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Anisotropic
Terms modified by Anisotropic Selected AbstractsAnalysis of Anisotropic Void System in Electron-Beam Physical-Vapour-Deposited (EB-PVD) Thermal-Barrier Coatings,ADVANCED ENGINEERING MATERIALS, Issue 6 2009Bilge Saruhan Anisotropic and nanosized pores in PYSZ-based TBCs are analysed by means of small-angle neutron scattering (SANS). Three different coating morphologies are produced by varying the process parameters. In order to differentiate between closed and open pores in 400,,m thick coatings, a contrast-matching SANS technique is employed. In situ high-temperature SANS measurements demonstrate the occurrence of thermally activated surface area and pore-surface changes. Thermally derived changes in the pore size and morphology are correlated with the thermal conductivity measured using laser-flash analysis (LFA). [source] Finite element formulation for modelling large deformations in elasto-viscoplastic polycrystalsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 14 2004Karel Matou Abstract Anisotropic, elasto-viscoplastic behaviour in polycrystalline materials is modelled using a new, updated Lagrangian formulation based on a three-field form of the Hu-Washizu variational principle to create a stable finite element method in the context of nearly incompressible behaviour. The meso-scale is characterized by a representative volume element, which contains grains governed by single crystal behaviour. A new, fully implicit, two-level, backward Euler integration scheme together with an efficient finite element formulation, including consistent linearization, is presented. The proposed finite element model is capable of predicting non-homogeneous meso-fields, which, for example, may impact subsequent recrystallization. Finally, simple deformations involving an aluminium alloy are considered in order to demonstrate the algorithm. Copyright © 2004 John Wiley & Sons, Ltd. [source] Anisotropic, isothermal, turbulent swirling flow in a complex combustor geometryINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 10-11 2005L. N. Jones Abstract The performance of popular second moment closure (LRR, SSG) turbulence models is assessed and compared against experimental data for anisotropic swirling flow in a cylindrical combustion chamber. In contrast to previous studies, where the dissipation anisotropy is correlated with the stress anisotropy, the benefit of approximating the former for swirling flows in terms of the mean strain and vorticity is investigated. Second moment closure models are found to predict mean and turbulent flow quantities reasonably well everywhere except near the wall. The anisotropic dissipation model is found to improve prediction of mean flow quantities near the chamber axis and acts to preserve turbulence further downstream. Copyright © 2005 John Wiley & Sons, Ltd. [source] Anisotropic and hydrogen bonding effects in phenylglyoxamides and mandelamides: theoretical and NMR conformational evaluationMAGNETIC RESONANCE IN CHEMISTRY, Issue 5 2008Biank T. Gonçalves Abstract Interesting anisotropic effects were observed for phenylglyoxamides and their respective mandelamides. Such effects were observed in experimental 1H and 13C NMR (in CDCl3, CD3OD, and DMSO- d6 solvents) and in some cases with good correlation to theoretical 1H and 13C NMR DFT,GIAO (B3LYP/6-311 + + G**//B3LYP/6-31G*) calculations. A systematic conformational analysis of these compounds was performed in a two-step methodology, using PM3 and DFT (B3LYP/6-31G*) calculations; with good accomplishment and computational time economy. It was observed that intramolecular hydrogen bonding plays a significant role in the conformation of such compounds. Finally, a geminal nonequivalence of an NCH2 moiety, in one of the alkyl side chain (R1 = R2), was found for the tertiary mandelamides studied. Copyright © 2008 John Wiley & Sons, Ltd. [source] Anisotropic a posteriori error estimate for an optimal control problem governed by the heat equationNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 6 2006Marco Picasso Abstract The abstract framework of Becker et al. is considered to solve an optimal control problem governed by a parabolic equation. Existence and uniqueness of a solution are proved using the inf-sup framework and space-time functional spaces. A Crank-Nicolson time discretization is proposed, together with continuous, piecewise linear finite elements in space. Existence and uniqueness of a solution to the discretized problem is also proved using the inf-sup framework. An a posteriori error estimate is proposed, the goal being to control the error between the true and computed cost functional. The error estimate remains valid on strongly anisotropic meshes and an anisotropic error indicator is proposed when the time step is small. Finally, the quality of this error indicator is studied numerically on isotropic and anisotropic meshes. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006 [source] Anisotropic and antisymmetric double exchange in mixed-valence clustersPHYSICA STATUS SOLIDI (A) APPLICATIONS AND MATERIALS SCIENCE, Issue 15 2004Moisey I. Belinsky Abstract In the mixed-valence dn,dn+1 clusters of transition metal ions, taking the spin,orbit coupling into account in the Anderson,Hasegawa double exchange model results in anisotropic double exchange and antisymmetric double exchange. The anisotropic double exchange results in the zero-field splittings of the double exchange levels. These zero-field splittings are described by the the effective ZFS Hamiltonian, which is active between the states of different localization of the extra electron. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Rendering natural waters taking fluorescence into accountCOMPUTER ANIMATION AND VIRTUAL WORLDS (PREV: JNL OF VISUALISATION & COMPUTER ANIMATION), Issue 5 2004By E. Cerezo Abstract The aim of the work presented here is to generalize a system, developed to treat general participating media, to make it capable of considering volumetric inelastic processes such as fluorescence. Our system, based on the discrete ordinates method, is adequate to treat a complex participating medium such as natural waters as it is prepared to deal with not only anisotropic but also highly peaked phase functions, as well as to consider the spectral behaviour of the medium's characteristic parameters. It is also able to generate detailed quantitative illumination information, such as the amount of light that reaches the medium boundaries or the amount of light absorbed in each of the medium voxels. First, we present an extended form of the radiative transfer equation to incorporate inelastic volumetric phenomena. Then, we discuss the necessary changes in the general calculation scheme to include inelastic scattering. We have applied all this to consider the most common inelastic effect in natural waters: fluorescence in chlorophyll-a. Copyright © 2004 John Wiley & Sons, Ltd. [source] Thermal relaxation and coherence dynamics of spin 3/2.CONCEPTS IN MAGNETIC RESONANCE, Issue 2 2003Abstract The relaxation dynamics of the spin 3/2 density operator in the presence of fluctuating and static quadrupolar interactions is reviewed. The nuclear magnetic resonance (NMR) line shapes are analyzed for any value of the static quadrupolar interaction, ranging from isotropic systems to systems exhibiting large splitting far exceeding the line widths. Pulse sequences optimized for the elimination of line broadening due to an inhomogeneous static quadrupolar interaction and for the detection of nuclei involved in slow molecular motion and/or in anisotropic, liquid crystalline environment are discussed. In Part II, the dynamics of spin 3/2 in the presence of a (pulsed) radio frequency (RF) field is reviewed. © 2003 Wiley Periodicals, Inc. Concepts Magn Reson Part A 19A: 97,116, 2003. [source] Anisotropic contraction in forisomes: Simple models won't fitCYTOSKELETON, Issue 5 2008Winfried S. Peters Abstract Forisomes are ATP-independent, Ca2+ -driven contractile protein bodies acting as reversible valves in the phloem of plants of the legume family. Forisome contraction is anisotropic, as shrinkage in length is associated with radial expansion and vice versa. To test the hypothesis that changes in length and width are causally related, we monitored Ca2+ - and pH-dependent deformations in the exceptionally large forisomes of Canavalia gladiata by high-speed photography, and computed time-courses of derived geometric parameters (including volume and surface area). Soybean forisomes, which in the resting state resemble those of Canavalia geometrically but have less than 2% of the volume, were also studied to identify size effects. Calcium induced sixfold volume increases in forisomes of both species; in soybean, responses were completed in 0.15 s, compared to about 0.5 s required for a rapid response in Canavalia followed by slow swelling for several minutes. This size-dependent behavior supports the idea that forisome contractility might rest on similar mechanisms as those of polyelectrolyte gels, a class of artificial "smart" materials. In both species, time-courses of forisome length and diameter were variable and lacked correlation, arguing against a simple causal relationship between changes in length and width. Moreover, changes in the geometry of soybean forisomes differed qualitatively between Ca2+ - and pH-responses, suggesting that divalent cations and protons target different sites on the forisome proteins. Cell Motil. Cytoskeleton 2008. © 2008 Wiley-Liss, Inc. [source] A Geostatistical Analysis of Soil, Vegetation, and Image Data Characterizing Land Surface VariationGEOGRAPHICAL ANALYSIS, Issue 2 2007Sarah E. Rodgers The elucidation of spatial variation in the landscape can indicate potential wildlife habitats or breeding sites for vectors, such as ticks or mosquitoes, which cause a range of diseases. Information from remotely sensed data could aid the delineation of vegetation distribution on the ground in areas where local knowledge is limited. The data from digital images are often difficult to interpret because of pixel-to-pixel variation, that is, noise, and complex variation at more than one spatial scale. Landsat Thematic Mapper Plus (ETM+) and Satellite Pour l'Observation de La Terre (SPOT) image data were analyzed for an area close to Douna in Mali, West Africa. The variograms of the normalized difference vegetation index (NDVI) from both types of image data were nested. The parameters of the nested variogram function from the Landsat ETM+ data were used to design the sampling for a ground survey of soil and vegetation data. Variograms of the soil and vegetation