Showing papers on "Isotropy published in 1978"

An extension of the self-consistent scheme to plastically-flowing polycrystals

Abstract: T he general formulation of the self-consistent scheme is specified for an isotropic elasto-plastic approximation of the “constraint” tensor. This leads to an explicit interaction law, modified from that of E. k roner (1961), which takes elasto-plastic accommodation into account via a simple scalar “accommodation function”. This model is applied to uniaxial tension tests for fee polycrystals. Both plastic flow and texture development are investigated. Internal stresses are shown to be significantly lowered with respect to the Kroner model predictions, due to the occurrence of plastic stress relaxation. As a result, the specific plastic properties of the material which are studied, as expressed by a single crystal “hardening matrix”, are found to have a significant influence on the final results.

Random anisotropy in amorphous ferromagnets

Abstract: Random anisotropy is present in all amorphous magnetic materials, and depending on its strength, it can dramatically affect the magnetic behavior. We describe the effect of strong random anisotropy in materials such as amorphous Tb‐Fe and Dy‐Fe at low temperature and also examine the role which weak random anisotropy might play in even ideally homogeneous soft materials. Much of our analysis is based on the simple model proposed by Harris, Plischke and Zuckerman for a ferromagnet with random‐axis uniaxial anisotropy. We describe computer simulation results for this model and then develop scale length arguments which allow us to describe fluctuations in the magnetization direction. For a perfectly isotropic distribution of anisotropy axis we find that the conventional ferromagnetic ground state is unstable. The new ground state has large frozen in fluctuations but probably has a considerable moment and is, therefore, not spin glass‐like. This system does not support domain walls of the conventional type. For a system with both a macroscopic anisotropy axis and random anisotropy, we can have domain walls. We present a theory for the intrinsic coercivity which gives values of about 10−6 Oe for Fe‐metalloids and 0.2 Oe for Gd‐Co‐Mo. This indicates that inhomogeneities of larger than atomic scale are limiting the behavior of present materials. A model illustrating aspects of magnetic resonance behavior is also described.

The isotropic intermolecular potential for H2 and D2 in the solid and gas phases

Abstract: A semiempirical pair potential for molecular hydrogen and deuterium has been derived by fitting to solid state data. The potential is bounded to conform asymptotically to short‐ and long‐range theoretical results. In the solid, many‐body effects are accounted for by including a spherical form of the nonnegligible Axilrod–Muto–Teller three‐body forces. The potential can be used to successfully describe isotropic properties in the solid and gas phases.

