Showing papers on "Isotropy published in 1995"

Soft magnetic nanocrystalline materials

Abstract: The microstructure property relationship in soft magnetic nanocrystalline Fe-base materials is surveyed: The basic mechanism is that the magneto-crystalline anisotropy of the small, randomly oriented bcc-Fe grains is averaged out by exchange interaction. The resulting magnetic behaviour can be well described with the random anisotropy model. The latter has been extended to multiphase materials including the case that the grain size exceeds the exchange length and, is able now to describe the hardening mechanism in the overannealed nanocrystalline state due to the precipitation of borides. Further, the crucial role of the coupling mechanism between the grains is discussed. Thus, as a function of temperature, a single sample combines a variety of phenomena ranging from soft, over hard to finally superparamagnetic behaviour. Finally it is shown, how the structural phases present lead to low or vanishing magnetostriction; the random anisotropy effect guarantees an essentially isotropic behaviour comparable to the amorphous case. Together with the suppressed magneto-crystalline anisotropy, the low magnetostriction provides the basis for the superior soft magnetic properties observed in particular compositions.

Which Elasticity Tensors are Realizable

Abstract: It is shown that any given positive definite fourth order tensor satisfying the usual symmetries of elasticity tensors can be realized as the effective elasticity tensor of a two-phase composite comprised of a sufficiently compliant isotropic phase and a sufficiently rigid isotropic phase configured in an suitable microstructure. The building blocks for constructing this composite are what we call extremal materials. These are composites of the two phases which are extremely stiff to a set of arbitrary given stresses and, at the same time, are extremely compliant to any orthogonal stress. An appropriately chosen subset of the extremal materials are layered together to form the composite with elasticity tensor matching the given tensor.

Mechanics of collisional motion of granular materials. Part 1. General hydrodynamic equations

Abstract: Collisional motion of a granular material composed of rough inelastic spheres is analysed on the basis of the kinetic Boltzmann–Enskog equation. The Chapman–Enskog method for gas kinetic theory is modified to derive the Euler-like hydrodynamic equations for a system of moving spheres, possessing constant roughness and inelasticity. The solution is obtained by employing a general isotropic expression for the singlet distribution function, dependent upon the spatial gradients of averaged hydrodynamic properties. This solution form is shown to be appropriate for description of rapid shearless motions of granular materials, in particular vibrofluidized regimes induced by external vibrations.The existence of the hydrodynamic state of evolution of a granular medium, where the Euler-like equations are valid, is delineated in terms of the particle roughness, β, and restitution, e, coefficients. For perfectly elastic spheres this state is shown to exist for all values of particle roughness, i.e. − 1≤β≤1. However, for inelastically colliding granules the hydrodynamic state exists only when the particle restitution coefficient exceeds a certain value em(β)< 1.In contrast with the previous results obtained by approximate moment methods, the partition of the random-motion kinetic energy of inelastic rough particles between rotational and translational modes is shown to be strongly affected by the particle restitution coefficient. The effect of increasing inelasticity of particle collisions is to redistribute the kinetic energy of their random motion in favour of the rotational mode. This is shown to significantly affect the energy partition law, with respect to the one prevailing in a gas composed of perfectly elastic spheres of arbitrary roughness. In particular, the translational specific heat of a gas composed of inelastically colliding (e = 0.6) granules differs from its value for elastic particles by as much as 55 %.It is shown that the hydrodynamic Euler-like equation, describing the transport and evolution of the kinetic energy of particle random motion, contains energy sink terms of two types (both, however, stemming from the non-conservative nature of particle collisions) : (i) the term describing energy losses in incompressibly flowing gas; (ii) the terms accounting for kinetic energy loss (or gain) associated with the work of pressure forces, leading to gas compression (or expansion). The approximate moment methods are shown to yield the Euler-like energy equation with an incorrect energy sink term of type (ii), associated with the ‘dense gas effect’. Another sink term of the same type, but associated with the energy relaxation process occurring within compressed granular gases, was overlooked in all previous studies.The speed of sound waves propagating in a granular gas is analysed in the limits of low and high granular gas densities. It is shown that the particle collisional properties strongly affect the speed of sound in dense granular media. This dependence is manifested via the kinetic energy sink terms arising from gas compression. Omission of the latter terms in the evaluation of the speed of sound results in an error, which in the dense granular gas limit is shown to amount to a several-fold factor.