data showed that their variation was anisotropic and their scales of variation were similar to those of NDVI from the SPOT data. The short- and long-range components of variation in the SPOT data were filtered out separately by factorial kriging. The map of the short-range component appears to represent the patterns of vegetation and associated shallow slopes and drainage channels of the tiger bush system. The map of the long-range component also appeared to relate to broader patterns in the tiger bush and to gentle undulations in the topography. The results suggest that the types of image data analyzed in this study could be used to identify areas with more moisture in semiarid regions that could support wildlife and also be potential vector breeding sites. [source] The design of an optimal filter for monthly GRACE gravity modelsGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 2 2008R. Klees SUMMARY Most applications of the publicly released Gravity Recovery and Climate Experiment monthly gravity field models require the application of a spatial filter to help suppressing noise and other systematic errors present in the data. The most common approach makes use of a simple Gaussian averaging process, which is often combined with a ,destriping' technique in which coefficient correlations within a given degree are removed. As brute force methods, neither of these techniques takes into consideration the statistical information from the gravity solution itself and, while they perform well overall, they can often end up removing more signal than necessary. Other optimal filters have been proposed in the literature; however, none have attempted to make full use of all information available from the monthly solutions. By examining the underlying principles of filter design, a filter has been developed that incorporates the noise and full signal variance,covariance matrix to tailor the filter to the error characteristics of a particular monthly solution. The filter is both anisotropic and non-symmetric, meaning it can accommodate noise of an arbitrary shape, such as the characteristic stripes. The filter minimizes the mean-square error and, in this sense, can be considered as the most optimal filter possible. Through both simulated and real data scenarios, this improved filter will be shown to preserve the highest amount of gravity signal when compared to other standard techniques, while simultaneously minimizing leakage effects and producing smooth solutions in areas of low signal. [source] Amplitude fluctuations due to diffraction and refraction in anisotropic random media: implications for seismic scattering attenuation estimatesGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 1 2003T. M. Müller SUMMARY We calculate the variance of the log-amplitude within the Rytov approximation for plane waves propagating in weakly inhomogeneous and statistically anisotropic random media. Since there is a simple relation between the log-amplitude variance and the attenuation coefficient of seismic primaries in the weak wavefield fluctuation regime, we also obtain scattering attenuation estimates that additionally depend on the aspect ratio of longitudinal and transverse correlation scales of the inhomogeneities. These estimates can be useful for the statistical characterization of anisotropic, large-scale inhomogeneities (large compared with the wavelength of the probing pulse) in the Earth crust and mantle, such as fault zones. With the help of plane-wave-transmission numerical experiments using the finite-difference method we compute the log-amplitude variance as a function of the propagation distance and observe reasonable agreement with the analytical results. We discuss the implications of our results in the context of seismic scattering attenuation estimations. [source] Upper mantle stratification by P and S receiver functionsGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 3 2000Véronique Farra Summary Seismic stratification of the upper mantle is investigated by applying two complementary techniques to the records of the Graefenberg array in southern Germany. The anisotropic P receiver function technique (Kosarev et al. 1984; Vinnik & Montagner 1996) is modified by using summary seismic events instead of individual events and different weighting functions instead of the same function for the harmonic angular analysis of the SV and T components of the Pds phases. The summary events provide better separation of the second azimuthal harmonic than the individual events. The parameters of the second harmonics of SV and T thus evaluated should be similar if they reflect the effects of azimuthal anisotropy. This can be used as a criterion to identify the anisotropy. To detect the Sdp phases and their azimuthal variations caused by azimuthal anisotropy we have developed a stacking technique, which can be termed the S receiver function technique It includes axis rotation to separate interfering P and S arrivals, determination of the principal (M) component of the S -wave motion, deconvolution of the P components of many recordings by their respective M components and stacking of the deconvolved P components with weights depending on the level of noise and the angle between the M direction and the backazimuth of the event. Both techniques yield consistent results for the Graefenberg array. As