have to be allowed for.
TL;DR: In this article, the rheological properties of thermotropic polyester were determined in the nematic and isotropic states, and the results were discussed with reference to analogous observations in small-molecule liquid crystals and in thermotropic aromatic co-polyesters.
Abstract: The rheological properties of a thermotropic polyester were determined in the nematic and isotropic states. In the isotropic state, the viscosity is almost constant and the polymer is only slightly elastic. The nematic phase has a lower viscosity than the isotropic, except at low frequencies or shear rates, where the viscosity increases as though the polymer had a yield stress. There is a marked dependence of the rheology on shear history. The effects of shearing can be erased by returning the material first to the isotropic state and then back to the nematic state. The results are discussed with reference to analogous observations in small-molecule liquid crystals and in thermotropic aromatic co-polyesters.
TL;DR: In this article, the theory of orthorhombic layers is successively applied to analyse the stress-deformation behavior of rock masses containing one, two and three sets of joints, where joints in each set are assumed to be planar and to be approximately equally spaced.
TL;DR: In this article, a linear functional of the solutions to the equilibrium boundary-value problem is minimized under additional restrictions upon the control variables, such as the material characteristics of rigidity of an elastic nonhomogeneous medium.
Abstract: In this paper, we consider a number of optimal design problems for elastic bars and plates. The material characteristics of rigidity of an elastic nonhomogeneous medium are taken as the control variables. A linear functional of the solutions to the equilibrium boundary-value problem is minimized under additional restrictions upon the control variables. Special variations of the control within a narrow strip provide a necessary condition for a strong local minimum (Weierstrass test). This necessary condition can be used for the detailed analysis of the following problems: bar of extremal torsional rigidity; optimal distribution of isotropic material with variable shear modulus within a plate; and optimal orientation of principal axes of elasticity in an orthotropic plate. For all of these cases, the stationary solutions violate the Weierstrass test and therefore are not optimal. This is because, in the course of the approximation of the optimal solution, the curve dividing zones occupied by materials with different rigidities displays rapid oscillations sweeping over a two-dimensional region. Within this region, the material behaves as a composite medium assembled of materials of the initial class.
TL;DR: In this article, the asymptotic form of the stress and displacement components near the tip of a straight crack in a generally rectilinear anisotropic plane elastic body are resolved.
TL;DR: In this paper, a combined finite element and analytical technique has been used to study the problems of scattering by semi-circular and triangular canyons, and the results for the former case were compared with the known exact solution and those for the latter case are compared with some available approximate solutions.
Abstract: Scattering of antiplane shear waves (SH) in two dimensions by surface and near-surface defects in a homogeneous, isotropic elastic semi-infinite medium has been studied. Attention has been focused here in the range of medium to long wavelengths. A combined finite element and analytical technique has been used to study the problems of scattering by semi-circular and triangular canyons. The results for the former case are compared with the known exact solution and those for the latter case are compared with some available approximate solutions. Finally a problem of multiple scattering by a triangular canyon and a nearby circular tunnel is studied. Numerical results are presented showing the effects of multiple scattering and different angles of incidence. These results are of interest in earthquake engineering.
TL;DR: In this paper, a stable and efficient mixed-frame method has been formulated for the solution of the time-dependent equation of radiative transfer with full retention of all velocity dependent terms to O ( v c ).
TL;DR: In this article, the elastic buckling of rectangular Mindlin plates is considered using two related methods of analysis, the Rayleight-Ritz method and one of its piece-wise forms, the finite strip method.
TL;DR: In this paper, a method used to study the evolution of radiating fluid spheres is extended to the case of anisotropic spheres, and explicit forms of the equations are written down for two models.
Abstract: A method used to study the evolution of radiating fluid spheres is extended to the case of anisotropic spheres. Explicit forms of the equations are written down for two models. One of the models is numerically integrated to display the difference between the isotropic and the anisotropic models for different degrees of anisotropy.
TL;DR: In this article, the authors demonstrate that the neglect of elastic end effects, usually justified by appealing to Saint-Venant's principle, cannot be applied routine ly in problems involving composite materials, and that the characteristic decay length over which end effects are significant is, in general, several times longer than the corresponding length for isotropic materials.
Abstract: In this paper, we demonstrate that the neglect of elastic end effects, usually justified by appealing to Saint-Venant's principle, cannot be applied routine ly in problems involving composite materials. In particular, for fiber rein forced composites, the characteristic decay length over which end effects are significant is, in general, several times longer than the corresponding length for isotropic materials. For plane strain or generalized plane stress of a highly anisotropic transversely isotropic (or orthotropic) material, modeling a fiber- reinforced composite, the characteristic decay length is of order b(E/G) 1/2, where b is the maximum dimension perpendicular to the fibers and E, G are the longitudinal Young's modulus and shear modulus respectively. Thus when E/G is large, as for fiber-reinforced composites, end effects are transmitted over a distance which is of the order of several specimen widths. This is in marked contrast with the situation for isotropic materials where decay lengths of one ...
TL;DR: In this paper, a method is developed which predicts the elastic moduli of homogeneous isotropic two-phase materials of arbitrary phase geometry using three parameters, the magnitudes of which characterize any type of composite (particulate, phase-symmetric powder materials etc.).
TL;DR: In this paper, the 3D elastic moduli were measured from testing simple ten sion, compression, and shear specimens, and the bounds of Poisson's ratio for transversely isotropic materials were shown to be zero and unity.
