Showing papers on "Isotropy published in 1999"
TL;DR: In this article, a study on the vibration of cylindrical shells made of a functionally gradient material (FGM) composed of stainless steel and nickel is presented, the objective is to study the natural frequencies, the influence of constituent volume fractions and the effects of configurations of the constituent materials on the frequencies.
726 citations
TL;DR: In this paper, the effects of material inhomogeneity on the response of linearly elastic isotropic hollow circular cylinders or disks under uniform internal or external pressure were investigated, and the results were illustrated using a specific radially inhomogeneous material model for which explicit exact solutions were obtained.
Abstract: The purpose of this research is to investigate the effects of material inhomogeneity on the response of linearly elastic isotropic hollow circular cylinders or disks under uniform internal or external pressure. The work is motivated by the recent research activity on functionally graded materials (FGMs), i.e., materials with spatially varying properties tailored to satisfy particular engineering applications. The analog of the classic Lame problem for a pressurized homogeneous isotropic hollow circular cylinder or disk is considered. The special case of a body with Young"s modulus depending on the radial coordinate only, and with constant Poisson"s ratio, is examined. It is shown that the stress response of the inhomogeneous cylinder (or disk) is significantly different from that of the homogeneous body. For example, the maximum hoop stress does not, in general, occur on the inner surface in contrast with the situation for the homogeneous material. The results are illustrated using a specific radially inhomogeneous material model for which explicit exact solutions are obtained.
259 citations
TL;DR: The individual elastic constants of magnesium oxide (MgO) have been determined throughout Earth's lower mantle (LM) pressure-temperature regime with density functional perturbation theory and it is shown that temperature effects on seismic observables are monotonically suppressed with increasing pressure.
Abstract: The individual elastic constants of magnesium oxide (MgO) have been determined throughout Earth's lower mantle (LM) pressure-temperature regime with density functional perturbation theory. It is shown that temperature effects on seismic observables (density, velocities, and anisotropy) are monotonically suppressed with increasing pressure. Therefore, at realistic LM conditions, the isotropic wave velocities of MgO remain comparable to seismic velocities, as previously noticed in athermal high-pressure calculations. Also, the predicted strong pressure-induced anisotropy is preserved toward the bottom of the LM, so lattice-preferred orientations in MgO may contribute substantially to the observed seismic anisotropy in the D" layer.
253 citations
TL;DR: Sundaram et al. as mentioned in this paper performed direct numerical simulations of a turbulent fluid with finite-sized particles and found that particle inertia was observed to increase both the viscous and drag dissipations; however, it also caused particle velocities to correlate for longer distances.
Abstract: Direct numerical simulations of a turbulent fluid laden with finite-sized particles are performed. The computations, on a 1283 grid along with a maximum of 262 144 particles, incorporated both direct particle interactions via hard-sphere collisions and particle feedback. The ‘reverse’ coupling is accomplished in a manner ensuring correct discrete energy conservation (Sundaram & Collins 1996). A novel two-field formalism (Sundaram & Collins 1994a) is employed to calculate two-point correlations and equivalent spectral densities. An important consideration in these simulations is the initial state of fluid and particles. That is, the initial conditions must be chosen so as to allow a meaningful comparison of the different runs. Using such a carefully initialized set of runs, particle inertia was observed to increase both the viscous and drag dissipations; however, simultaneously, it also caused particle velocities to correlate for longer distances. The combination of effects suggests a mechanism for turbulence enhancement or suppression that depends on the parameter values. Like previous investigators, ‘pivoting’ or crossover of the fluid energy spectra was observed. A possible new scaling for this phenomenon is suggested. Furthermore, investigations of the influence of particle mass and number densities on turbulence modulation are also carried out.
236 citations
TL;DR: In this paper, the elastic field of complex shape ensembles of dislocation loops is developed as an essential ingredient in the dislocation dynamics method for computer simulation of mesoscopic plastic deformation.