indicated by the P receiver functions, the upper layer of the mantle between the Moho and 80 km depth is anisotropic with dVs/Vs around 0.03 and the fast direction close to 20° clockwise from north. The fast direction of anisotropy below this layer is around 110°, The boundary between the upper and the lower anisotropic layers is manifested by the detectable Pds and Sdp converted phases. Shear wave splitting in SKS is strongly dominated by azimuthal anisotropy in the lower layer (asthenosphere). [source] Paraxial ray methods for anisotropic inhomogeneous mediaGEOPHYSICAL PROSPECTING, Issue 1 2007Tijmen Jan Moser ABSTRACT A new formalism of surface-to-surface paraxial matrices allows a very general and flexible formulation of the paraxial ray theory, equally valid in anisotropic and isotropic inhomogeneous layered media. The formalism is based on conventional dynamic ray tracing in Cartesian coordinates along a reference ray. At any user-selected pair of points of the reference ray, a pair of surfaces may be defined. These surfaces may be arbitrarily curved and oriented, and may represent structural interfaces, data recording surfaces, or merely formal surfaces. A newly obtained factorization of the interface propagator matrix allows to transform the conventional 6 × 6 propagator matrix in Cartesian coordinates into a 6 × 6 surface-to-surface paraxial matrix. This matrix defines the transformation of paraxial ray quantities from one surface to another. The redundant non-eikonal and ray-tangent solutions of the dynamic ray-tracing system in Cartesian coordinates can be easily eliminated from the 6 × 6 surface-to-surface paraxial matrix, and it can be reduced to 4 × 4 form. Both the 6 × 6 and 4 × 4 surface-to-surface paraxial matrices satisfy useful properties, particularly the symplecticity. In their 4 × 4 reduced form, they can be used to solve important boundary-value problems of a four-parametric system of paraxial rays, connecting the two surfaces, similarly as the well-known surface-to-surface matrices in isotropic media in ray-centred coordinates. Applications of such boundary-value problems include the two-point eikonal, relative geometrical spreading, Fresnel zones, the design of migration operators, and more. [source] Analytical solution for the electric potential in arbitrary anisotropic layered media applying the set of Hankel transforms of integer orderGEOPHYSICAL PROSPECTING, Issue 5 2006E. Pervago ABSTRACT The analytical solution and algorithm for simulating the electric potential in an arbitrarily anisotropic multilayered medium produced by a point DC source is here proposed. The solution is presented as a combination of Hankel transforms of integer order and Fourier transforms based on the analytical recurrent equations obtained for the potential spectrum. For the conversion of the potential spectrum into the space domain, we have applied the algorithm of the Fast Fourier Transform for logarithmically spaced points. A comparison of the modelling results with the power-series solution for two-layered anisotropic structures demonstrated the high accuracy and computing-time efficiency of the method proposed. The results of the apparent-resistivity calculation for both traditional pole-pole and tensor arrays above three-layered sequence with an azimuthally anisotropic second layer are presented. The numerical simulations show that both arrays have the same sensitivity to the anisotropy parameters. This sensitivity depends significantly on the resistivity ratio between anisotropic and adjacent layers and increases for the models with a conductive second layer. [source] Seismic characterization of vertical fractures described as general linear-slip interfacesGEOPHYSICAL PROSPECTING, Issue 2 2003Vladimir Grechka ABSTRACT Fluid flow in many hydrocarbon reservoirs is controlled by aligned fractures which make the medium anisotropic on the scale of seismic wavelength. Applying the linear-slip theory, we investigate seismic signatures of the effective medium produced by a single set of ,general' vertical fractures embedded in a purely isotropic host rock. The generality of our fracture model means the allowance for coupling between the normal (to the fracture plane) stress and the tangential jump in displacement (and vice versa). Despite its low (triclinic) symmetry, the medium is described by just nine independent effective parameters and possesses several distinct features which help to identify the physical model and estimate the fracture compliances and background velocities. For example, the polarization vector of the vertically propagating fast shear wave S1 and the semi-major axis of the S1 -wave normal-moveout (NMO) ellipse from a horizontal reflector always point in the direction of the fracture strike. Moreover, for the S1 -wave both the vertical velocity and the NMO velocity along the fractures are equal to the shear-wave velocity in the host rock. Analysis of seismic signatures in the limit of small fracture weaknesses allows us to select the input data needed for unambiguous fracture characterization. The fracture and background parameters can be estimated using the NMO ellipses from horizontal reflectors and vertical velocities of P-waves and two split S-waves, combined with a portion of the P-wave slowness surface reconstructed from multi-azimuth walkaway vertical seismic profiling (VSP) data. The stability of the parameter-estimation procedure is verified by performing non-linear inversion based on the exact equations. [source] Traveltime computation with the linearized eikonal equation for anisotropic mediaGEOPHYSICAL PROSPECTING, Issue 4 2002Tariq Alkhalifah A linearized eikonal equation is developed for transversely isotropic (TI) media with a vertical symmetry axis (VTI). It is linear with respect to perturbations in the horizontal velocity or the anisotropy parameter ,. An iterative linearization of the eikonal equation is used as the basis for an algorithm of finite-difference traveltime computations. A practical implementation of this iterative technique is to start with a background model that consists of an elliptically anisotropic, inhomogeneous medium, since traveltimes for this type of medium can be calculated efficiently using eikonal solvers, such as the fast marching method. This constrains the perturbation to changes in the anisotropy parameter , (the parameter most responsible for imaging improvements in anisotropic media). The iterative implementation includes repetitive calculation of , from traveltimes, which is then used to evaluate the perturbation needed for the next round of traveltime calculations using the linearized eikonal equation. Unlike isotropic media, interpolation is needed to estimate , in areas where the traveltime field is independent of ,, such as areas where the wave propagates vertically. Typically, two to three iterations can give sufficient accuracy in traveltimes for imaging applications. The cost of each iteration is slightly less than the cost of a typical eikonal solver. However, this method will ultimately provide traveltime solutions for VTI media. The main limitation of the method is that some smoothness of the medium is required for the iterative implementation to work, especially since we evaluate derivatives of the traveltime field as part of the iterative approach. If a single perturbation is sufficient for the traveltime calculation, which may be the case for weak anisotropy, no smoothness of the medium is necessary. Numerical tests demonstrate the robustness and efficiency of this approach. [source] Out-of-plane geometrical spreading in anisotropic mediaGEOPHYSICAL PROSPECTING, Issue 4 2002Norman Ettrich Two-dimensional seismic processing is successful in media with little structural and velocity variation in the direction perpendicular to the plane defined by the acquisition direction and the vertical axis. If the subsurface is anisotropic, an additional limitation is that this plane is a plane of symmetry. Kinematic ray propagation can be considered as a two-dimensional process in this type of medium. However, two-dimensional processing in a true-amplitude sense requires out-of-plane amplitude corrections in addition to compensation for in-plane amplitude variation. We provide formulae for the out-of-plane geometrical spreading for P- and S-waves in transversely isotropic and orthorhombic media. These are extensions of well-known isotropic formulae. For isotropic and transversely isotropic media, the ray propagation is independent of the azimuthal angle. The azimuthal direction is defined with respect to a possibly tilted axis of symmetry. The out-of-plane spreading correction can then be calculated by integrating quantities which describe in-plane kinematics along in-plane rays. If, in addition, the medium varies only along the vertical direction and has a vertical axis of symmetry, no ray tracing need be carried out. All quantities affecting the out-of-plane geometrical spreading can be derived from traveltime information available at the observation surface. Orthorhombic media possess no rotational symmetry and the out-of-plane geometrical spreading includes parameters which, even in principle, are not invertible from in-plane experiments. The exact and approximate formulae derived for P- and S-waves are nevertheless useful for modelling purposes. [source] Structural Transformations during Formation of Quasi-Amorphous BaTiO3,ADVANCED FUNCTIONAL MATERIALS, Issue 7 2007D. Ehre Abstract A model of structural transformations of amorphous into quasi-amorphous BaTiO3 is suggested. The model is based on previously published data and on X-ray photoelectron spectroscopy data presented in the current report. Both amorphous and quasi-amorphous phases of BaTiO3 are made up of a network of slightly distorted TiO6 octahedra connected in three different ways: by apices (akin to perovskite), edges, and faces. Ba ions in these phases are located in the voids between the octahedra, which is a nonperovskite environment. These data also suggest that Ba ions compensate electrical-charge imbalance incurred by randomly connected octahedra and, thereby, stabilize the TiO6 network. Upon heating, the edge-to-edge and face-to-face connections between TiO6 octahedra are severed and then reconnected via apices. Severing the connections between TiO6 octahedra requires a volume increase, suppression of which keeps some of the edge-to-edge and face-to-face connections intact. Transformation of the amorphous thin films into the quasi-amorphous phase occurs during pulling through a steep temperature gradient. During this process, the volume increase is inhomogeneous and causes both highly anisotropic strain and a strain gradient. The strain