Showing papers on "Isotropy published in 2002"
TL;DR: In this paper, the elastic constants of the ensemble of spheres embedded in a continuous and isotropic elastic matrix were computed through the finite element analysis of the three-dimensional periodic unit cells, whose size was chosen as a compromise between the minimum size required to obtain accurate results in the statistical sense and the maximum one imposed by the computational cost.
Abstract: Three-dimensional cubic unit cells containing 30 non-overlapping identical spheres randomly distributed were generated using a new, modified random sequential adsortion algorithm suitable for particle volume fractions of up to 50% The elastic constants of the ensemble of spheres embedded in a continuous and isotropic elastic matrix were computed through the finite element analysis of the three-dimensional periodic unit cells, whose size was chosen as a compromise between the minimum size required to obtain accurate results in the statistical sense and the maximum one imposed by the computational cost Three types of materials were studied: rigid spheres and spherical voids in an elastic matrix and a typical composite made up of glass spheres in an epoxy resin The moduli obtained for different unit cells showed very little scatter, and the average values obtained from the analysis of four unit cells could be considered very close to the “exact” solution to the problem, in agreement with the results of Drugan and Willis (J Mech Phys Solids 44 (1996) 497) referring to the size of the representative volume element for elastic composites They were used to assess the accuracy of three classical analytical models: the Mori–Tanaka mean-field analysis, the generalized self-consistent method, and Torquato's third-order approximation
516 citations
TL;DR: In this article, velocity field statistics in the inertial to dissipation range of three-dimensional homogeneous steady turbulent flow are studied using a high-resolution DNS with up to N=10243 grid points.
Abstract: Velocity field statistics in the inertial to dissipation range of three-dimensional homogeneous steady turbulent flow are studied using a high-resolution DNS with up to N=10243 grid points. The range of the Taylor microscale Reynolds number is between 38 and 460. Isotropy at the small scales of motion is well satisfied from half the integral scale (L) down to the Kolmogorov scale (η). The Kolmogorov constant is 1.64±0.04, which is close to experimentally determined values. The third order moment of the longitudinal velocity difference scales as the separation distance r, and its coefficient is close to 4/5. A clear inertial range is observed for moments of the velocity difference up to the tenth order, between 2λ≈100η and L/2≈300η, where λ is the Taylor microscale. The scaling exponents are measured directly from the structure functions; the transverse scaling exponents are smaller than the longitudinal exponents when the order is greater than four. The crossover length of the longitudinal velocity struct...
438 citations
TL;DR: In this article, a generalized isoparametric formulation of graded finite elements is presented for boundary value problems involving continuously nonhomogeneous isotropic and orthotropic materials, and the performance of graded elements is compared to that of conventional homogeneous elements with reference to analytical solutions.
Abstract: Graded finite elements are presented within the framework of a generalized isoparametric formulation. Such elements possess a spatially varying material property field, e.g. Young's modulus (E) and Poisson's ratio () for isotropic materials; and principal Young's moduli (E11,E22), in-plane shear modulus (G12), and Poisson's ratio (12) for orthotropic materials. To investigate the influence of material property variation, both exponentially and linearly graded materials are considered and compared. Several boundary value problems involving continuously nonhomogeneous isotropic and orthotropic materials are solved, and the performance of graded elements is compared to that of conventional homogeneous elements with reference to analytical solutions. Such solutions are obtained for an orthotropic plate of infinite length and finite width subjected to various loading conditions. The corresponding solutions for an isotropic plate are obtained from those for the orthotropic plate. In general, graded finite elements provide more accurate local stress than conventional homogeneous elements, however, such may not be the case for four-node quadrilateral (Q4) elements. The framework described here can serve as the basis for further investigations such as thermal and dynamic problems in functionally graded materials. ©2002 ASME
380 citations
TL;DR: In this article, free and forced vibration analyses for initially stressed functionally graded plates in thermal environment are presented, where material properties are assumed to be temperature dependent, and graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents.
336 citations
01 Jan 2002
TL;DR: In this article, a review of the basic physical principles that lead to the boundary conditions for media in welded contact is given, along with an overview of the reflection and transmission problem in isotropic media.