Theory of Thermoelasticity With Applications

Abstract: 1 Introduction.- 2 Mathematical groundwork.- 2.1 Tensor calculus.- 2.2 List of useful formulas.- 3 Fundamentals of thermodynamics.- 3.1 System. State. State parameters and functions.- 3.2 The laws of thermodynamics.- 3.3 Nonuniform systems.- 4 Thermodynamics of elastic deformations.- 5 Modes of heat transfer.- 5.1 Radiation.- 5.2 Convection.- 5.3 Conduction.- 6 Theory of heat conduction.- 6.1 Classical differential equation of heat conduction.- 6.2 Initial and boundary conditions.- 7 An hyperbolic equation of heat conduction.- 8 The linear thermoelastic solid.- 8.1 Anisotropy of materials.- 8.2 Certain types of thermoelastic coupling.- 9 The temperature field.- 9.1 Integral transforms.- 9.1a The Laplace transform.- 9.1b Fourier transforms.- 9.1c Hankel transforms.- 9.2 Separation of variables.- 9.3 Green's, or influence, functions.- 9.3a Steady states.- 9.3b Time-dependent states.- 9.4 Duhamel's superposition theorems.- 9.5 Solidification and melting.- 10 Stress and deformation fields.- 10.1 Goodier's thermoelastic potential.- 10.2 Method of biharmonic representations.- 10.3 Betti-Maysel reciprocal method.- 10.4 Thermoelastic-elastic correspondence principle.- 10.5 Method of Green's function.- 10.6 Method of a complex variable.- 10.6a General concepts and theorems.- 10.6b Series expansions.- 10.6c Conformai mapping.- 10.6d Applications to elasticity.- 10.6e Uniqueness of solution. Connectivity of regions.- 10.6f Cauchy integrals.- 10.7 The extended Boussinesq-Papkovich-Neuber solution.- 11 Uniqueness of solution. Stress-free thermoelastic fields.- 11.1 Uniqueness of solution.- 11.2 Stress-free thermoelastic fields.- 11.2a Three-dimensional regions.- 11.2b Two-dimensional regions.- 12 Anisotropic bodies.- 12.1 Correspondence principle for anisotropic bodies.- 12.2 Thermal stresses in an orthotropic hollow cylinder.- 12.3 Thermal stresses in a transversely isotropic half-space.- 13 Stresses due to solidification.- 14 Thermoelastic stresses in plates.- 14.1 General equations.- 14.2 Boundary conditions.- 14.3 Correspondence principle for isotropic plates.- 14.4 Two characteristic cases.- 14.5 Laminated composite plates.- 15 Thermoelastic stresses in shells.- 15.1 Deformation of shells of revolution under axisymmetric mechanical and thermal load.- 15.2 State of stress in shells of revolution deformed axisymmetrically.- 15.3 General theory of shells.- 15.4 Shells of revolution deformed arbitrarily.- 15.5 Donnell's theory of cylindrical shells.- 15.6 Boundary conditions.- 15.7 Equation of heat conduction for shells.- 16 Thermoelastic stresses in bars.- 16.1 Bars of solid cross-section.- 16.2 Bars of thin-walled open cross-section.- 16.3 Bars of thin-walled closed cross-section.- 16.4 Torsion of bars of thin-walled open cross-section.- 17 Thermoelastic stresses around cracks.- 18 Thermoelastic stability of bars and plates.- 18.1 Bars of solid and thin-walled closed cross-section.- 18.2 Bars of thin-walled open cross-section.- 18.3 Plates.- 18.4 Post-buckling behavior of plates.- 19 Moving and periodic fields.- 19.1 General remarks.- 19.2 Illustrative examples.- 20 Thermoelastic vibrations and waves.- 20.1 General concepts and equations.- 20.2 Thermoelastic harmonic waves in infinite media.- 20.3 Thermoelastic Rayleigh waves.- 20.4 Thermoelastic vibrations of a spinning disk.- 20.5 Wave discontinuities.- 21 Coupled thermoelasticity.- 22 Thermoelasticity of porous materials.- 23 Electromagnetic thermoelasticity.- 23.1 Basic concepts of electromagnetism.- 23.2 Maxwell's equations.- 23.3 Lorentz force. Maxwell stresses.- 23.4 Moving bodies.- 23.5 Electromagnetic energy.- 23.6 Electromagnetic thermoelastic equations.- 23.6a Thermoelasticity of dielectrics.- 23.6b Thermoelasticity of ferromagnetic bodies.- 23.6c Applications.- 24 Piezothermoelasticity.- 25 Random thermoelastic processes.- 25.1 General concepts and equations.- 25.1a Random variables.- 25.1b Random processes.- 25.2 Spectral density.- 26 Variational methods in thermoelasticity.- 26.1 General remarks.- 26.2 Virtual work.- 26.3 Principles of stationary energy of Hemp.- 26.4 Principle of Washizu.- 26.5 Principle of Biot.- Literature.- Author index.