Abstract: The elastic field of complex shape ensembles of dislocation loops is developed as an essential ingredient in the dislocation dynamics method for computer simulation of mesoscopic plastic deformation. Dislocation ensembles are sorted into individual loops, which are then divided into segments represented as parametrized space curves. Numerical solutions are presented as fast numerical sums for relevant elastic field variables (i.e., displacement, strain, stress, force, self-energy, and interaction energy). Gaussian numerical quadratures are utilized to solve for field equations of linear elasticity in an infinite isotropic elastic medium. The accuracy of the method is verified by comparison of numerical results to analytical solutions for typical prismatic and slip dislocation loops. The method is shown to be highly accurate, computationally efficient, and numerically convergent as the number of segments and quadrature points are increased on each loop. Several examples of method applications to calculations of the elastic field of simple and complex loop geometries are given in infinite crystals. The effect of crystal surfaces on the redistribution of the elastic field is demonstrated by superposition of a finite-element {ital image force} field on the computed results. {copyright} {ital 1999} {ital The American Physical Society}
209 citations
TL;DR: A method based on the Green's function technique for calculating strain in quantum dot (QD) structures has been developed in this article, where an analytical formula in the form of a Fourier series has been obtained for the strain tensor for arrays of QDs of arbitrary shape taking into account the anisotropic of elastic properties.
Abstract: A method based on the Green’s function technique for calculating strain in quantum dot (QD) structures has been developed. An analytical formula in the form of a Fourier series has been obtained for the strain tensor for arrays of QDs of arbitrary shape taking into account the anisotropy of elastic properties. Strain distributions using the anisotropic model for semiconductor QDs are compared to results of a simplified model in which the elastic properties are assumed to be isotropic. It is demonstrated that, in contrast to quantum wells, both anisotropic and isotropic models give similar results if the symmetry of the QD shape is less than or equal to the cubic symmetry of the crystal. The strain distribution for QDs in the shape of a sphere, cube, pyramid, hemisphere, truncated pyramid, and flat cylinder are calculated and analyzed. It is shown that the strain distributions in the major part of the QD structure are very similar for different shapes and that the characteristic value of the hydrostatic st...
198 citations
TL;DR: The results support the hypothesis; for practical purposes, the concept of an 'effective isotropic tissue modulus' concept is a viable one and it is suggested that the value of such a modulus for individual cases might be inferred from the average tissue density, hence the degree of mineralization.
197 citations
TL;DR: In this article, a numerical model using the LS-DYNA computer code was used to study the response of square aluminium tubes, varying the mass of the projectile and the impact velocity.
184 citations
TL;DR: It is shown that surface curvatures significantly affect stress and strain within cartilage when using a biphasic transversely isotropic model and that with transverse isotropy cartilage stresses are more sensitive to convexity and concavity of the surfaces than with isotropy.
173 citations
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TL;DR: In this paper, conformal invariance was used to constrain the multipoint correlation functions of isotropic critical two-dimensional systems, which provided highly efficient computational tools for the practical calculations of central charges and scaling dimensions.
Abstract: In the last chapter, conformal invariance was used to constrain the multipoint correlation functions of isotropic critical two-dimensional systems. Before following the field-theoretic developments further, we shall describe important applications to the study of finite-size effects. Besides being of interest in their own right, these results provide highly efficient computational tools for the practical calculations of central charges and scaling dimensions.
162 citations
TL;DR: A new set of scaled invariants that have the proper magnitude of actual diffusion constants and that are directly related to the physical attributes of the diffusion ellipsoid, namely, its average radius, surface, and volume are defined.