Discontinuous and continuous damage evolution in Ogden-type large-strain elastic materials

Abstract: The paper presents an application of continuum damage mechanics to large-strain Ogden-type elastic materials. A Eulerian setting of elasticity with isotropic damage-caused softening effect is discussed exclusively in terms of the Finger tensor as a strain measure. The local damage accumulation is related to two phenomenological variables, the maximum value and the arclength of effective free energy attained during a typical loading process. The frame is specified for a rigorously decoupled volumetric-isochoric response based on a multiplicative split of the Finger tensor into spherical and unimodular parts. In this context, the damage is related to the isochoric part of the deformation only, which is assumed to be governed by an Ogden-type effective free-energy function formulated in terms of the eigenvalues of the unimodular part of the Finger tensor. A constitutive algorithm for the computation of the nominal stresses and nominal tangent moduli for plane problems is developed. Finally, some fundamental finite-element simulations for rubber-like materials are presented.

The elastic coefficients of double‐porosity models for fluid transport in jointed rock

Abstract: Phenomenological equations (with coefficients to be determined by specified experiments) for the poroelastic behavior of a dual porosity medium are formulated, and the coefficients in these linear equations are identified. The generalization from the single-porosity case increases the number of independent coefficients for volume deformation from three to six for an isotropic applied stress. The physical interpretations are based upon considerations of different temporal and spatial scales. For very short times, both matrix and fractures behave in an undrained fashion. For very long times, the double-porosity medium behaves like an equivalent single-porosity medium. At the macroscopic spatial level, the pertinent parameters (such as the total compressibility) may be determined by appropriate field tests. At an intermediate or mesoscopic scale, pertinent parameters of the rock matrix can be determined directly through laboratory measurements on core, and the compressibility can be measured for a single fracture. All six coefficients are determined from the three poroelastic matrix coefficients and the fracture compressibility from the single assumption that the solid grain modulus of the composite is approximately the same as that of the matrix for a small fracture porosity. Under this assumption, the total compressibility and three-dimensional storage coefficient of the composite are the volume averages of the matrix and fracture contributions.

Scaling invariance of crack surfaces

Abstract: The morphology of fractured rock surfaces is studied in terms of their scaling invariance. Fresh brittle fractures of granite and gneiss were sampled with a mechanical laboratory profilometer, and (1 + 1)-dimensional parallel profiles were added to build actual maps of the surfaces. A first step in the scaling invariance description is a self-affine analysis using three independent methods. The root-mean-square and the maximum-minimum difference of the height are shown to follow a power law with the sample length. The return probability and the Fourier spectrum are also computed. All these approaches converge to a unique self-affine exponent: ζ = 0.80. Analysis over a broad statistical set provides a reproducibility error of ±0.05. No significant differences between the isotropic granite and the markedly anisotropic gneiss appear for the scaling exponents. An analysis of the profilometer shows that the two main drawbacks of the setup are not significant in these analyses. The systematic errors of the scaling analysis are estimated for the different methods. Isotropy of the scaling invariance within the mean fracture plane is shown either with the result obtained from different fracture orientations or with the two-dimensional Fourier spectrum of the surface topography itself. The analysis is brought further into the multifractal framework. The structure functions are shown to have power law behavior, and their scaling exponent varies nonlinearly with the moment order. Finally, the corresponding conserved process belongs to a universal multifractal class with α = 1.5 for the Levy index and C1 = 0.3 for the fractal codimension of the mean singularities. The three indices (ζ, α and C1) completely characterize the scale invariance. The multifractal behavior is significant for physical properties which depend on high-order moments like contact. According to this study and that of other groups, the self-affine exponent ζ is constant over a large range of scales and for different fracture modes and various materials. This opens the possibility that there exists a form of universality in the cracking process. It appears that only the prefactor of the roughness is dependent on material and mode.

Optimized isotropic diffusion weighting

Abstract: The authors introduce several sets of time-efficient gradient waveforms for applying isotropic diffusion weighting in NMR experiments. This creates signal attenuation that depends on the trace of the diffusion tensor and is therefore rotationally invariant. Numerical methods for the calculation of such gradient sets are outlined, and results are shown for isotropic and anisotropic gradient hardware and first order flow moment nulled diffusion weighting gradients. Preliminary experimental results from the human brain validate this new technique.

