Showing papers on "Isotropy published in 2005"
TL;DR: In this paper, it is proposed that the effective thermal conductivity region bounded by the Hashin-Shtrikman bounds may be divided into internal porosity and external porosity regions by the Effective Medium Theory (EMT) equation.
531 citations
TL;DR: The components of the macroscopic mechanical stress tensor of a stressed thin film, coating, multilayer or the region near the surface of a bulk material can in principle be determined by X-ray diffraction as discussed by the authors.
Abstract: The components of the macroscopic mechanical stress tensor of a stressed thin film, coating, multilayer or the region near the surface of a bulk material can in principle be determined by X-ray diffraction. The various analysis methods and measurement strategies, in dependence on specimen and measurement conditions, are summarized and evaluated in this paper. First, different X-ray diffraction geometries (conventional or grazing incidence) are described. Then, the case of macroscopically elastically isotropic, untextured specimens is considered: from the simplest case of a uniaxial state of stress to the most complicated case of a triaxial state of stress. The treatment is organized according to the number of unknowns to be determined (i.e. the state of stress, principal axes known or unknown), the use of one or several values of the rotation angle φ and the tilt angle ψ of the sample, and one or multiple hkl reflections. Next, the focus is on macroscopically elastically anisotropic (e.g. textured) specimens. In this case, the use of diffraction (X-ray) elastic constants is not possible. Instead, diffraction (X-ray) stress factors have to be used. On the basis of examples, it is demonstrated that successful diffraction stress analysis is only possible if an appropriate grain-interaction model is applied.
529 citations
TL;DR: In this article, the effect of the aspect ratio of the plate and the volume fractions of the constituents on the centroidal deflection were scrutinized and the computed results were found to agree well with the solution of the problem.
386 citations
TL;DR: In this paper, a small deformation theory of strain-gradient plasticity for isotropic materials in the absence of plastic rotation was developed, based on a system of microstresses consistent with a microforce balance.
Abstract: This study develops a small-deformation theory of strain-gradient plasticity for isotropic materials in the absence of plastic rotation. The theory is based on a system of microstresses consistent with a microforce balance; a mechanical version of the second law that includes, via microstresses, work performed during viscoplastic flow; a constitutive theory that allows:
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the microstresses to depend on ∇E˙p, the gradient of the plastic strain-rate, and
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the free energy ψ to depend on the Burgers tensor G=curlEp.
The microforce balance when augmented by constitutive relations for the microstresses results in a nonlocal flow rule in the form of a tensorial second-order partial differential equation for the plastic strain. The microstresses are strictly dissipative when ψ is independent of the Burgers tensor, but when ψ depends on G the gradient microstress is partially energetic, and this, in turn, leads to a back stress and (hence) to Bauschinger-effects in the flow rule. It is further shown that dependencies of the microstresses on ∇E˙p lead to strengthening and weakening effects in the flow rule.
Typical macroscopic boundary conditions are supplemented by nonstandard microscopic boundary conditions associated with flow, and, as an aid to numerical solutions, a weak (virtual power) formulation of the nonlocal flow rule is derived.
375 citations
TL;DR: This analysis describes a technique to extend the reconstruction to anisotropic elastic properties in terms of a so‐called transversely isotropic model, which is capable of describing elastic shear anisotropy of parallel fibers.
Abstract: MR-elastography is a new technique for assessing the viscoelastic properties of tissue. One current focus of elastography is the provision of new physical parameters for improving the specificity in breast cancer diagnosis. This analysis describes a technique to extend the reconstruction to anisotropic elastic properties in terms of a so-called transversely isotropic model. Viscosity is treated as being isotropic. The particular model chosen for the anisotropy is appealing because it is capable of describing elastic shear anisotropy of parallel fibers. The dependence of the reconstruction on the particular choice of Poisson's ratio is eliminated by extracting the compressional displacement contribution using the Helmholtz-Hodge decomposition. Results are presented for simulations, a polyvinyl alcohol breast phantom, excised beef muscle, and measurements in two patients with breast lesions (invasive ductal carcinoma and fibroadenoma). The results show enhanced anisotropic and viscous properties inside the lesions and an indication for preferred fiber orientation.