Elastic waves in rods and clad rods

Abstract: Clad rods have been investigated for use as long delay lines because they offer isolation of the signal from the surface and low dispersion. In addition, single‐mode propagation is achieved with a larger (and hence more conveniently transduced) cross section than is possible with a homogeneous rod at the same frequency. This paper describes the modes that have a steady‐state sin(ωt−βz) dependence on (t,z), with emphasis on the modes and ranges of parameters that are of interest for delay lines. Only rods of circular cross section, and isotropic, linear elastic materials are considered. Attention is drawn to correspondences with homogeneous rods and with the hypothetical case of infinite thickness cladding, which is most useful as a model for understanding the behavior of corresponding modes in an actual clad rod. Written for the nonspecialist, the paper includes a tutorial review of the concepts and results needed to understand wave propagation in rods and clad rods. In addition, the following new results are reported: (1) for homogeneous rods, a representation of the lowest flexural mode dispersion curve that is for practical purposes independent of Poisson’s ratio; (2) for homogeneous rods, displacement distributions of the first three high‐frequency shear modes, i.e., the ’’flexural’’ modes that are asymptotic to the shear velocity (it was found that the distribution previously attributed to the lowest such mode actually belongs to the next); (3) for clad rods, the first demonstration of interface modes of the Stoneley type for nonaxially symmetric waves; (4) classification of clad rods according to the nature and ordering of their asymptotic velocities showing that there are eight types of clad rod, rather than four as stated in the previous literature; (5) for infinitely clad rods having the same shear modulus, proof that the dispersion of torsional waves and their penetration into cladding are universal functions of f/fc∞. The ratio of the shear velocities of the two materials affects the cutoff frequency fc∞, but not the universal penetration and dispersion functions. Subjects on which significant tutorial or descriptive material is given include typical waveguide dispersion, characteristic velocities of an isotropic elastic material, the effect of coupling of dilatational and shear waves at a boundary, waves in homogeneous rods, the connection of isolation to total internal reflection (with Love waves and SH waves in a clad plate as an example), Stoneley waves at a plane interface, and previous results on the clad rod.

The Effect of A General Aspherical Perturbation on the Free Oscillations of the Earth

Abstract: summary. The Lagrangian governing the infinitesimal elastic-gravitational oscillations of a completely general earth model with interior fluid—solid boundaries is given. Rayleigh's principle is then used to derive a formula for calculating the first-order perturbations in the eigenfrequencies due to an arbitrary slight perturbation of a spherically symmetric, non-rotating, isotropic starting model. The perturbations considered include rotation, asphericity, elastic anisotropy, and a deviatoric initial stress, as well as a change in the positions of both welded and fluid—solid boundaries.

Bifurcation in Onsager's model of the isotropic-nematic transition

Abstract: In this paper Onsager's theory of the orientational order in a three-dimensional system of hard rods is reanalyzed as a nonlinear eigenvalue problem. Bifurcation is found and the equation of state is calculated from the orientational distribution function for a nematic phase. We also investigate the corresponding twodimensional system of hard lines. The existence and order of a phase transition are shown to depend on both the direction of bifurcation and on properties of the global solutions. The analysis can be adapted to other nonlinear equations obtained in theories of liquid crystals.

A molecular dynamics simulation of dephasing in liquid nitrogen

Abstract: We relate the dephasing of molecular vibrations in liquids to certain correlation functions involving only the translational and rotational degrees of freedom; these correlation functions are then determined through a classical molecular dynamics simulation of rigid, nonvibrating molecules. Using a Lennard‐Jones atom–atom potential for N2 (liq) near its boiling point, we calculate a dephasing time of 62 psec, in good agreement with picosecond pulse and isotropic Raman linewidth measurements. The importance and characterisic time scales of different dephasing mechanisms are studied, and the significant effect of vibrational anharmonicity is demonstrated.

Theoretical analysis of the stability of slopes

Abstract: The problem of limiting equilibrium of a slope in a state of plane strain is formulated in terms of the variational calculus. Formulated that way, the analysis is carried out without any a priori assumptions with respect to the shape of the slip surface, or the normal stress distribution along it. Thus, on the basis of only a formal definition of the concepts of limiting equilibrium, and factor of safety with respect to strength, it is proven that the minimal factor of safety must occur on slip surfaces with a special geometrical property. This geometrical property ensures that the resultant of the infinitesimal normal and frictional forces either pass through a common point or are parallel to a common direction. It is shown that as a result of this geometrical property the minimal factor of safety is independent of the normal stress distribution along the critical slip surface. In the homogeneous and isotropic case the analysis shows that the critical slip surface may be either a log-spiral or a straight...

