Showing papers on "Isotropy published in 1993"
TL;DR: In this paper, a gspeneral expression for the yield surface of polycrystalline materials is developed, which can describe both isotropic and anisotropic materials.
Abstract: A gspeneral Expression for the yield surface of polycrystalline materials is developed. The proposed yield surface can describe both isotropic and anisotropic materials. The isotropic surface can be reduced to either the Tresca or von Mises surface if appropriate, or can be used to capture the yield behavior of materials (e.g. aluminum) which do not fall into either category. Anisotropy can be described by introducing a set of irreducible tensorial state variables. The introduced linear transformation is capable of describing different anisotropic states, including the most general anisotropy (triclinic) as opposed to existing criteria which describe only orthotropic materials. Also, it can successfully describe the variation of the plastic strain ratio (R-ratio), where polycrystalline plasticity models usually fail. A method for obtaining the material constants using only uniaxial test data is described and utilized for the special case of orthotropic anisotropy. Finally, the use of tensorial state variables together with the introduced mathematical formulation make the proposed yield function a very convenient tool for numerical implementation in finite element analysis.
622 citations
TL;DR: In this article, the elastic strain and stress fields in an infinite medium constituted of an n-layered isotropic spherical inclusion, embedded in a matrix subjected to uniform stress or strain conditions at infinity, were derived.
427 citations
TL;DR: In this article, the authors derived a general expression for the lattice strain which corresponds to the x-ray diffraction measurement on the polycrystalline specimen (cubic system) compressed nonhydrostatically in an opposed anvil device.
Abstract: A general expression has been derived using anisotropic elasticity theory for the lattice strain which corresponds to the x‐ray diffraction measurement on the polycrystalline specimen (cubic system) compressed nonhydrostatically in an opposed anvil device. The expressions for the various diffraction geometries emerge as the special cases of this equation. The strain calculated using isotropic elasticity theory corresponds to the macroscopic strain in the specimen, and can be obtained from the present equation by letting the anisotropy factor 2(S11−S12)/S44=1. Further, it is shown that the ratio of the lattice strain to the macroscopic strain (in the direction of the lattice strain) produced by the deviatoric stress component depends on the Miller indices (hkl) of the lattice planes and the elastic anisotropy factor. This ratio is unity only if the crystallites constituting the specimen are elastically isotropic, and increases with increasing anisotropy of the crystallites.
306 citations
TL;DR: In this paper, a method for bounding the overall properties of a class of composite materials in terms of the properties of individual phases and of their arrangement is proposed, which applies to power law materials and, as a special case, to rigid ideally plastic materials.
Abstract: A method is proposed for bounding the overall properties of a class of composite materials in terms of the properties of the individual phases and of their arrangement. It applies to power law materials and, as a special case, to rigid ideally plastic materials. A link between the overall potential of a nonlinear composite and the overall energy of a fictitious linear composite is presented with no assumptions on the arrangement of the phases. With this method, any upper bound available for linear materials can easily be transposed to nonlinear materials. A new characterizing of the external surface of ideally plastic composites is given. The possible applications of these bounds are illustrated in a study on two-phase isotropic composites and the predictions of the bounds are compared with Finite Element cell calculations.
281 citations
TL;DR: The unloading process in an indentation experiment is often modelled as a contact problem of a rigid punch on an elastically isotropic half space as discussed by the authors, which allows one to derive simple formulae to determine the indentation modulus from experimental data.
Abstract: The unloading process in an indentation experiment is often modelled as a contact problem of a rigid punch on an elastically isotropic half space. This allows one to derive simple formulae to determine the indentation modulus from experimental data. We have studied the contact problem of a flat circular punch and a paraboloid on an elastically anisotropic half space and have shown that the formulae used for isotropic materials can be used for anisotropic materials as long as the half space has three or fourfold rotational symmetry. In the case of lower symmetry, the indentation modulus depends on the shape of the indenter. We have calculated the indentation modulus of {100}, {111} and {110} surfaces of cubic crystals for a wide range of elastic constants. The {110} indentation modulus was calculated for the case of a flat circular punch. The single-crystal indentation moduli differ substantially from the isotropic polycrystalline indentation moduli and the differences increase with increasing anisotropy f...
275 citations
TL;DR: In this paper, a three-dimensional study of the turbulence and sheared flow generated by the drift resistive ballooning modes in tokamak edge plasmas has been completed.