Seismic evaluation of concrete dams via continuum damage models

Abstract: In this paper a general methodology for the analysis of large concrete dams subjected to seismic excitation is outlined. It is valid both for gravity dams (2D representation) and arch dams (3D representation). The method allows for non-linear material behaviour of the dam, ‘transparent fictitious boundaries’ for dealing properly with in-coming and out-going seismic waves, and an efficient procedure to deal with dam-soil-fluid interaction. The mechanical behaviour of concrete is modelled using an isotropic damage model which allows for tension and compression damage, and exhibits stiffness recovery upon load reversals. Emphasis is placed in the treatment of fluid-structure interaction, regarding both formulation and efficiency aspects. A gravity dam and an arch dam are analysed subjected to artificially generated earthquakes of different intensities, and the results are used to study the degree of (un)safety of the dams.

Predicting stress-induced velocity anisotropy in rocks

Abstract: A simple transformation, using measured isotropic V P and V S versus hydrostatic pressure, is presented for predicting stress-induced seismic velocity anisotropy in rocks. The compliant, crack-like portions of the pore space are characterized by generalized compressional and shear compliances that are estimated from the isotropic V P and V S . The physical assumption that the compliant porosity is crack-like means that the pressure dependence of the generalized compliances is governed primarily by normal tractions resolved across cracks and defects. This allows the measured pressure dependence to be mapped from the hydrostatic stress state to any applied nonhydrostatic stress. Predicted P- and S-wave velocities agree reasonably well with uniaxial stress data for Barre Granite and Massillon Sandstone. While it is mechanically similar to methods based on idealized ellipsoidal cracks, the approach is relatively independent of any assumed crack geometry and is not limited to small crack densities.

Shape evolution by surface diffusion and surface attachment limited kinetics on completely faceted surfaces

Abstract: The evolution of two-dimensional shapes to equilibrium shapes is investigated for two kinetic mechanisms, surface diffusion and surface attachment limited kinetics. Qualitative differences are found that may be used in experiments for easy distinction among the two mechanisms, and find topological changes not expected for the corresponding isotropic problems. We take advantage of the mathematical developments for surface evolution and equilibration problems when surface energy anisotropy is “crystalline”, so extreme that crystals are fully faceted. We confirm the prediction that with this anisotropy these problems are more easily solvable than for lesser anisotropies, and the techniques developed may even be useful for approximating isotropic problems.

Effective plastic response of two-phase composites

Abstract: Finite element analyses of the overall stress-strain response of metal-matrix composites are carried out using axisymmetric and plane strain unit cell formulations. The metal matrix is characterized as an isotropically hardening elastic-plastic solid and the ceramic reinforcement is taken to be isotropic elastic. Perfect bonding between the matrix and the reinforcement is assumed. The focus is on the effects of reinforcement shape, size and spatial distribution. Under monotonic loading, the stress-carrying capacity in the plastic range increases in the following order for the reinforcement shapes considered: double-cone → sphere → truncated cylider → unit cylinder → whisker. The extent of the Bauschinger effect under reversed loading increases in the same order for particle reinforced composites. The effects of reinforcement size and distribution are analyzed by considering a plane strain model with two sizes of reinforcing particles. For certain distributions, it is found that the smaller family of particles plays virtually no role in affecting the stress-strain response. Thermal residual stresses are also considered and their effects are seen to persist far into the plastic range. The predicted plastic stress-strain behavior can be rationalized in terms of the evolution of matrix field quantities and, in particular, in terms of the effect of the constraint on plastic flow.

Finite element modeling of isotropic elastic porous materials coupled with acoustical finite elements

Abstract: In this paper the development of a two‐dimensional elastic‐absorption finite element model of isotropic elastic porous noise control materials is described. A method for coupling elastic‐absorption finite elements with conventional acoustic finite elements is also presented for the cases when the interface between the adjacent air space and the foam is either unfaced or sealed by a membrane. The accuracy of the acoustic/elastic‐absorption model has been verified by comparing its predictions with analytical solutions for the case of wave propagation in a foam‐filled waveguide. Further, the finite element model has been used to investigate the effect of edge constraints on the surface normal impedance of a foam sample in a standing‐wave tube. As expected, edge constraints were found to stiffen the foam acoustically at low frequencies.