372 citations
TL;DR: In this article, the authors show that linear forcing gives the same results as in spectral implementations, and that the linearly forced system converges to a stationary state that depends on domain size and Reynolds number, but not on the spectral shape of the initial condition.
Abstract: Numerical simulations of forced isotropic turbulence are most often formulated in Fourier space, where forcing is applied to low-wavenumber modes. For applications in physical space, low-wavenumber forcing is difficult to implement. The linear forcing recently proposed by Lundgren [“Linearly forced isotropic turbulence,” in Annual Research Briefs (Center for Turbulence Research, Stanford, 2003), pp. 461–473], where a force proportional to velocity is applied, is an attractive alternative but not much is known about its properties. Using numerical experimentation, various properties of the linear forcing are explored: (i) it is shown that when implemented in physical space, linear forcing gives the same results as in spectral implementations; (ii) it is shown that the linearly forced system converges to a stationary state that depends on domain size and Reynolds number, but not on the spectral shape of the initial condition; (iii) it is also shown that the extent of Kolmogorov −5∕3 range is similar to that...
346 citations
TL;DR: In this paper, a finite element calculation of frictionless, non-adhesive, contact between a rigid plane and an clasto-plastic solid with a self-affine fractal surface was conducted within an explicit dynamic Lagrangian framework.
Abstract: This paper presents a finite element calculation of frictionless, non-adhesive, contact between a rigid plane and an clasto-plastic solid with a self-affine fractal surface. The calculations are conducted within an explicit dynamic Lagrangian framework. The elastoplastic response of the material is described by a J(2) isotropic plasticity law. Parametric studies are used to establish general relations between contact properties and key material parameters. In all cases, the contact area A rises linearly with the applied load. The rate of increase grows as the yield stress sigma(y) decreases, scaling as a power of sigma(y) over the range typical of real materials. Results for A from different plasticity laws and surface morphologies can all be described by a simple scaling formula. Plasticity produces qualitative changes in the distributions of local pressures in the contact and of the size of connected contact regions. The probability of large local pressures is decreased, while large clusters become more likely. Loading-unloading cycles are considered and the total plastic work is found to be nearly constant over a wide range of yield stresses. (c) 2005 Elsevier Ltd. All rights reserved.
341 citations
TL;DR: In this paper, a two-dimensional solution for bending analysis of simply supported ceramic-metal sandwich plates is presented, where the sandwich plate faces have isotropic, two-constituent material distribution through the thickness, and the modulus of elasticity and Poisson's ratio of the faces are assumed to vary according to a power-law distribution in terms of the volume fractions of the constituents.
336 citations
TL;DR: In this article, the authors present a detailed description of the new tools that allow effective data analysis and systematic theoretical studies such as to separate isotropic from anisotropic aspects of turbulent statistical fluctuations.
319 citations
TL;DR: Results suggest that finite-element analyses can be adversely affected when elastic properties are modeled imprecisely, and that modelers should attempt to obtain elastic properties data about the species and skeletal elements that are the subjects of their analyses.
Abstract: The influence of elastic properties on finite-element analysis was investigated using a finite-element model of a Macaca fascicularis skull. Four finite-element analyses were performed in which the model was assigned different sets of elastic properties. In analysis 1, elastic properties were modeled isotropically using published data obtained from human limb bones. Analyses 2– 4 used data obtained from skulls of a closely allied species, M. mulatta, but varied as to how those data were incorporated into the model. In analysis 2, the model was assigned a single set of isotropic elastic properties. In analysis 3, each region within the model was assigned its own set of isotropic elastic properties. Finally, in analysis 4, each region received its own set of orthotropic elastic properties. Although a qualitative assessment indicates that the locations of strain concentrations across the model are broadly similar in all analyses, a quantitative assessment of strain indicates some differences between the analyses. When strain data from the finite-element analyses were compared to strain data derived from in vivo experiments, it was found that the model deformed most realistically using the orthotropic elastic properties employed in analysis 4. Results suggest that finite-element analyses can be adversely affected when elastic properties are modeled imprecisely, and that modelers should attempt to obtain elastic properties data about the species and skeletal elements that are the subjects of their analyses. © 2005 Wiley-Liss, Inc.