Abstract: Reflection and transmission of plane waves at a plane boundary between two isotropic media are two of the most fundamental subjects in wave propagation. Zoeppritz (1919) w as among the first to investigate and publish their analytic solutions. Given the medium properties on both sides of a reflector and invoking continuity of stress and displacement across the interface, he came up with a set of equations to describe the amplitudes of the scattered (i.e., reflected and transmitted) waves.
Chapter [2][1] provides an overview of the reflection and transmission problem in isotropic media. It also introduces the notation that is used throughout the text and contains a review of the basic physical principles that lead to the boundary conditions for media in welded contact. Because of the algebraic complexity of the Zoeppritz equations, the inverse problem of esti-mating medium properties from the reflection signature is based mostly on approximate analytic expressions for reflection coefficients. Several approximations for isotropic models have been described in the literature (Richards and Frasier, 1976; Aki and Richards, 1980; Shuey, 1985; Thomsen, 1990). As described in Chapter [2][1], they differ in their assumptions, as well as in the choice of medium parameters.
[1]: /gswbk/9781560801764/9781560801764/SEC2.atom
301 citations
TL;DR: It appears that pore shape can modulate hepatocyte morphogenesis in 3-D alginate scaffolds fabricated by the freeze-dry method.
294 citations
TL;DR: In this paper, an approach to estimate the large-scale permeability of reservoirs using seismic emission (microseismicity) induced by fluid injection is presented. But this approach is based on the hypothesis that the triggering front of hydraulically-induced microseismic propagates like a diffusive process (pore pressure relaxation) in an effective homogeneous anisotropic poroelastic fluid-saturated medium.
Abstract: We systematically describe an approach to estimate the large-scale permeability of reservoirs using seismic emission (microseismicity) induced by fluid injection. We call this approach seismicity-based reservoir characterization (SBRC). A simple variant of the approach is based on the hypothesis that the triggering front of hydraulically-induced microseismicity propagates like a diffusive process (pore pressure relaxation) in an effective homogeneous anisotropic poroelastic fluid-saturated medium. The permeability tensor of this effective medium is the permeability tensor upscaled to the characteristic size of the seismically active heterogeneous rock volume. We show that in a homogeneous medium the surface of the seismicity triggering front has the same form as the group-velocity surface of the low-frequency anisotropic, second-type Biots wave (i.e., slow wave). Further, we generalize SBRC for 3-D mapping of the permeability tensor of heterogeneous reservoirs and aquifers. For this we apply an approach similar to the geometric optics approximation. We derive an equation describing kinematic aspects of triggering-front propagation in a way similar to the eikonal equation for seismic wavefronts. In the case of isotropic heterogeneous media, the inversion for the hydraulic properties of rocks follows from a direct application of this equation. In the case of an anisotropic heterogeneous medium, only the magnitude of a global effective permeability tensor can be mapped in a 3-D spatial domain. We demonstrate the method on several field examples and also test the eikonal equation-based inversion.
293 citations
TL;DR: In this article, the effects of anisotropic pressure on the properties of spherically symmetric, gravitationally bound objects were studied and exact solutions for various forms of the equation of state connecting the radial and tangential pressures were obtained.
Abstract: We study the effects of anisotropic pressure on the properties of spherically symmetric, gravitationally bound objects. We consider the full general-relativistic treatment of this problem and obtain exact solutions for various forms of the equation of state connecting the radial and tangential pressures. It is shown that pressure anisotropy can have significant effects on the structure and properties of stellar objects. In particular, the maximum value of 2M / R can approach unity (2M / R < 8/9 for isotropic objects) and the surface redshift can be arbitrarily large.
288 citations
TL;DR: In this paper, a general constitutive theory of the stress-modulated growth of biomaterials is presented with a particular accent given to pseudo-elastic soft living tissues, and the governing equations of the mechanics of solids with a growing mass are revisited within the framework of finite deformation continuum thermodynamics.
284 citations
TL;DR: The gyroresonance with fast modes is the dominant contribution to cosmic ray scattering for the typical interstellar conditions and Alfvénic and slow modes are inefficient because they are far from the isotropy usually assumed.