The ground state of two quantum models of magnetism

Abstract: The ground state energy and pair correlations have been computed exactly for the spin XY magnet and isotropic Heisenberg antiferromagnet, for a sequence of finite cells on the square and honeycomb ...

Measured spectral bidirectional reflection properties of four vegetated surfaces.

Abstract: Spectral bidirectional reflectance values are presented at the 0.52-microm wavelength based on measured values of the radiation field of four vegetated surfaces: savannah, bog, pasture land, and coniferous forest, which cover a wide range of natural vegetated canopies. The results are given as examples of the full set of bidirectional reflectance values which consists of data at seven wavelengths between 0.43microm and 2.20 microm for each of the four surfaces. (From July 1977, the full set of data is available from the author on request.) The data may be applied for calculations of the radiative transfer in the atmosphere with realistic ground properties instead of isotropic albedo values.

Plasticity theory for soil stress-strain behavior

Abstract: A general analytical model that describes both drained and undrained, anisotropic, elastoplastic, path-dependent stress-strain-strength properties of inviscid saturated soils is presented. For any loading (or unloading) history, the instantaneous configuration of the field of yield surfaces is determined by calculating the translation and contraction (or expansion) of each yield surface during successive changes in load. The material behavior can thus be determined for complex, and, in particular, for cyclic loading paths. The inverse stress-strain relations always exist and are uniquely defined if and only if the yield surfaces do not overlap. In order to avoid such overlappings, a new isotropic/kinematic hardening rule is introduced which couples the simultaneous translation of consecutive surfaces. The isotropic/kinematic hardening of the outer surfaces is thus made compatible with any isotropic/kinematic hardening rule assumed for the inner surfaces.

Charge-density waves and isotropic metals

Abstract: Fermi-surface instability leading to charge density waves is a common malady in anisotropic metals, and there is now evidence that it also infects isotropic ones.

Nearly isochoric elastic deformations: Application to rubberlike solids

Abstract: An the assumption that volume changes taking place during the deformation of an elastic solid are of a small order of magnitude, an expression is obtained for the local volume change at arbitrary deformation and independently of any elastic symmetry (such as isotropy). It is given in terms of the deformation appropriate to the associated incompressible material under the same boundary conditions. The results are specialized to isotropic elastic solids and, more particularly, to a class of strain-energy functions which are appropriate to rubberlike solids. An analysis of simple tension on these lines has been given previously (o gden , 1976), but from a more specialized starting-point. The present work clarifies some features of the problem. Here, results are given for a non-homogeneous deformation, namely, torsion of a solid circular cylinder superposed on uniaxial tension. Calculations are made of the local and overall volume changes due to this combined deformation, and the predictions of the theory are assessed in the light of the limited experimental data which are available. The need for further experimental work is emphasized.

On the motion of suspended particles in stationary homogeneous turbulence

Abstract: The closed equations for the velocity correlation tensor and for the mean-squared displacement of a particle suspended in a stationary homogeneous turbulent flow, with an arbitrary linear law of fluid-particle interaction, are obtained using two assumptions suggested previously for the problem of turbulent self-diffusion: the ‘independence approximation’ and the Gaussian property of the functional distribution of particle velocities. The numerical solution of the derived equations is given for an isotropic system with a model turbulence spectrum. The following characteristics of the particle motion are obtained: ( a ) the mean kinetic energy, ( b ) diffusivity, ( c ) rate of energy dissipation, ( d ) velocity correlation function, and ( e ) the correlation function of the relative fluid-particle velocity. The impact of various spectral modes on the characteristics of the particle motion is discussed.

Spin-Glass and Ferromagnetic Behavior Induced by Random Uniaxial Anisotropy.