Abstract: Diffusion tensor imaging can provide a complete description of the diffusion process in tissue. However, this description is not unique but is orientation dependent, and, to quantify properly the intrinsic orientation-independent diffusion properties of the tissue, a set of three rotationally invariant quantities is needed. Instead of using the tensor eigenvalues for this, we define a new set consisting of scaled invariants that have the proper magnitude of actual diffusion constants and that are directly related to the physical attributes of the diffusion ellipsoid, namely, its average radius, surface, and volume. Using these three physical invariants, a new family of anisotropy measures is defined that are normalized between zero (isotropic) and one (completely anisotropic). Because rotational invariants are used, this approach does not require tensor diagonalization and eigenvalue determination and is therefore not susceptible to potential artifacts induced during these number manipulations. The relationship between the new anisotropy definitions and existing orientation-independent anisotropy indices obtained from eigenvalues is discussed, after which the new approach is evaluated for a group of healthy volunteers.
TL;DR: In this paper, a unified approach for the treatment of general material properties in time-domain simulation based on transmission-line modeling (TLM) is presented, where linear frequency-dependent isotropic materials are dealt with in the first instance.
Abstract: This paper presents the fundamentals of a unified approach for the treatment of general material properties in time-domain simulation based on transmission-line modeling (TLM). Linear frequency-dependent isotropic materials are dealt with in the first instance. The iteration schemes for one-dimensional (1-D) and three-dimensional (3-D) models are developed from Maxwell's curl equations and the constitutive relations. Results are presented showing the accuracy of this approach.
TL;DR: In this paper, the scalar damage model is compared to another model where damage-induced orthotropy is described, with the possibility of rotation of the principle axes of orthots.
Abstract: Scalar damage models are very often implemented in computational analyses in order to predict the response and failure modes of concrete and reinforced concrete structures. In most situations, however, damage is not isotropic but has preferential directions. Therefore, there have been many questions about the pertinence and range of applicability of isotropic, scalar, damage models for describing a degradation process which is strongly geometrically oriented. In order to assess what are the limitations of such a simplifying assumption, a comparative study is presented. The constitutive relations used for this purpose derive from the same class of models with a gradual enhancement of the description of damage. The scalar damage model is compared to another model where damage-induced orthotropy is described, with the possibility of rotation of the principle axes of orthotropy. Both models incorporate crack closure effects and a plasticity damage coupling. Structural analyses on bending beams, compression-shear and tension-shear concrete panels are presented. Although it may appear to be simplistic, the scalar damage model provides accurate predictions when failure is mainly due to uniaxial extension. Crack closure introduces an additional anisotropy which is important in compression-shear problems. Finally, damage-induced anisotropy seems important when failure is due to multiaxial extensions, such as in shear-tension problems. Copyright © 1999 John Wiley & Sons, Ltd.
TL;DR: In this article, a generalization of Yaglom's equation is deduced and tested, in heated grid turbulence (Rλ=66), in order to shed some light on the influence of the large scales on inertial-range properties, in this case, the main phenomenon responsible for the nonuniversal inertial range behaviour is the nonstationarity of the second-order moments, acting as a negative production term.
Abstract: In most real or numerically simulated turbulent flows, the energy dissipated at small scales is equal to that injected at very large scales, which are anisotropic. Despite this injection-scale anisotropy, one generally expects the inertial-range scales to be locally isotropic. For moderate Reynolds numbers, the isotropic relations between second-order and third-order moments for temperature (Yaglom's equation) or velocity increments (Kolmogorov's equation) are not respected, reflecting a non-negligible correlation between the scales responsible for the injection, the transfer and the dissipation of energy. In order to shed some light on the influence of the large scales on inertial-range properties, a generalization of Yaglom's equation is deduced and tested, in heated grid turbulence (Rλ=66). In this case, the main phenomenon responsible for the non-universal inertial-range behaviour is the non-stationarity of the second-order moments, acting as a negative production term.
TL;DR: A mathematical model of a four-layer medium (muscle+fat+skin+air+air) is investigated and it is clear that the subcutaneous tissue layers produce an attenuation and widening of the potential distribution present at the muscle surface.