262 citations
TL;DR: Numerical simulations of the response of a two-dimensional granular slab to an external load reveal that both approaches are valid—albeit on different length scales.
Abstract: For years, engineers have used elastic and plastic models to describe the properties of granular solids, such as sand piles and grains in silos. However, there are theoretical and experimental results that challenge this approach. Specifically, it has been claimed that stress in granular solids propagates in a manner described by wave-like (hyperbolic) equations, rather than the elliptic equations of static elasticity. Here we report numerical simulations of the response of a two-dimensional granular slab to an external load, revealing that both approaches are valid--albeit on different length scales. For small systems that can be considered mesoscopic on the scale of the grains, a hyperbolic-like, strongly anisotropic response is expected. However, in large systems (those typically considered by engineers), the response is closer to that predicted by traditional isotropic elasticity models. Static friction, often ignored in simple models, plays a key role: it increases the elastic range and renders the response more isotropic, even beyond this range.
TL;DR: A light-induced isothermal transition of a polymer film from an isotropic solid to an anisotropic liquid state in which the degree of mechanical anisotropy can be controlled by light is reported.
Abstract: An increase in random molecular vibrations of a solid owing to heating above the melting point leads to a decrease in its long-range order and a loss of structural symmetry. Therefore conventional liquids are isotropic media. Here we report on a light-induced isothermal transition of a polymer film from an isotropic solid to an anisotropic liquid state in which the degree of mechanical anisotropy can be controlled by light. Whereas during irradiation by circular polarized light the film behaves as an isotropic viscoelastic fluid, it shows considerable fluidity only in the direction parallel to the light field vector under linear polarized light. The fluidization phenomenon is related to photoinduced motion of azobenzene-functionalized molecular units, which can be effectively activated only when their transition dipole moments are oriented close to the direction of the light polarization. We also describe here how the photofluidization allows nanoscopic elements of matter to be precisely manipulated.
TL;DR: In this paper, a finite-deformation, Coulomb-Mohr type constitutive theory for the elastic-viscoplastic response of pressure-sensitive and plastically-dilatant isotropic materials is developed.
Abstract: This study develops a finite-deformation, Coulomb–Mohr type constitutive theory for the elastic–viscoplastic response of pressure-sensitive and plastically-dilatant isotropic materials. The constitutive model has been implemented in a finite element program, and the numerical capability is used to study the deformation response of amorphous metallic glasses. Specifically, the response of an amorphous metallic glass in tension, compression, strip-bending, and indentation is studied, and it is shown that results from the numerical simulations qualitatively capture major features of corresponding results from physical experiments available in the literature.
TL;DR: In this article, it was shown that Poisson's ratio for anisotropic elastic materials can have an arbitrarily large positive or negative value under the prerequisite of positive definiteness of strain energy density.
Abstract: Poisson's ratio for isotropic elastic materials is bounded between -1 and 1 / 2 . It is shown that Poisson's ratio for anisotropic elastic materials can have an arbitrarily large positive or negative value under the prerequisite of positive definiteness of strain energy density. The large Poisson's ratio for cubic materials is physically realistic because the strains are bounded.
TL;DR: In this paper, a negative effective permeability is shown to exist at infrared frequencies in a three-dimensional collection of polaritonic spheres, which is demonstrated by an effective medium theory which relates the Mie resonances of the constituent spheres to the bulk response of the composite.
Abstract: A negative effective permeability is shown to exist at infrared frequencies in a three-dimensional collection of polaritonic spheres This is demonstrated by an effective medium theory which relates the Mie resonances of the constituent spheres to the bulk response of the composite The derived permittivity and permeability are shown to be isotropic The results are verified by a comparison with multiple-scattering photonic band calculations The existence of an anomalous dispersion region with a negative group velocity and the appropriate signs associated with the imaginary parts of the permittivity and permeability are also discussed
TL;DR: In this article, the authors introduce a class of models in which statistical isotropy is broken spontaneously in the CMB by a nonlinear response to long-wavelength fluctuations in a mediating field.