Abstract: The effect of a random uniaxial anisotropy axis on the magnetic properties of an amorphous ferromagnet is considered. It is found that in a quenched system random anisotropy with an isotropic angular distribution destroys the ferromagnetic state in fewer than four dimensions. The low-temperature phase is, instead, an Edwards-Anderson spin-glass. In more than four dimensions ferromagnetism or spin-glass ordering is found depending on the degree of disorder. Some properties of the ferromagnetic state are outlined.

Internal dynamics of van der Waals complexes. II. Determination of a potential energy surface for ArHCl

Abstract: The Born–Oppenheimer angular‐radial separation method for calculating ground state properties of atom‐diatomic complexes has been used to determine a potential energy surface for ArHCl. Using a nonlinear least squares procedure, the calculated properties from trial surfaces were fit to molecular beam electric resonance data including both radial and angular expectation values. The inclusion of coriolis coupling terms in the Hamiltonian were found to have a small but discernable effect on the calculated properties. Both the number and type of parameters used to describe the surface affected their correlations dramatically. Fitting the angular properties of the complex required the potential to have an anisotropic to isotropic strength ratio of about 1:2. The isotropic portion of the potential could not be uniquely determined from the bound‐state data alone, but was fixed by predicted differential elastic scattering cross‐sections. In terms of R, the length of the vector connecting the Ar and the center of ...

On the incremental equations in non-linear elasticity — II. Bifurcation of pressurized spherical shells

Abstract: Bifurcations of spherical elastic shells subsequent to a finite radially-symmetric inflation are analysed. In the case of a membrane, necessary and sufficient conditions for the initiation of asymmetric deformation modes are obtained in respect of an arbitrary (incompressible, isotropic) form of elastic strain-energy function. The method used differs from that used anywhere before, and the results obtained generalize, extend and elucidate those given previously for this problem. In particular, we find that aspherical bifurcations first become possible when the surface tension reaches a maximum. The corresponding analysis is given for thick shells, also for an arbitrary form of the strain-energy function. Despite the inhomogeneity of the deformation in this case, some analytical results are derived which have certain features in common with the membrane results. However, the bifurcation criteria for thick shells are not equivalent to those for the membrane. This is illustrated for particular forms of the strain-energy function. The results depend very much on the shell thickness. In particular, aspherical bifurcations are not possible for shells whose thickness is beyond some critical value. Nevertheless, membrane theory provides a good prediction of the behaviour of shells of moderate finite thickness.

A reinvestigation of the Raman spectrum of water

Abstract: The Raman spectrum of liquid water has been reinvestigated using a technique which automatically records the depolarization ratio along with the polarized Raman spectrum. The exceptionally accurate depolarization ratios thus obtained, as well as the isotropic and the anisotropic spectra of water, indicate that the libration region extends to higher frequencies than previously thought and that a new polarized band originating from restricted translation occurs near 290 cm−1. The translational spectrum is in good agreement with that calculated by Weres and Rice.

The effect of anisotropy on the creep of polycrystalline ice

Abstract: Quantitative effects of crystallographic orientation fabrics are incorporated into the flow law for isotropic polycrystalline ice by the introduction of an enhancement factor applied to the isotropic fluidity. An aggregate is viewed to a first approximation as a collection of grains deforming independently by basal glide. The influence of preferred orientations on the mean intragranular rate of strain is treated in terms of a redistribution of the magnitude and orientation of resolved basal shear stress. A quantitative measure of this effect on the fluidity of the aggregate is provided through the development of a geometric tensor and a stress configuration parameter. Intergranular interference is then considered as a dissipative process modifying the fluidity of the aggregate. Empirical justification for the model at low octahedral shear stresses is provided by several laboratory creep tests on naturally anisotropic bore-hole specimens under both in situ and anomalous stress situations. Predicted enhancement factors ranged from approximately 0.2 to 2.8 and agree well with measured values. The tests were carried out in uniaxial compression and simple shear.