Abstract: A three‐dimensional study of the turbulence and sheared flow generated by the drift‐resistive ballooning modes in tokamak edge plasmas has been completed. The fluid simulations show that 10%–15% percent density fluctuations can develop in the nonlinear state when the self‐consistently generated shear flow is suppressed. These modes are also found to give rise to poloidally asymmetric particle transport. Characteristic scale lengths of these fluctuations are isotropic in the plane transverse to B and smaller than the connection length along the field line. Sheared poloidal flow is self‐consistently driven by both the Reynolds stress and the Stringer mechanisms. In the presence of self‐consistent shear flow, the transverse spectrum is no longer isotropic transverse to B. The vortices become elongated in the poloidal direction. Also, there is a substantial reduction in both the level of fluctuations of the density and potential and the associated particle transport. These features are in qualitative agreement with L–H transitions observed in tokamaks.
240 citations
TL;DR: In this article, the authors measured velocities on a block composed of lucite plates with roughened surfaces pressed together with a static normal stress to simulate a fractured medium and found that for wavelength much larger than the thickness of an individual plate, the block can be modeled as a particular type of transversely isotropic (TI) medium that depends on four parameters.
Abstract: Ultrasonic velocities were measured on a block composed of lucite plates with roughened surfaces pressed together with a static normal stress to simulate a fractured medium. The measurements, normal, parallel, and oblique to the fractures, show that for wavelength much larger than the thickness of an individual plate, the block can be modeled as a particular type of transversely isotropic (TI) medium that depends on four parameters. This TI medium behavior is the same as that of an isotropic solid in which are embedded a set of parallel linear slip interfaces, specified by (1) the excess compliance tangential to the interfaces and (2) the excess compliance normal to the interfaces. At all static stress levels, the authors inverted the data for the background isotropic medium parameters and the excess compliances. The background parameters obtained were basically independent of stress level and agreed well with the bulk properties of the lucite. The excess compliances decreased with increasing static closing stress, implying that increasing static stress forces asperities on either side of a fracture into greater contact, gradually eliminating the excess compliance that gives rise to the anisotropy. A medium with such planes of excess compliance has been shown, theoretically, to describemore » the behavior of a medium with long parallel joints, as well as a medium with embedded parallel microcracks.« less
225 citations
TL;DR: The concept of kinematic conditioning is recalled and used as a performance index for the optimization of the manipulators and it is shown that this leads to designs having at least one isotropic configuration.
Abstract: This article studies the kinematic design of different types of spherical three-degree-of-freedom parallel manipulators. The mechanical architectures presented have been introduced elsewhere. However, designs having at least one isotropic configuration are suggested here for the first time. Isotropic configurations are defined, in turn, as those configurations in which the Jacobian matrix, mapping the angular velocity vector of the effector into the joint velocities, is proportional to an orthogonal matrix. First, a review of the direct and inverse kinematics of spherical three-degree-of-freedom parallel manipulators is outlined, and a general form for the Jacobian matrix is given. Parallel manipulators with revolute or prismatic actuators are discussed. Then, the concept of kinematic conditioning is recalled and used as a performance index for the optimization of the manipulators. It is shown that this leads to designs having at least one isotropic configuration. Finally, a few examples of such designs are presented. 15 refs.
209 citations
TL;DR: In this article, a numerical simulation is presented that combines the flow simulation during injection molding with an efficient algorithm for predicting the orientation of short fibers in thin composite parts, represented in terms of a second-order orientation tensor.
Abstract: A numerical simulation is presented that combines the flow simulation during injection molding with an efficient algorithm for predicting the orientation of short fibers in thin composite parts. Fiber-orientation state is represented in terms of a second-order orientation tensor. Fiber-fiber interactions are modeled by means of an isotropic rotary diffusion. The simulation predicts flow-aligned fiber orientation (shell region)near the surface with transversely aligned (core region) fibers in the vicinity of the mid-plane. The effects of part thickness and injection speed on fiber orientation are analyzed. Experimental measurements of fiber orientation in plaque-shaped parts for three different combinations of cavity thickness and injection speed are reported. It is found that gapwise-converging flow due to the growing layer of solidified polymer near the walls tends to flow-align the fibers near the entrance, whereas near the melt front, gapwise-diverging flow due to the diminishing solid layer tends to lign the fibers transverse to the flow. The effect of this gapwise-converging-diverging flow is found to be especially significant for thin parts molded at slower injection speeds, which have a proportionately thicker layer of solidified polymer during the filling process. If the fiber orientation is known, predictions of the anisotropic tensile moduli and thermal-expansion coefficients of the composite are obtained by using the equations for unidirectional composites and taking an orientation average. These predictions are found to agree reasonably well with corresponding experimental measurements.
206 citations
TL;DR: In this paper, the authors show that the low-altitude IB position of 30-to 300-keV protons is strongly controlled by the equatorial magnetic field in the tail.