TL;DR: This paper exemplifies the theory context of isotropic turbulence in the context of third order tensorial structure functions and in weakly anisotropic turbulence (for the second order structure function) and the utility of the resulting expressions for the analysis of experimental data is demonstrated.
Abstract: The theory of fully developed turbulence is usually considered in an idealized homogeneous and isotropic state. Real turbulent flows exhibit the effects of anisotropic forcing. The analysis of correlation functions and structure functions in isotropic and anisotropic situations is facilitated and made rational when performed in terms of the irreducible representations of the relevant symmetry group which is the group of all rotations SO(3). In this paper we first consider the needed general theory, and explain why we expect different (universal) scaling exponents in the different sectors of the symmetry group. We exemplify the theory context of isotropic turbulence (for third order tensorial structure functions) and in weakly anisotropic turbulence (for the second order structure function). The utility of the resulting expressions for the analysis of experimental data is demonstrated in the context of high Reynolds number measurements of turbulence in the atmosphere.
TL;DR: In this paper, a 3D version of the structure function is presented, any section for which is equivalent to an ensemble average of profile structure functions, and the angular variation of topothesy and fractal dimension obtained from such sections describes the anisotropy of the parent surface.
TL;DR: In this paper, the authors studied the two-dimensional crack problem in a piezoelectric material containing an elliptic hole subjected to uniform remote loads and showed that the field intensity factors are the same as that of isotropic material.
TL;DR: In this paper, the role of anisotropy on aerodynamic mixing noise is explored based on the source terms of the Lilley's equation, and flowlacoustic interaction is accounted for in terms of a high-frequency solution to the axisymmetric version of the model.
Abstract: The objective is to explore the role of anisotropy on aerodynamic mixing noise because of fine-scale turbulence. The usual assumption of isotropic turbulence is replaced with that of axisymmetric turbulence. The analysis is based on source terms of Lilley's equation. In addition, flowlacoustic interaction is accounted for in terms of a high-frequency solution to the axisymmetric Lilley's equation. In the limiting case of isotropy, various source correlation terms derived here simplify to those obtained with an isotropic turbulence model of Batchelor. A Reynolds-averaged Navier-Stokes solution with a k-∈ turbulence model for a Mach 1.0 jet is used to make flow and acoustic predictions. A parametric study of the turbulence scales indicates that anisotropy increases the peak noise level.
TL;DR: In this article, the authors give a statistical-mechanical theory of stress transmission in disordered arrays of rigid grains with perfect friction, starting from the equations of microscopic force and torque balance, derive the fundamental equations of stress equilibrium.
Abstract: We give a statistical-mechanical theory of stress transmission in disordered arrays of rigid grains with perfect friction. Starting from the equations of microscopic force and torque balance we derive the fundamental equations of stress equilibrium. We illustrate the validity of our approach by solving the stress distribution of a homogeneous and isotropic array.
TL;DR: In this article, the authors consider materials which can be described by plasticity laws exhibiting nonlinearkinematic and nonlinear isotropic hardening effects and show that the material parameters governing the constitutive behavior may be determined from data obtained by spherical indentation.
Abstract: We consider materials which can be described by plasticity laws exhibiting nonlinearkinematic and nonlinear isotropic hardening effects. The aim is to show that the materialparameters governing the constitutive behavior may be determined from data obtained byspherical indentation. Note that only the measurable global quantities (load and indentationdepth) should be utilized, which are available, e.g. from depth-sensing indentation tests. For thisgoal use is made of the method of neural networks. The developed neural networks apply also tothe case of pure kinematic as well as pure isotropic hardening. Moreover it is shown how amonotonic strain–stress curve can be assigned to the spherical indentation test.
TL;DR: It is suggested that the linear transversely isotropic biphasic model could not simultaneously describe the observed stress relaxation and equilibrium behavior of calf cartilage.
TL;DR: In this paper, the effects of material inhomogeneity on the response of linearly elastic isotropic solid circular disks or cylinders, rotating at constant angular velocity about a central axis, were investigated.