Coherent electromagnetic waves in pair‐correlated random distributions of aligned scatterers

Abstract: Recent results for the corresponding scalar problem are generalized to coherent electromagnetic waves in random distribution of pair‐correlated obstacles (aligned or averaged over alignment). Proceeding essentially as before, we obtain dispersion equations by averaging the vector–dyadic functional equation relating the multiple and single scattered amplitudes of the obstacles. In general, for aligned nonradially symmetric scatterers, the resulting bulk indices of refraction specify anisotropic media; the anisotropy arises either from the scatterers’ properties (physical parameters or shape, or both) or from their distribution, or from both. The illustrations include both isotropic and anisotropic cases, and the explicit results generalize earlier ones.

Solar wind velocity estimation from multi-station IPS

Abstract: Three-station and four-station observations at 74 MHz are used to study the spatial structure and temporal rearrangement of the intensity pattern of interplanetary scintillations (IPS) in weak scattering. Velocity estimators from three models, two of which include rearrangement, are applied to the data and evaluated. It is shown that for certain radio sources the spatial anisotropy of the pattern is determined by elongated source structure. An upper bound on the average pattern axial ratio for an isotropic ecliptic source is 1.3 for data of mid-1972. An upper bound on the average random velocity for the same period is 40% of the bulk velocity. We discuss a simple velocity estimator that is independent of the spatial anisotropy and has a low sensitivity to the random velocity.

The reflection, refraction, and diffraction of waves in media with an elliptical velocity dependence

Abstract: Assuming media having a velocity dependence on angle which is an ellipse, we have confirmed previously reported time‐distance relations for reflections from single interfaces, for reflections from sections of beds separated by horizontal interfaces, for refraction arrivals, and added the expression for diffractions. We also have derived expressions for plane‐wave reflection and transmission coefficients at an interface separating two transversely isotropic media. None of the properties differs greatly from those for isotropic media. However, velocities found from seismic surface reflections or refractions are horizontal components. There seems to be no way of obtaining vertical components of velocity from surface measurements alone and hence no way to compute depths from surface data.

On the theory of elssticity of a nonhomogeneous medium

Abstract: In this paper the equation of equilibrium for a nonhomogeneous isotropic elastic solid under shear has been solved in rectangular Cartesian coordinates as well as in cylindrical polar coordinates. The modulus of rigidity of the material is assumed to vary in lateral as well as vertical directions. As an example, the above solution has been used to solve the problem of a Griffith crack in an infinite solid under shear.

Anisotropic undrained stress-strain behavior of clays

Abstract: A general analytical model that describes the anisotropic, elasto-plastic path-dependent stress-strength properties of inviscid saturated clays under undrained loading conditions is presented. The model combines properteis of isotropic and kinematic plasticity by introducing the concept of a field of shear moduli. This field is defined in stress space by the relative configuration of yield surfaces. For any loading history, the instantaneous configuration is determined by calculating the translation and contraction (or expansion) of each yeld surface. The material behavior can thus be determined for complex loading paths. The model parameters can be derived entirely from the results of conventional triaxial tests. The model predictions agree very well with experimental test results from triaxial, plane strain, and simple shear laboratory tests and account for stress induced anisotropy in a simple manner. /Author/

The oblique compression of two elastic spheres

Abstract: A fundamental problem in the behaviour of the packing of spheres is that of the oblique compression of just two spheres. Here, the solution of this problem is obtained for the case of two identical homogeneous isotropic elastic spheres, since much use can then be made of the existing symmetry. In particular, the normal and shear components of traction on the contact area can be treated separately. Considerations of the normal force show that the contact area is circular and, furthermore, that this part of the solution is precisely that of normal Hertzian contact. To obtain that part of the solution corresponding to shear, two criteria are used. The first is that of no slip between the spheres, and the second is that the energy flux across the contact area must obey the appropriate symmetries of the problem. These symmetries are sufficient to make the solution unique. This solution differs greatly from that obtained when the spheres are first compressed normally and then sheared. In particular, it is shown that if slip does occur, then it will be in the form of sliding; whereas in the latter case, slip occurs only within a circular annulus.