Abstract: Simultaneous measurements of the low-altitude energetic particle flux by NOAA spacecraft and the geostationary magnetic field by GOES 2 spacecraft are used to test the recently proposed isotropic boundary algorithm (IBA) method to evaluate the instantaneous magnetospheric configuration. According to the IBA method, the equatorward boundary of the isotropic proton precipitation, in brief the isotropic boundary (IB), corresponds to the boundary separating adiabatic and chaotic regimes of particle motion in the tail current sheet and is controlled by the properties of the equatorial magnetic field. In this study we confirm some of the fundamental features of the IBA method. First, we show that the low-altitude IB position of 30- to 300-keV protons is strongly controlled by the equatorial magnetic field in the tail. (The corresponding correlation coefficient exceeds 0.9.) Second, the MLT dependence of the nightside IB latitude is in good agreement with that computed using magnetospheric models. Third, the observed magnetic field and the field predicted by the IBA method using the measured IB position have similar values and are well correlated with a correlation coefficient of at least 0.84 for the main components and a standard deviation of only about 10% of the dynamic range of these components. This shows that the threshold condition separating the two particle motion regimes is fulfilled in the proximity of the IB field line. We argue that the remaining inconsistencies between the calculated and observed magnetic fields are mainly due to the fact that the available magnetospheric models seem to underestimate the amount of tailward stretching of both the tail field lines during active conditions as well as field lines starting from the dayside. In view of its good capabilities to remotely determine the instantaneous magnetic field, we expect that the IBA method will find wide applications in the mapping of magnetic field lines and in testing of existing and new magnetospheric models.
195 citations
TL;DR: In this paper, an approximate equation governing the turbulent fluid velocity encountered along discrete particle path is used to derive the fluid/particle turbulent moments required for dispersed two-phase flows modelling, and closure model predictions are compared with results obtained from large-eddy simulation of particle fluctuating motion in forced isotropic fluid turbulence.
Abstract: An approximate equation governing the turbulent fluid velocity encountered along discrete particle path is used to derive the fluid/particle turbulent moments required for dispersed two-phase flows modelling. Then, closure model predictions are compared with results obtained from large-eddy simulation of particle fluctuating motion in forced isotropic fluid turbulence.
TL;DR: Reciprocating shear is found to increase the isotropic-to-lamellar transition temperature in a symmetric diblock copolymer melt, anticipated by a recent theory that accounts for the suppression of fluctuations by a symmetry breaking field in this class of weakly first-order phase transitions.
Abstract: Reciprocating shear is found to increase the isotropic-to-lamellar transition temperature in a symmetric diblock copolymer melt. The temperature at which the isotropic state becomes unstable rapidly approaches the ordering transition as the shear rate increases. Shear-induced ordering results in lamellae orientation with wave vectors directed normal to the shear and velocity gradient directions. These results are anticipated by a recent theory that accounts for the suppression of fluctuations by a symmetry breaking field in this class of weakly first-order phase transitions.
TL;DR: In this article, an analytical model for the prediction of the thermoelastic properties of composite laminates containing matrix cracks is presented, and the model has been verified against numerically determined stiffnesses, thermal expansion coefficients, strain contributions from release of residual stresses and local average ply stresses and strains do solely contain known ply property data and matrix crack densities.
TL;DR: The effective dielectric constants of several classes of photonic-band-gap structures are computed and it is found that in the long-wavelength limit, they can be isotropic, uniaxial, or biaXial, depending on the symmetry of the structure under consideration.
Abstract: Using a plane-wave-expansion method, we obtained expressions for the effective dielectric constants of composite periodic dielectric materials as the long-wavelength limit of the photonic-band-structure problem. The effective dielectric constants of several classes of photonic-band-gap structures are computed and we found that in the long-wavelength limit, they can be isotropic, uniaxial, or biaxial, depending on the symmetry of the structure under consideration. We also found that the scalar wave approximation gives poor results for effective dielectric constants while the Maxwell-Garnett theory offers very good approximations in the low-filling-ratio regimes.
TL;DR: In this paper, a study of the one-dimensional thermoelastic wave produced by an instantaneous plane source of heat in homogeneous isotropic infinite and semi-infinite bodies of the Green-Lindsay (G-L) type is presented.
Abstract: A study of the one-dimensional thermoelastic waves produced by an instantaneous plane source of heat in homogeneous isotropic infinite and semi-infinite bodies of the Green-Lindsay (G-L) type is presented. Closed-form Green's functions corresponding to the plane heat source are obtained using the decomposition theorem for a potential-temperature wave of the G-L theory. Qualitative analysis of the results is included.