Abstract: We introduce a class of models in which statistical isotropy is broken spontaneously in the CMB by a nonlinear response to long-wavelength fluctuations in a mediating field. These fluctuations appear as a gradient locally and pick out a single preferred direction. The nonlinear response imprints this direction in a range of multipole moments. We consider two manifestations of isotropy breaking: additive contributions and multiplicative modulation of the intrinsic anisotropy. Since the Wilkinson microwave anisotropy probe (WMAP) exhibits an alignment of power deficits, an additive contribution is less likely to produce the observed alignments than the usual isotropic fluctuations, a fact which we illustrate with an explicit cosmological model of long-wavelength quintessence fluctuations. This problem applies to other models involving foregrounds or background anisotropy that seek to restore power to the CMB. Additive models that account directly for the observed power exacerbate the low power of the intrinsic fluctuations. Multiplicative models can overcome these difficulties. We construct a proof of principle model that significantly improves the likelihood and generates stronger alignments than WMAP in 30%--45% of realizations.
TL;DR: A novel constructive method for the preparation of random, isotropic assemblies of contacting circular discs with a user-defined grain size distribution is introduced.
Abstract: A discrete element simulation of a mechanical problem involving granular materials begins with the definition of the geometry of the sample to be analyzed. Since the dynamic sample preparation methods typically used in the practice are very time-consuming, constructive algorithms are becoming increasingly popular. This paper introduces a novel constructive method for the preparation of random, isotropic assemblies of contacting circular discs with a user-defined grain size distribution. The proposed approach is compared with other currently applied sample preparation methods.
TL;DR: Some mean field approximation methods are considered in this paper, with the objective to transfer any arbitrary local plasticity constitutive description to an overall analytical continuum description, and the results show that only the isotropic approximations of the tangent operators are able to deliver acceptable overall responses.
TL;DR: This analysis, using the Tersoff-Brenner potential and ab initio calculations, shows that the elasticity of the model thin shell evolves from isotropic to square symmetric with the decreasing tube diameter, leading to significant diameter dependence for all the elastic moduli and the representative wall thickness.
Abstract: There has been much debate on the choice for the representative wall thickness for the thin-shell model, although this model has demonstrated remarkable success in capturing many types of behavior of single-walled carbon nanotubes (SWNTs), in determining the buckling strains under compression, torsion, and bending, in particular. This analysis, using the Tersoff-Brenner potential and ab initio calculations, shows that the elasticity of the model thin shell evolves from isotropic to square symmetric with the decreasing tube diameter, leading to significant diameter dependence for all the elastic moduli and the representative wall thickness. Furthermore, the elastic moduli of multiwalled carbon nanotubes of diameters up to 10 nm are also size dependent.
TL;DR: It is shown that the driving force for nonAffine displacements is a spatial derivative of the random elastic constant tensor times the constant affine strain, though the randomness in elastic moduli it may generate does not drive nonaffine response.
Abstract: Materials characterized by spatially homogeneous elastic moduli undergo affine distortions when subjected to external stress at their boundaries, i.e., their displacements from a uniform reference state grow linearly with position , and their strains are spatially constant. Many materials, including all macroscopically isotropic amorphous ones, have elastic moduli that vary randomly with position, and they necessarily undergo nonaffine distortions in response to external stress. We study general aspects of nonaffine response and correlation using analytic calculations and numerical simulations. We define nonaffine displacements as the difference between and affine displacements, and we investigate the nonaffinity correlation function and related functions. We introduce four model random systems with random elastic moduli induced by locally random spring constants (none of which are infinite), by random coordination number, by random stress, or by any combination of these. We show analytically and numerically that scales as where the amplitude is proportional to the variance of local elastic moduli regardless of the origin of their randomness. We show that the driving force for nonaffine displacements is a spatial derivative of the random elastic constant tensor times the constant affine strain. Random stress by itself does not drive nonaffine response, though the randomness in elastic moduli it may generate does. We study models with both short- and long-range correlations in random elastic moduli.