Abstract: Recent advances in understanding of magnetohydrodynamic (MHD) turbulence call for substantial revisions in our understanding of cosmic ray transport. We use recently obtained scalings of MHD modes to calculate the scattering frequency for cosmic rays. We consider gyroresonance with MHD modes (Alfvenic, slow, and fast) and transit-time damping by fast modes. We conclude that the gyroresonance with fast modes is the dominant contribution to cosmic ray scattering for the typical interstellar conditions. In contrast to earlier studies, we find that Alfvenic and slow modes are inefficient because they are far from the isotropy usually assumed.
273 citations
TL;DR: In this paper, the Eliashberg equations were solved for both an isotropic one-band model and a twoband model with different superconducting gaps on the π-band and σ-band Fermi surfaces.
Abstract: The heat capacity anomaly at the transition to superconductivity of the layered superconductor MgB2 is compared to first-principles calculations with the Coulomb repulsion, µ*, as the only parameter which is fixed to give the measured Tc. We solve the Eliashberg equations for both an isotropic one-band model and a two-band model with different superconducting gaps on the π-band and σ-band Fermi surfaces. The agreement with experiments is considerably better for the two-band model than for the one-band model.
TL;DR: In this paper, it was shown that Young's modulus, E, is practically independent of Poisson's ratio of the solid phase, nu(s), over the entire solid fraction range, and Poisson ratio, nu, becomes independent of Nu(s) as the percolation threshold is approached.
Abstract: A finite-element method is used to study the elastic properties of random three-dimensional porous materials with highly interconnected pores. We show that Young's modulus, E, is practically independent of Poisson's ratio of the solid phase, nu(s), over the entire solid fraction range, and Poisson's ratio, nu, becomes independent of nu(s) as the percolation threshold is approached. We represent this behaviour of nu in a flow diagram. This interesting but approximate behaviour is very similar to the exactly known behaviour in two-dimensional porous materials. In addition, the behaviour of nu versus nu(s) appears to imply that information in the dilute porosity limit can affect behaviour in the percolation threshold limit. We summarize the finite-element results in terms of simple structure-property relations, instead of tables of data, to make it easier to apply the computational results. Without using accurate numerical computations, one is limited to various effective medium theories and rigorous approximations like bounds and expansions. The accuracy of these equations is unknown for general porous media. To verify a particular theory it is important to check that it predicts both isotropic elastic moduli, i.e. prediction of Young's modulus alone is necessary but not sufficient. The subtleties of Poisson's ratio behaviour actually provide a very effective method for showing differences between the theories and demonstrating their ranges of validity. We find that for moderate- to high-porosity materials, none of the analytical theories is accurate and, at present, numerical techniques must be relied upon.
TL;DR: In this article, the springback angles and anticlastic curvatures reported for a series of draw-bend tests have been analyzed in detail using a new anisotropic hardening model, four common sheet metal yield functions, and finite element procedures developed for this problem.
TL;DR: A key feature of the method is that it does not require separability of overall tumbling and internal motions, which makes it applicable to a wide range of systems, such as folded, partially folded, and unfolded biomolecular systems and other macromolecules in solution.
Abstract: A general framework is presented for the interpretation of NMR relaxation data of proteins. The method, termed isotropic reorientational eigenmode dynamics (iRED), relies on a principal component analysis of the isotropically averaged covariance matrix of the lattice functions of the spin interactions responsible for spin relaxation. The covariance matrix, which is evaluated using a molecular dynamics (MD) simulation, is diagonalized yielding reorientational eigenmodes and amplitudes that reveal detailed information about correlated protein dynamics. The eigenvalue distribution allows one to quantitatively assess whether overall and internal motions are statistically separable. To each eigenmode belongs a correlation time that can be adjusted to optimally reproduce experimental relaxation parameters. A key feature of the method is that it does not require separability of overall tumbling and internal motions, which makes it applicable to a wide range of systems, such as folded, partially folded, and unfol...
TL;DR: In this article, the phase behavior of achiral banana-shaped molecules was studied by computer simulation and the dependence on temperature of systems of N=1024 rigid banana-shape molecules with bending angle φ =140° has been studied by means of Monte Carlo simulations in the isobaric-isothermal ensemble.