TL;DR: In this paper, the authors derived the necessary extension to the FDTD equations to accommodate nondiagonal tensors and obtained excellent agreement between FDTD and exact analytic results for a one-dimensional anisotropic scatterer.
Abstract: The popularity of the finite-difference time-domain (FDTD) method stems from the fact that it is not limited to a specific geometry and it does not restrict the constitutive parameters of a scatterer. Furthermore, it provides a direct solution to problems with transient illumination, but can also be used for harmonic analysis. However, researchers have limited their investigation to materials that are either isotropic or that have diagonal permittivity, conductivity, and permeability tensors. The authors derive the necessary extension to the FDTD equations to accommodate nondiagonal tensors. Excellent agreement between FDTD and exact analytic results is obtained for a one-dimensional anisotropic scatterer. >
TL;DR: If enamel is indeed anisotropic, its function differs greatly from that suggested in previous hypotheses, as it would provide a hard-wearing protective surface-coating while simultaneously diverting the load away from this brittle, low-tensile-strength phase, thus reducing the potential for tooth fracture.
Abstract: Enamel is thought to have highly anisotropic stiffness characteristics, because of its prismatic structure. It is probable that the enamel is stiffer in the prism direction compared with a direction perpendicular to it. The prisms are thought to run approximately perpendicular to the enamel-dentin junction. The curvilinear anisotropy that will result can readily be modeled by TOMECH, a finite element program developed at the University of Sheffield, since curvilinearity of mechanical properties is available as an automated feature of this program. The patterns of stress due to an external load were investigated in two-dimensional abstract models, and in a model of a mandibular second premolar, for both anisotropic and isotropic enamel. Results were compared with the commercial code ANSYS and good agreement obtained. Enamel with anisotropic properties was found to have a profoundly different stress distribution under load when compared with models with isotropic enamel. For isotropic enamel, the load path ...
TL;DR: In this article, the statistical characterization of residual stress generated in polycrystalline ceramics during cooling from the fabrication temperature is studied. Butler et al. show that the distribution of normal and shear tractions induced by thermal contraction mismatch among grains is gaussian and that these tractions are statistically independent random variables.
Abstract: The problem addressed in this paper concerns the statistical characterization of the state of residual stress generated in polycrystalline ceramics during cooling from the fabrication temperature. Detailed finite element simulations are carried out for an ensemble of large numbers of randomly oriented, planar hexagonal grains with elastic and thermal expansion anisotropy, and brittle grain interfaces. The calculations show that the distribution of normal and shear tractions induced by thermal contraction mismatch among grains is gaussian and that these tractions are statistically independent random variables. Although the gaussian nature of the distributions remains unaffected by the introduction of elastic anisotropy, the results indicate that elastic anisotropy has a significant effect on the residual stresses for finite departures from isotropy. When the hexagonal grains are randomly distorted, the magnitude and distribution of residual stresses are found to be insignificantly altered. Spontaneous microfracture due to the generation of internal stresses is also simulated in the analysis by allowing for the nucleation and growth of intergranular microcracks when the fracture energy along the grain facets exceeds a certain critical value. When such microcracking is incorporated into the computation, the levels of residual stress are markedly reduced as a consequence of stress dissipation. The dependence of intergranular microcracking on grain size and temperature variation is examined and the predicted trends on material degradation or the complete suppression of microfracture are discussed in the light of available experimental results.
TL;DR: In this paper, a comprehensive analytical treatment of the three-dimensional response of a transversely isotropic elastic half space subjected to time-harmonic excitations is presented, where general solutions for equations of equilibrium expressed in terms of displacements are derived by applying Fourier expansion and Hankel integral transforms with respect to the circumferential coordinate and radial coordinate.
Abstract: This paper presents a comprehensive analytical treatment of the three-dimensional response of a transversely isotropic elastic half space subjected to time-harmonic excitations. General solutions for equations of equilibrium expressed in terms of displacements are derived by applying Fourier expansion with respect to the circumferential coordinate and Hankel integral transforms with respect to the radial coordinate. The general solutions are used to derive the explicit solutions for Green’s functions (displacements and stresses) corresponding to a set of time-harmonic circular ring loads acting inside a half space. The circumferential variation of the ring loads are assumed to be cos \Im\Nθ\N for loadings in the vertical and radial directions and sin \Im\Nθ\N for the loading in the circumferential direction. These Green’s functions can be used as the kernel functions of the boundary-integral-equation method and in the development of solutions for a variety of elastodynamic boundary value problems. Comparisons with existing numerical solutions for an isotropic half space are presented to confirm the accuracy of the present solutions. Selected numerical results for displacements and stresses are presented to portray the dependence of the response of the half space on the frequency of excitation and the degree of anisotropy of the medium.