TL;DR: In this article, a three-dimensional s3Dd isotropic LHM design that allows left-handed behavior for any direction of propagation and any polarization of the electromagnetic wave was proposed.
Abstract: We investigate three-dimensional left-handed and related metamaterials based on a fully symmetric multigap single-ring split-ring resonator sSRRd design and crossing continuous wires We demonstrate isotropic transmission properties of a SRR-only metamaterial and the corresponding left-handed material that possesses a negative effective index of refraction due to simultaneously negative effective permeability and permittivity Minor deviations from complete isotropy are due to the finite thickness of the metamaterial The realization of a perfect lens 1 and other applications of negative refraction require the fabrication of threedimensional, homogeneous, isotropic left-handed materials 2 sLHMd with simultaneously negative permittivity « and magnetic permeability m So far, no such materials exist, either in nature or in the laboratory Today’s available LHM structures, based on the periodic arrangement of split-ring resonators 3 sSRRd and continuous metallic wires, 4 are only one dimensional 5‐7 s1Dd, supporting left-handed properties only for propagation with fixed polarization in one direction, or two dimensional 8‐10 s2Dd, where propagation in two directions with fixed polarization or one direction with arbitrary polarization is possible Earlier attempts to design at least an isotropic SRR sRef 11d were lacking the symmetry of SRR and unit cell and required individual tuning of the parameters in the different spatial directions In this paper, we propose a three-dimensional s3Dd isotropic LHM design that allows left-handed behavior for any direction of propagation and any polarization of the electromagnetic wave Using numerical transfer matrix simulations, we verify the isotropic transmission properties of the proposed structures Our data show excellent agreement with results expected for a homogeneous slab with the corresponding negative « and m Our metamaterials are defined as a 3D periodic continuation of a single rectangular unit cell, consisting of SRRs and continuous wires The sample is a slab of metamaterial with a finite thickness of an integral number of unit cells and infinite extent in the perpendicular direction The two surfaces of the slab are parallel to any face of the unit cell An incident electromagnetic plane wave with wave vector k can be characterized by two angles: the incidence angle q P f 0, p /2 d between k and the surface normal n of the sample, and the angle f P s˛p , pg between the projection of k into and some chosen edge of the unit cell inside the surface plane of the sample The frequency of the incident wave is chosen such that the vacuum wavelength is approximately 10 times larger than the linear size of the unit cell and we expect effective medium behavior
TL;DR: In this paper, a theoretical, computational, and experimental study for a two-element superdirective array of resonant monopoles was conducted, and it was shown that the measured gain of the monopole array does indeed continually increase with decreasing spacing, provided the relative magnitudes and phases are maintained.
Abstract: In principle, the end-fire directivity of a linear periodic array of N isotropic radiators can approach N/sup 2/ as the spacing between elements decreases, provided the magnitude and phase of the input excitations are properly chosen. Thus, the directivity of a two-element array of isotropic radiators would approach a value of four, that is, 6 dB higher than that of a single isotropic radiator. We have conducted a theoretical, computational, and experimental study for a two-element superdirective array of resonant monopoles. In agreement with the theoretical and computational curves, the measured gain of the monopole array does indeed continually increase with decreasing spacing of the monopoles, provided the relative magnitudes and phases are maintained. However, for very small separation, maximum achievable gain is not reached due to the presence of ohmic loss.
TL;DR: In this article, a two-dimensional approach to model fracture of reinforced concrete structures under (increasing) static loading conditions is described, where the concrete is described in compression by a non-local isotropic damage constitutive law.
TL;DR: This work presents an accurate and efficient approach to the calculation of long-range interactions for molecular modeling and simulation using the isotropic periodic sum method, which can be applied to potentials of any functional form and to fully and partially homogenous systems as well as finite systems.