Abstract: The phase behaviour of achiral banana-shaped molecules was studied by computer simulation. The banana-shaped molecules were described by model intermolecular interactions based on the Gay-Berne potential. The characteristic molecular structure was considered by joining two calamitic Gay-Berne particles through a bond to form a biaxial molecule of point symmetry group C 2v with a suitable bending angle. The dependence on temperature of systems of N=1024 rigid banana-shaped molecules with bending angle φ =140° has been studied by means of Monte Carlo simulations in the isobaric-isothermal ensemble (NpT). On cooling an isotropic system, two phase transitions characterized by phase transition enthalpy, entropy and relative volume change have been observed. For the first time by computer simulation of a many-particle system of banana-shaped molecules, at low temperature an untilted smectic phase showing a global phase biaxiality and a spontaneous local polarization in the layers, i.e. a local polar arrangement...
TL;DR: In this paper, an extensive laboratory investigation of the mechanical properties of a porous sandstone which exhibits transversely isotropic behaviour is presented, focusing on the influence of the structural anisotropy on the progressive development of pre-peak damage.
TL;DR: In this article, the classical vibrational modes for a thin-walled hollow cylinder of isotropic material were calculated for a single-wall carbon nanotube and an analytical solution was obtained for all of the modes.
Abstract: The classical vibrational modes are calculated for a thin-walled hollow cylinder of isotropic material. An analytical solution is obtained for all of the modes. The results are applied to calculate the low-frequency vibrational modes of a single-wall carbon nanotube. Analytical formulas are obtained for the Raman frequencies, and for the velocities of acoustical modes.
TL;DR: In this paper, a complete description of the behavior of embedded convex curves moving by equations of the form (1.1) is provided, for which the following holds: If a = 1 then Equation (1) was the curve-shortening flow.
Abstract: with a 5 0, and initial condition x(p, 0) = xzo(p). This produces a family of curves yt = x(Si, t). Here n is the curvature, and n is the outward-pointing unit normal vector. These equations are particularly natural in that they are isotropic (equivariant under rotations in the plane) and homogeneous (equivariant under dilation of space, if time is also scaled accordingly). The main aim of this paper is to provide a complete description of the behaviour of embedded convex curves moving by equations of the form (1.1). In certain cases this description has already been provided: If a = 1 then Equation (1.1) is the curve-shortening flow, for which the following holds:
TL;DR: In this article, the Schmidt number was used to study the effects of Schmidt number on passive scalars mixed by forced isotropic and homogeneous turbulence, and the scaling of spectra, structure functions, local isotropy and intermittency.
Abstract: We study by direct numerical simulations the effects of Schmidt number (Sc) on passive scalars mixed by forced isotropic and homogeneous turbulence. The scalar field is maintained statistically stationary by a uniform mean gradient. We consider the scaling of spectra, structure functions, local isotropy and intermittency. For moderately diffusive scalars with Sc=1/8 and 1, the Taylor-scale Reynolds number of the flow is either 140 or 240. A modest inertial-convective range is obtained in the spectrum, with a one-dimensional Obukhov–Corrsin constant of about 0.4, consistent with experimental data. However, the presence of a spectral bump makes a firm assessment somewhat difficult. The viscous-diffusive range is universal when scaled by Obukhov–Corrsin variables. In a second set of simulations we keep the Taylor-microscale Reynolds number fixed at 38 but vary Sc from 1/4 to 64 (a range of over two decades), roughly by factors of 2. We observe a gradual evolution of a −1 roll-off in the viscous-convective region as Sc increases, consistent with Batchelor’s predictions. In the viscous-diffusive range the spectra follow Kraichnan’s form well, with a coefficient that depends weakly on Sc. The breakdown of local isotropy manifests itself through differences between structure functions with separation distances in directions parallel and perpendicular to the mean scalar gradient, as well as via finite values of odd-order moments of scalar gradient fluctuations and of mixed velocity-scalar gradient correlations. However, all these indicators show, to varying degrees, an increasing tendency to isotropy with increasing Sc. The moments of scalar gradients and the scalar dissipation rate peak at Sc≈4. The intermittency exponent for the scale-range between the Kolmogorov and Batchelor scales is found to decrease with Sc, suggesting qualitative consistency with previous dye experiments in water [Sc=O(1000)].