TL;DR: In this paper, a molecular dynamics simulation study of a flexible model mesogen composed of seven tangential spheres is presented, where bonded atoms are constrained to lie within narrow potential wells.
Abstract: Results are reported for a molecular dynamics simulation study of a flexible model mesogen composed of seven tangential spheres. We follow the ‘rattling spheres’ method by which bonded atoms are constrained to lie within narrow potential wells. The dynamics of the system is that of a hard sphere fluid with added constraints. The phase diagram of our model system is calculated as a function of density and shows the presence of three fluid phases. These are assigned to be isotropic, nematic and smectic-A phases. Results are reported for the orientational order, radial distribution functions, structure factors and single-particle structural data within these phases. A small but significant change in shape is measured as the nematic phase is entered from the isotropic liquid. This is interpreted in terms of a quenching of allowed conformations parallel to the director.
TL;DR: In this paper, the authors considered Rayleigh diffraction in elastic materials with a periodic microstructure whose heterogeneities are in finite concentration or show great contrasts in properties, and established the developments up to the third order.
TL;DR: In this paper, a simple inversion procedure can be obtained to determine three of the five elasticities of a transversely isotropic (TI) formation tilted at some known angle with respect to the borehole axis.
Abstract: Tube‐wave speed in the presence of a weakly anisotropic formation can be expressed in terms of an effective shear modulus for an equivalent isotropic formation. When combined with expressions for the speeds of the SH‐ and quasi‐SV‐waves along the borehole axis, a simple inversion procedure can be obtained to determine three of the five elasticities of a transversely isotropic (TI) formation tilted at some known angle with respect to the borehole axis. Subsequently, a fourth combination of elastic moduli can be estimated from the expression for the qP‐wave speed along the borehole axis. The possibility of determining all five elasticities of a TI formation based on an assumed correlation between two anisotropy parameters is discussed.
TL;DR: In this paper, the authors studied plane incremental vibrations superimposed on the pure homogeneous deformation of a rectangular block of incompressible isotropic elastic material and derived the frequencies of symmetric and antisymmetric modes of vibration in terms of the underlying deformation and stress and of the inplane aspect ratio of the block.
TL;DR: In this article, a simple and exact solution procedure for linear free vibration of isotropic and orthotropic conical shells is presented, in the form of a power series in terms of a particularly convenient coordinate system, obtained directly from the governing equations for the three displacements.
TL;DR: In this paper, an explicit formulation and a procedure for the computation of isotropic tensor-valued tensor functions are discussed, based on a spectral decomposition in terms of second-order eigenvalue bases, which avoids the costly computation of eigenvectors.
Abstract: An explicit formulation and a procedure for the computation of isotropic tensor-valued tensor functions is discussed The formulation is based on a spectral decomposition in terms of second-order eigenvalue bases, which avoids the costly computation of eigenvectors As an important result a compact structure of the fourth-order derivatives of general second-order isotropic tensor functions is presented
TL;DR: In this article, two tensors (called fabric tensors) are introduced to measure the inherent and induced anisotropy for granular materials, explicitly used in the framework of soil plasticity.
TL;DR: In this article, the authors performed diffusion Monte Carlo simulations for the ground states of several SF6HeN clusters in the range N=1−499. The authors used novel trial wave functions to describe both the shell structure of these clusters and the anisotropy arising from the potential.
Abstract: Variational and diffusion Monte Carlo results are presented for the ground states of several SF6HeN clusters in the range N=1–499. The diffusion Monte Carlo computations are well converged, yielding an expected accuracy in the energy well under 1%. Computations are performed employing both an isotropic and an anisotropic He–SF6 interaction potential. Novel trial wave functions are used to describe both the shell structure of these clusters and the anisotropy arising from the potential. The ground state helium densities show the SF6 located at the cluster center, inducing a large degree of localization and a shell‐like structure in the surrounding helium. Although the full potential causes a large degree of anisotropy in the helium density, general characteristics such as the energy and size are not greatly affected by the potential anisotropy. Finally, we compute spectral shifts for the ν3 SF6 vibration due to the instantaneous dipole–induced dipole mechanism and compare with recent experiments. We find a...
TL;DR: In this article, a variational algorithm for computing dendritic solidification is presented, which reproduces the Gibbs-Thomson relation as a balance between bulk and surface energy and is able to operate in the infinite-mobility limit with no unphysical time-step restriction.