Microstructures minimizing the energy of a two phase elastic composite in two space dimensions. II: The vigdergauz microstructure

Abstract: For modeling coherent phase transformations, and for applications to structural optimization, it is of interest to identify microstructures with minimal energy or maximal stiffness. The existence of a particularly simple microstructure with extremal elastic behavior, in the context of two-phase composites made from isotropic components in two space dimensions, has previously been shown. This “Vigdergauz microstructure” consists of a periodic array of appropriately shaped inclusions. We provide an alternative discussion of this microstructure and its properties. Our treatment includes an explicit formula for the shape of the inclusion, and an analysis of various limits. We also discuss the significance of this microstructure (i) for minimizing the maximum stress in a composite, and (ii) as a large volume fraction analog of Michell trusses in the theory of structural optimization.

Effect of particle shape on the strength and deformation mechanisms of ellipse‐shaped granular assemblages

Abstract: This paper presents the results of a Discrete Element Method study on the influence of particle shape on the strength and deformation behaviour of two dimensional assemblages of ellipse‐shaped particles. Assemblages of particles with varying individual particle aspect ratio were formed with a preferred bedding plane, isotropically compressed with varying isotropic confining stresses and then sheared with biaxial compression. The results indicate that Discrete Element analysis using two dimensional ellipse‐shaped particles produces mechanical behaviour which is similar both quantitatively and qualitatively to the behaviour of real granular materials. Even small particle out‐of‐roundness increases the observed macroscopic strength significantly. In systems composed of flatter particles, particle rotations are greatly inhibited. Decomposing relative contact displacements into contributions due to particle rotation and translation demonstrates that most of the displacements in round particle systems are due to individual particle rotation.

Comparative simulation of excitation and body surface electrocardiogram with isotropic and anisotropic computer heart models

Abstract: Comparative simulations between isotropic and anisotropic computer heart models were conducted to study the effects of myocardial anisotropy on the excitation process of the heart and on body surface electrocardiogram. The isotropic heart model includes atria, ventricles, and a special conduction system, and is electrophysiologically specified by parameters relative to action potential, conduction velocity, automaticity, and pacing. The anisotropic heart model was created by incorporating rotating fiber directions into the ventricles of the isotropic heart model. The orientation of the myocardial fibers in the ventricles of the model was gradually rotated counterclockwise from the epicardial layer to the endocardial layer for a total rotation of 90/spl deg/. The anisotropy of conduction velocity and intracellular electric conductivity was included in the simulation. Comparative simulations of the normal heart, LBBB, and RBBB showed no significant differences between the two models in the excitation processes of the whole heart or in the body surface electrocardiograms. However, it was easier to induce ventricular fibrillation in the anisotropic model than in the isotropic model. The comparative simulation is useful for investigating the effects of myocardial anisotropy at the whole heart level and for evaluating limitations of the isotropic heart model. >

Gaussian beam depth migration for anisotropic media

Abstract: Gaussian beam migration (GBM), as it is implemented today, efficiently handles isotropic inhomogeneous media. The approach is based on the solution of the wave equation in ray‐centered coordinates. Here, I extend the method to work for 2-D migration in generally anisotropic inhomogeneous media. Extension of the Gaussian‐beam method from isotropic to anisotropic media involves modification of the kinematics and dynamics in the required ray tracing. While the accuracy of the paraxial expansion for anisotropic media is comparable to that for isotropic media, ray tracing in anisotropic media is much slower than that in isotropic media. However, because ray tracing is just a small portion of the computation in GBM, the increased computational effort in general anisotropic GBM is typically only about 40%. Application of this method to synthetic examples shows successful migration in inhomogeneous, transversely isotropic media for reflector dips up to and beyond 90°. Further applications to synthetic data of lay...