TL;DR: In this paper, an analytical solution for the principal tensile stress at the disc center of a gneiss disc is presented, where the key expansion coefficients are obtained from a complex-valued 2×2 matrix equation.
TL;DR: In this paper, a failure criterion for fiber-reinforced sand with an anisotropic distribution of fiber orientation was derived, and a deformation-induced anisotropy was detected in experiments.
TL;DR: Heat-capacity measurements of a 39 microg MgB2 single crystal in fields up to 14 T and below 3 K allow the determination of the low-temperature linear term of the specific heat, its field dependence, and its anisotropy.
Abstract: Heat-capacity measurements of a 39 microg MgB2 single crystal in fields up to 14 T and below 3 K allow the determination of the low-temperature linear term of the specific heat, its field dependence, and its anisotropy. Our results are compatible with two-band superconductivity, the band carrying the smaller gap being isotropic, that carrying the larger gap having an anisotropy of approximately 5. Three different upper critical fields are thus needed to describe the superconducting state of MgB2.
TL;DR: In this article, a general formulation for the electromagnetic wave interaction with stratified media and then specialize to slabs of negative isotropic media is presented. And the authors demonstrate and locate the positions of the perfect images of the antenna sources in the presence of the slabs.
Abstract: In this paper we provide a general formulation for the electromagnetic wave interaction with stratified media and then specialize to slabs of negative isotropic media. The field solutions are obtained in all regions of the stratified medium. The characteristic waves in negative isotropic media are backward waves. We derive the field solutions and show that a Gaussian beam is laterally shifted by a negative isotropic slab. The amount of beam center shift is calculated for both cases of transmission and reflection. Guided waves in stratified media are studied. Placing a linear antenna and all types of Hertzian dipole antennas in a stratified medium, we obtained solutions in all regions. We demonstrate and locate the positions of the perfect images of the antenna sources in the presence of negative isotropic slabs.
TL;DR: In this paper, a single-plug method for measuring seismic velocities and transverse isotropy in rocks has been rigorously validated and laboratory tested, which requires only one sample to measure the velocity needed to derive the five independent elastic constants for transversely isotropic materials.
Abstract: A single-plug method for measuring seismic velocities and transverse isotropy in rocks has been rigorously validated and laboratory tested. The method requires only one sample to measure the velocities needed to derive the five independent elastic constants for transversely isotropic materials. In this method, piezoelectric transducers are fitted to the top, bottom, and sides of the cylindrical sample. Laboratory velocity and anisotropy can be measured as functions of pressure, temperature, fluid saturation, and fluid displacement. Because this method uses a horizontal core plug that has much higher permeability than a vertical core plug, it is especially suitable for low-permeability shale measurements. It reduces the sample preparation and velocity measurement time by more than two-thirds.
TL;DR: In this article, the Fourier transform spectral densities of these responses are presented for each liquid and are interpreted in terms of the molecular and interaction-induced contributions to the many-body polarizability.
Abstract: Spatially masked optical Kerr effect (SM-OKE) spectroscopy is a nonresonant femtosecond pump–probe technique capable of measuring isotropic contributions to the transient birefringence of molecular liquids. In conjunction with traditional optical-heterodyne-detected optical Kerr effect spectroscopy, polarization-selective SM-OKE measurements are used to experimentally measure the anisotropic and isotropic third-order nonlinear response of CS2, acetonitrile, methanol, and water. These two responses, which allow the intermolecular dynamics to be separated by symmetry, form a complete and independent basis for describing the polarization dependence of nonresonant third-order experiments. The Fourier transform spectral densities of these responses are presented for each liquid and are interpreted in terms of the molecular and interaction-induced contributions to the many-body polarizability. The molecular contributions are suppressed in the isotropic response for all liquids, while the line shape in the inter...
TL;DR: In this article, a novel six-component force sensor with its force-sensing member in the form of four identical T-shaped bars is presented, which is subjected to finite element analysis in conjunction with a design optimization for high measurement sensitivities.