Abstract: The purpose of this research is to investigate the effects of material inhomogeneity on the response of linearly elastic isotropic solid circular disks or cylinders, rotating at constant angular velocity about a central axis. The work is motivated by the recent research activity on functionally graded materials (FGMs), i.e., materials with spatially varying properties tailored to satisfy particular engineering applications. The analog of the classic problem for a homogeneous isotropic rotating solid disk or cylinder is considered. The special case of a body with Young"s modulus depending on the radial coordinate only, and with constant Poisson"s ratio, is examined. For the case when the Young"s modulus has a power-law dependence on the radial coordinate, explicit exact solutions are obtained. It is shown that the stress response of the inhomogeneous disk (or cylinder) is significantly different from that of the homogeneous body. For example, the maximum radial and hoop stresses do not, in general, occur at the center as in the case for the homogeneous material. Furthermore, for the case where the Young"s modulus increases with radial distance from the center, it is shown that radially symmetric solutions exist provided the rate of growth of the Young"s modulus is, at most, cubic in the radial variable. It is also shown for the general inhomogeneous isotropic case how the material inhomogeneity may be tailored so that the radial and hoop stress are identical throughout the disk.
TL;DR: In this article, an analytic simplified form for the 4 × 4 propagation matrix of a general homogeneous biaxial layer is presented, which is applicable to any linear homogeneous, absorbing, biaaxial, gyrotropic, magneto-optic, arbitrarily oriented anisotropic structure.
Abstract: We present an analytic simplified form for the 4 × 4 propagation matrix of a general homogeneous biaxial layer. The expression is applicable to any linear homogeneous, absorbing, biaxial, gyrotropic, magneto-optic, arbitrarily oriented anisotropic structure. Its simple form speeds up the calculation of the optical properties of inhomogeneous anisotropic media and allows real-time analysis of ellipsometric experimental data. A simplified analytic expression for the propagation matrix is also derived for the case of mode degeneration such as for propagation at certain angles and for the isotropic case. Using this analytic method it is found that the time required for calculating the propagation matrix is shorter by a factor of two than that using direct numerical calculation.
TL;DR: It is shown that when the same fluorescent group is localized at different depths within the bilayer, the degrees to which their fluorescence properties exhibit solvent-induced effects are markedly different, for example, the headgroup-labeled NBD-PE exhibits...
Abstract: The biological membrane is a highly organized anisotropic molecular assembly. While the center of the bilayer is nearly isotropic, the upper portion, only a few angstroms away toward the membrane surface, is highly ordered. How this organization correlates with the degree of water penetration into the bilayer interior is not clear. In general, it is believed that there is not much water in the deeper hydrocarbon regions of the bilayer. In this study, we have utilized the phenomenon of wavelength-selective fluorescence to address this question. We show here that when the same fluorescent group (i.e., 7-nitrobenz-2-oxa-1,3-diazol-4-yl or NBD) is localized at different depths within the bilayer (viz., near the membrane interface in case of the headgroup-labeled NBD-phosphatidylethanolamine (NBD-PE) and near the center of the bilayer in NBD-cholesterol), the degrees to which their fluorescence properties exhibit solvent-induced effects are markedly different. For example, the headgroup-labeled NBD-PE exhibits...
TL;DR: In this article, the wave motion in an infinite elastic layer due to the application of a time-harmonic point load of arbitrary direction, applied either internally or on one of the faces of the layer, is expressed as a sum of four expansions in Lamb-wave modes and horizontally polarized wave modes.
Abstract: Wave motion in an infinite elastic layer due to the application of a time-harmonic point load of arbitrary direction, applied either internally or on one of the faces of the layer, is expressed as a sum of four expansions in Lamb-wave modes and horizontally polarized wave modes. The point load is decomposed into components normal and parallel to the plate faces. Each of these cases is decomposed into a symmetric and an antisymmetric loading case, relative to the mid-plane of the layer. The displacement solutions for the symmetric and antisymmetric cases are expressed as expansions of symmetric and antisymmetric modes, respectively. Appropriate orthogonality relations are derived from reciprocity considerations. Elastodynamic reciprocity is also used in conjunction with dummy wave modes to obtain the coefficients in the wave-mode expansion.