Control of an Easy-Axis on Nematic-Polymer Interface by Light Action to Nematic Bulk

Abstract: An appearance of an easy orientation axis of a nematic liquid crystal on the isotropic aligning surface under the light absorption by in-bulk azo dye molecules is observed. It is shown that orientation of LC molecules in the irradiated region is close to the direction of the exciting beam polarization. Accompanying to aligning, the surface driven reorientation effect has been studied. A threshold as well as a nonthreshold reorientation of the director toward the light-induced easy axis were observed. The value of the light-induced anchoring energy depends on the exposure time and achieves 2.5×10-3 erg/cm2. The experimental data are explained within the framework of adsorption of phototransformed molecules from the LC bulk onto the aligning surface.

Dynamic weight functions for a moving crack. I. Mode I loading

Abstract: Dynamic weight functions are constructed for general time-dependent shear loading of a plane semi-infinite crack propagating with constant speed in an infinite isotropic elastic body. The use of Fourier transforms reduces the problem to the analysis of a matrix Wiener-Hopf equation. The solution of the Wiener-Hopf problem is presented. An expression is derived for the first-order perturbation to the stress intensity factors induced by a small time-dependent deviation from straightness of the crack front. The asymptotic procedure requires consideration of two terms of the asymptotic expansions of the displacement and stress tensor components in a neighbourhood of the crack front.

Continuum Damage Mechanics, Anisotropy and Damage Deactivation for Brittle Materials Like Concrete and Ceramic Composites

Abstract: The main lines of a Continuum Damage Mechanics Modelling are reviewed, for applications to brittle materials treated as elastic damageable ones.The proposed damage models consider in the same framework the cases of initially isotropic materials like concrete and anisotropic composites.Attention is focused on the damage deactivation effects and on the possibility to describe irreversible strains directly associated to the damaging processes without any additional dissipation. Finally, the model is applied to two particular SiC/SiC and C/SiC composites.

Orientation Model for Particles in Turbulence

Abstract: The problem of predicting the orientations of falling nonspherical particles has been addressed by the construction of a heuristic model that assumes the particles are subject to isotropic turbulence within or below the inertial subrange, that is, the Kolmogorov spectrum of eddies, depending on the particle dimensions. The rms tilt angle of a spheroidal particle of small eccentricity is determined by Langevin-type averaging over its equation of motion, taking into account the first-order restoring torque that arises when the stable fall mode is perturbed by either thermal or turbulent fluctuations. By invoking dimensional constraints concerning the nature of the main flow and turbulent stresses and by assuming the thermal and turbulent fluctuations are uncorrelated, an approximate expression for the variance of an assumed Gaussian orientation distribution for small tilt angles and small flow Reynolds numbers is obtained. The expression is then generalized to provide a semiquantitative, nearly Gau...

Normal moveout from dipping reflectors in anisotropic media

Abstract: Description of reflection moveout from dipping interfaces is important in developing seismic processing methods for anisotropic media, as well as in the inversion of reflection data. Here, I present a concise analytic expression for normal‐moveout (NMO) velocities valid for a wide range of homogeneous anisotropic models including transverse isotropy with a tilted in‐plane symmetry axis and symmetry planes in orthorhombic media. In transversely isotropic media, NMO velocity for quasi‐P‐waves may deviate substantially from the isotropic cosine‐of‐dip dependence used in conventional constant‐velocity dip‐moveout (DMO) algorithms. However, numerical studies of NMO velocities have revealed no apparent correlation between the conventional measures of anisotropy and errors in the cosine‐of‐dip DMO correction (“DMO errors”). The analytic treatment developed here shows that for transverse isotropy with a vertical symmetry axis, the magnitude of DMO errors is dependent primarily on the difference between Thomsen pa...

Isotropic-cholesteric phase transition in colloidal suspensions of filamentous bacteriophage fd

Abstract: The co-existence concentrations of the isotropic and cholesteric liquid crystalline phases of the semi-flexible rod-like virus fd in aqueous suspension were measured as a function of ionic strength at room temperature. At several ionic strengths the magnetic-field-induced birefringence, which is proportional to the number of particles in a correlation volume N corr, was measured for fd concentrations spanning the entire isotropic region. From this data the limiting concentration of stability (spinodal) of the isotropic phase, ρ*, was obtained. The co-existence concentrations and ρ* versus ionic strength compare well with predictions based on the theory of Khokhlov and Semenov, modified to include the effects of charge. A theoretical expression for the magnetic birefringence of persistent polymers was derived and agreed well with the data with the exception that N corr at the isotropic to liquid crystal transition was smaller than predicted.