Abstract: This work presents an accurate and efficient approach to the calculation of long-range interactions for molecular modeling and simulation. This method defines a local region for each particle and describes the remaining region as images of the local region statistically distributed in an isotropic and periodic way, which we call isotropic periodic images. Different from lattice sum methods that sum over discrete lattice images generated by periodic boundary conditions, this method sums over the isotropic periodic images to calculate long-range interactions, and is referred to as the isotropic periodic sum (IPS) method. The IPS method is not a lattice sum method and eliminates the need for a reciprocal space sum. Several analytic solutions of IPS for commonly used potentials are presented. It is demonstrated that the IPS method produces results very similar to that of Ewald summation, but with three major advantages, (1) it eliminates unwanted symmetry artifacts raised from periodic boundary conditions, (2) it can be applied to potentials of any functional form and to fully and partially homogenous systems as well as finite systems, and (3) it is more computationally efficient and can be easily parallelized for multiprocessor computers. Therefore, this method provides a general approach to an efficient calculation of long-range interactions for various kinds of molecular systems.
TL;DR: In this paper, the first-order shear deformation theory (FSDT) coupled with the finite element method (FEM) was used to study free vibrations of a functionally graded (FG) anisotropic rectangular plate with the objective of maximizing one of its first five natural frequencies.
TL;DR: A multidiffusion‐tensor model (MDT) is presented containing two anisotropic and one isotropic diffusion tensors that has the ability to detect areas of fiber crossings and resolve the direction of crossing fibers.
Abstract: A multidiffusion-tensor model (MDT) is presented containing two anisotropic and one isotropic diffusion tensors. This approach has the ability to detect areas of fiber crossings and resolve the direction of crossing fibers. The mean diffusivity and the ratio of the tensor compartments were merged to one independent parameter by fitting MDT to the diffusion-weighted intensities of a two-point data acquisition scheme. By an F-test between the errors of the standard single diffusion tensor and the more complex MDT, fiber crossings were detected and the more accurate model was chosen voxel by voxel. The performance of crossing detection was compared with the spherical harmonics approach in simulations as well as in vivo. Similar results were found in both methods. The MDT model, however, did not only detect crossings but also yielded the single fiber directions. The FACT algorithm and a probabilistic connectivity algorithm were extended to support the MDT model. For example, a mean angular error smaller than 10 degrees was found for the MDT model in a simulated fiber crossing with an SNR of 80. By tracking the corticospinal tract the MDT-based tracks reached a significantly greater area of the gyrus precentralis.
TL;DR: In this article, an exact solution procedure is formulated for the buckling analysis of rectangular plates having two opposite edges (x = 0 and a) simply supported when these edges are subjected to linearly varying normal stresses σx−−N0[1−α(y/b)]/h, where h is the plate thickness.
TL;DR: In this article, a complete solution in terms of retarded potential functions for the wave equations in transversely isotropic media is presented, and the required conditions for the torsionless and rotationally symmetric configuration with respect to the axis of symmetry of the material are discussed.
Abstract: A transversely isotropic material in the sense of Green is considered. A complete solution in terms of retarded potential functions for the wave equations in transversely isotropic media is presented. In this paper we reduce the number of potential functions to only one, and we discuss the required conditions. As a special case, the torsionless and rotationally symmetric configuration with respect to the axis of symmetry of the material is discussed. The limiting case of elastostatics is cited, where the solution is reduced to the Lekhnitskii–Hu–Nowacki solution. The solution is simplified for the special case of isotropy. In this way, a new series of potential functions (to the best knowledge of the author) for the elastodynamics problem of isotropic materials is presented This solution is reduced to a special case of the Cauchy–Kovalevski–Somigliana solution, if the displacements satisfy specific conditions. Finally, Boggio's Theorem is generalized for transversely isotropic media which may be of interest to the reader beyond the present application.
TL;DR: In this article, the authors developed a general framework for discussing both isotropic-viscoplastic materials and amorphous materials based on the Kroner-Lee decomposition of the deformation gradient into elastic and inelastic parts, a system of microforces consistent with its own balance, and a mechanical version of the second law.
TL;DR: Gurtin and Anand as mentioned in this paper developed a gradient theory for finite-deformation isotropic viscoplasticity in the absence of plastic spin, which is based on the Kroner-Lee decomposition of the deformation gradient into elastic and plastic parts.