Abstract: In this work, a novel six-component force sensor with its force-sensing member in the form of four identical T-shaped bars is presented. The force-sensing member is subjected to finite element analysis in conjunction with a design optimization for high measurement sensitivities. Although significant measurement couplings exist in this six-component force sensor, however, they distribute only in a few sparse places in the calibration matrix, making the calculations for the force components relatively easy and quick. The condition number under the full rated loading conditions for this sensor is 1.543, which represents a rather good measurement isotropy, as compared to approximately 2–4 for a Maltese crossbar sensor under similar conditions. In addition, only 20 strain gauges are required in the design, which is less than that used in a Maltese crossbar type sensor, in which at least 24 strain gauges are used.
TL;DR: In this article, the fractional Fokker-Planck equation is proposed for the kinetic description of relaxation and super-diffusion processes in constant magnetic and random electric fields, assuming that the random electric field acting on a test charged particle is isotropic and possesses non-Gaussian Levy stable statistics.
Abstract: Fractional Fokker–Planck equation is proposed for the kinetic description of relaxation and superdiffusion processes in constant magnetic and random electric fields. It is assumed that the random electric field acting on a test charged particle is isotropic and possesses non-Gaussian Levy stable statistics. These assumptions provide one with a straightforward possibility to consider formation of anomalous stationary states and superdiffusion processes, both properties are inherent to strongly nonequilibrium plasmas of solar systems and thermonuclear devices. The fractional kinetic equation is solved, the properties of the solution are studied, and analytical results are compared with those of numerical simulation based on the solution of the Langevin equations with a noise source having Levy stable probability density. It is found, in particular, that the stationary states are essentially non-Maxwellian ones and, at the diffusion stage of relaxation, the characteristic displacement of a particle grows superdiffusively with time and is inversely proportional to the magnetic field.
TL;DR: The low permeability values determined in this study provide insight into the extent of fluid pressurization in the meniscus and will impact modeling predictions of load support in theMeniscus.
Abstract: Tensile tests and biphasic finite element modeling were used to determine a set of transversely isotropic properties for the meniscus, including the hydraulic permeability coefficients and solid matrix properties. Stress-relaxation tests were conducted on planar samples of canine meniscus samples of different orientations, and the solid matrix properties were determined from equilibrium data. A 3-D linear biphasic and tranversely isotropic finite element model was developed to model the stress-relaxation behavior of the samples in tension, and optimization was used to determine the permeability coefficients, k1 and k2, governing fluid flow parallel and perpendicular to the collagen fibers, respectively. The collagen fibrillar orientation was observed to have an effect on the Young's moduli (E1=67.8 MPa, E2=11.1 MPa) and Poisson's ratios (v12=2.13, v21 =1.50, v23=1.02). However, a significant effect of anisotropy on permeability was not detected (k1 =0.09x10(-16) m4/Ns, k2=0.10x10(-16) m4/Ns). The low permeability values determined in this study provide insight into the extent of fluid pressurization in the meniscus and will impact modeling predictions of load support in the meniscus.
TL;DR: In this paper, the authors examined material instabilities in fiber-reinforced nonlinearly elastic solids and established sufficient conditions for the ellipticity of the governing equations of equilibrium for more general reinforcing models to be guaranteed.
Abstract: Material instabilities in fiber-reinforced nonlinearly elastic solids are examined under plane deformation. In particular, the materials under consideration are isotropic nonlinearly elastic models augmented by a function that accounts for the existence of a unidirectional reinforcing. This function describes the anisotropic (transversely isotropic) character of the material and is referred to as a reinforcing model. The onset of failure is signalled by the loss of ellipticity of the governing differential equations. Previous work has dealt with the analysis of specific reinforcing models and has established that the loss of ellipticity for such augmented isotropic materials requires contraction in the reinforcing direction. The loss of ellipticity was related to fiber kinking. Here we generalize these results and establish sufficient conditions for the ellipticity of the governing equations of equilibrium for more general reinforcing models to be guaranteed. We also establish necessary conditions for failure of ellipticity. The incipient loss of ellipticity is interpreted in terms of fiber kinking, fiber de-bonding, fiber splitting and matrix failure in fiber-reinforced composite materials. Attention is restricted to incompressible materials in this paper.
TL;DR: In this article, a temperature and rate-dependent viscoplastic polycrystal model is presented, which uses a single crystal constitutive response that is based on the isotropic Mechanical Threshold Stress continuum model.