TL;DR: In this paper, the response, evolution, and modelling of subgrid-scale (SGS) stresses during rapid straining of turbulence is studied experimentally, where the SGS stress is subdivided to a stress due to the mean distortion, a cross-term (the interaction between the mean and turbulence), and the turbulent S GS stress τ(T)ij.
Abstract: The response, evolution, and modelling of subgrid-scale (SGS) stresses during rapid straining of turbulence is studied experimentally. Nearly isotropic turbulence with low mean velocity and Rλ˜290 is generated in a water tank by means of spinning grids. Rapid straining (axisymmetric expansion) is achieved with two disks pushed towards each other at rates that for a while generate a constant strain rate. Time-resolved, two-dimensional velocity measurements are performed using cinematic PIV. The SGS stress is subdivided to a stress due to the mean distortion, a cross-term (the interaction between the mean and turbulence), and the turbulent SGS stress τ(T)ij. Analysis of the
time evolution of τ(T)ij at various filter scales shows that all scales are more isotropic than the prediction of rapid distortion theory, with increasing isotropy as scales decrease. A priori tests show that rapid straining does not affect the high correlation and low square-error exhibited by the similarity model. Analysis of the evolution of total SGS energy dissipation reveals, surprisingly, that the Smagorinsky model with a constant coefficient (determined from isotropic turbulence data) underpredicts the dissipation during rapid straining. While the partial dissipation −〈τ(T)ij
S˜ij〉 (due only to the turbulent part of the stress) is overpredicted by the Smagorinsky model, addition of the cross-terms reverses the trend. The similarity model with a constant coefficient appropriate for isotropic turbulence, on the other hand, overpredicts SGS dissipation. Owing to these opposite trends a linear combination of both models (mixed model) provides better prediction of SGS dissipation during rapid straining. However, the mixed model with coefficients determined from dissipation balance underpredicts the SGS stress.
TL;DR: In this article, it was shown that the theory of a fundamental paper of Chadwick and Powdrill on singular surfaces, propagating in a linear thermoelastic body which is stress-free, homogeneous, and isotropic, also holds when the medium is subjected to hydrostatic initial stress provided the two characteristic speeds are suitably changed.
Abstract: It will be shown that the theory of a fundamental paper of Chadwick and Powdrill on singular surfaces, propagating in a linear thermoelastic body which is stress-free, homogeneous, and isotropic, also holds when the medium is subjected to hydrostatic initial stress provided the two characteristic speeds are suitably changed. The result is obtained by using Biot’s linearization of the constitutive law for the stress.
TL;DR: The evolution of the magnetic helicity tensor for a nonzero mean magnetic field and for large magnetic Reynolds numbers in an anisotropic turbulence is studied and it is shown that even a small anisotropy of turbulence strongly modifies the flux of the magnet helicity.
Abstract: The evolution of the magnetic helicity tensor for a nonzero mean magnetic field and for large magnetic Reynolds numbers in an anisotropic turbulence is studied. It is shown that the isotropic and anisotropic parts of the magnetic helicity tensor have different characteristic times of evolution. The time of variation of the isotropic part of the magnetic helicity tensor is much larger than the correlation time of the turbulent velocity field. The anisotropic part of the magnetic helicity tensor changes for the correlation time of the turbulent velocity field. The mean turbulent flux of the magnetic helicity is calculated as well. It is shown that even a small anisotropy of turbulence strongly modifies the flux of the magnetic helicity. It is demonstrated that the tensor of the magnetic part of the alpha effect for weakly inhomogeneous turbulence is determined only by the isotropic part of the magnetic helicity tensor.