Abstract: The 3-dimensional elastic moduli are measured from testing simple ten sion, compression, and shear specimens. The results are in good agreement with the isotropic and reciprocal relations for a transversely isotropic material. Existing data obtained by ultrasonic techniques and another mechanical testing technique compare well with our data. The bounds of Poisson's ratio for transversely isotropic materials are shown to be zero and unity.
TL;DR: In this article, the equations for the source function, flux, and scattered intensity normal to the surface are formulated in cartesian coordinates for a 3D rectangular absorbing, emitting, isotropically scattering medium exposed to both diffuse and collimated radiation.
Abstract: The equations for the source function, flux, and scattered intensity normal to the surface are formulated in cartesian coordinates for a 3-D rectangular absorbing, emitting, isotropically scattering medium exposed to both diffuse and collimated radiation. Simplifications of these equations for certain important geometries and uniform loading are presented. Also, superposition of these equations and radiative equilibrium are discussed. For pure scattering, the source function at the center of the square and cubic geometries is analytically determined for the diffuse boundary condition. The generalized 3-D equations are shown to reduce to the familiar 1-D results. Also, the equations for a strongly anisotropic phase function which is made up of a spike in the forward direction superimposed on an otherwise isotropic phase function are expressed in terms of the isotropic expressions.
TL;DR: In this article, the horizontal displacement field along the interface between the half space and alluvial valey is evaluated along with known exact solutions for simple geometry provided the following conclusions: 1) the method provides excellent results for wide range of frequencies, 2) for a fixed number of sources, the results are more accurate at lower frequencies, and 3) as the number of source increases, the accuracy increases.
Abstract: Horizontally polarized shear waves in an elastic alluvial valley of arbitrary shape perfectly bonded to a linearly elastic, homogeneous and isotropic half space are considered. The valley is subjected to a steady state horizontal displacement field. Total displacement field is evaluated along the interface between the half space and alluvial valey. Comparison with known exact solutions for simple geometry provided the following conclusions: 1) the method provides excellent results for wide range of frequencies, 2) for a fixed number of sources, the results are more accurate at lower frequencies, and 3) as the number of sources increases, the accuracy increases.
TL;DR: In this paper, the dynamic axisymmetric behavior of clamped orthotropic shallow spherical shell subjected to instantaneously applied uniform step-pressure load of infinite duration, is investigated, and the resulting modal equations, two in number, are numerically integrated using Runge-Kutta method, and hence the load-deflection curves are plotted.
TL;DR: In this paper, interference effects between planar and normal components of magnetization in an isotropic tape are used to separate the contribution of each and address the question of transition lengths for so-called vertical recording.
Abstract: Interference effects between planar and normal components of magnetization in an isotropic tape are used to separate the contribution of each and address the question of transition lengths for so‐called vertical recording. For low level record signals (−4 dB relative to optimum band edge current) and high coercivity isotropic or anisotropic media, the dominant magnetization at short wavelength is found to be normal to the plane (vertical), and the transition length is nonexistent. The isotropic medium supports twice the normal component of the anisotropic medium. Constructive interference of the two components causes apparent departure from the Wallace equations although each component is exactly described by the Wallace model. Increasing current causes a log/linear attenuation which may be caused by factors other than transition length. Using the isotropic tape, densities of 10 000 transitions/mm (250 000 f.c.i.) are seen.
ARCO1
TL;DR: In this paper, the authors extend the wavefront curvature to the inhomogeneous case in which the ray velocity varies elliptically with the direction of propagation, which is known as velocity anisotropy.
Abstract: The concept of wavefront curvature has been discussed extensively in the literature to relate surface seismic reflection data to subsurface geologic parameters. Developed initially for the case of homogeneous, isotropic, but arbitrarily dipping layered media, this technique has been extended to the inhomogeneous case. Now with the advent of new seismic techniques, such as vertical seismic profiling, three‐dimensional seismic methods, and shear‐wave techniques, the problem of velocity anisotropy is of growing concern to exploration seismologists. The essence of this paper is to extend the method of wavefront curvature to the “elliptically anisotropic” case in which the ray velocity varies elliptically with the direction of propagation. A fundamental feature of wave propagation in the anisotropic medium is that the direction of propagation of the disturbance (or the ray velocity direction) generally differs from that of the wavefront (or the phase velocity direction). Based on the assumption of two‐dimensio...
TL;DR: In this paper, the drawing stress acting on the jet during the fiber drawing process causes an anisotropic, frozen-in network deformation which approaches the order of the thermal isotropic deformation.
Abstract: The following properties of continuously drawn fibers from a nozzle have been measured over a broad range of drawing parameters (temperature, pressure on the nozzle, drawing speed): density, thermal expansion, contraction, and birefringence. These properties show characteristic changes of the fiber structure as compared with the structure of the bulk glass. The structure of the fibers is influenced mainly by the following parameters: the cooling rate and the drawing stress. The cooling rate, which rises up to 105 K/s causes an isotropic effect on the glass network of the fiber: an open structure which corresponds to a fictive temperature of up to more than 100 K above the usual glass transition temperature of the bulk glass. The drawing stress acting on the jet during the fiber drawing process causes an anisotropic, frozen-in network deformation which approaches the order of the thermal isotropic deformation. Glass fibers which have been produced at different temperatures but with the same drawing stress show an increasing optical anisotropy with increasing temperature. This effect and similar effects for the density and shrinkage may be a direct indication of a structural orientation in the fiber direction. Although this orientation (anisometry) is negligibly small for a three-dimensional network structure of oxide glass fibers, the anisotropic effect for the frozen-in structural strain-stress is considerable, because these values are as much as 1 10 or more of those for the strength of the originating glass fibers.