gradient favors breaking those connections, which aligns the distorted TiO6 octahedra along the direction of the gradient. As a result, the structure becomes not only anisotropic and non-centrosymmetric, but also acquires macroscopic polarization. Other compounds may also form a quasi-amorphous phase, providing that they satisfy the set of conditions derived from the suggested model. [source] ZnSe,Si Bi-coaxial Nanowire Heterostructures,ADVANCED FUNCTIONAL MATERIALS, Issue 9 2005R. Wang Abstract We report on the fabrication, structural characterization, and luminescence properties of ZnSe/Si bi-coaxial nanowire heterostructures. Uniform ZnSe/Si bi-coaxial nanowire heterostructures are grown on silicon substrates by the simple one-step thermal evaporation of ZnSe powder in the presence of hydrogen. Both ZnSe and silicon are single-crystalline in the bi-coaxial nanowire heterostructures, and there is a sharp interface along the nanowire axial direction. Furthermore, secondary nanostructures of either ZnSe nanobrushes or a SiOx sheath are also grown on the primary bi-coaxial nanowires, depending on the ratio of the source materials. The experimental evidence strongly suggests that bi-coaxial nanowires are formed via a co-growth mechanism, that is, ZnSe terminates specific surfaces of silicon and leads to anisotropic, one-dimensional silicon growth, which simultaneously serves as preferential nucleation sites for ZnSe, resulting in the bi-coaxial nanowire heterostructures. In addition, the optical properties of ZnSe/Si nanowires are investigated using low-temperature photoluminescence spectroscopy. [source] Organic Electronics: Solution-Grown, Macroscopic Organic Single Crystals Exhibiting Three-Dimensional Anisotropic Charge-Transport Properties (Adv. Mater.ADVANCED MATERIALS, Issue 18 200918/2009) Organic single crystals have the potential to delivering novel electronic devices based on three-dimensional anisotropic electronic transport. The cover shows single crystals of 4-hydroxycyanobenzene (4HCB) grown from solution behind a distorted-perspective partial representation of the crystalline structure hinting at their molecular constituents. The carrier mobility, anisotropic along the three crystallographic axes, is discussed by Fraleoni-Morgera, Fraboni, Femoni, and co-workers on p. 1835. Dr. George Kourousias is acknowledged for the cover design and artwork. [source] Hyperelastic modelling of small-strain stiffness anisotropy of cyclically loaded sandINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 2 2010A. Gajo Abstract Experimental evidence shows that soil stiffness at very small strains is strongly anisotropic and depends on the stress level and void ratio. In particular, stiffness anisotropy varies considerably in sand when subjected to cyclic loading, following the stress cycles applied. To model this behaviour, an innovative hyperelastic formulation based on the elastoplastic coupling is incorporated in a new kinematic hardening elastoplastic model. The proposed hyperelastic,plastic model is the first to be capable of correctly simulating all aspects of the small-strain behaviour of granular materials subjected to monotonic and cyclic loads. This hyperelastic formulation is generally applicable to any elastoplastic model. Copyright © 2009 John Wiley & Sons, Ltd. [source] Directional response of a reconstituted fine-grained soil,Part I: experimental investigationINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 13 2006Daniele Costanzo Abstract This paper discusses the results of a large experimental program designed to investigate in a systematic manner the main features of the incremental response of fine-grained soils. The results are obtained from triaxial stress probing experiments carried out on a French silty clay (Beaucaire Marl). All the tests have been performed on reconstituted specimens, normally consolidated to an initial state which is either isotropic or anisotropic. In the interpretation of the experimental results, extensive use is made of the concept of strain response envelope. The response envelopes obtained for different stress increment magnitudes are remarkably consistent with each other and indicate an inelastic and irreversible material response, i.e. a strong dependence on the stress increment direction, also at relatively small strain levels. A companion paper (Int. J. Numer. Anal. Meth. Geomech., this issue, 2006) assesses the performance of some advanced constitutive models in reproducing the behaviour of reconstituted Beaucaire Marl as observed in this experimental program. Copyright © 2006 John Wiley & Sons, Ltd. [source] Porothermoelastic analyses of anisotropic hollow cylinders with applicationsINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 2 2005Mazen Kanj Abstract It has been known that material anisotropy and thermal stresses affect borehole stability significantly. Aiming at the experimental studies associated with borehole stability in anisotropic (transversely isotropic) poroelastic materials subject to non-isothermal conditions, this paper details and applies an anisotropic porothermoelastic solution to an unjacketed hollow cylinder in a triaxial set-up. Numerical analyses are presented to demonstrate thermal and material anisotropy effects on the pore pressure and the stress concentrations in and around the geometry of a hollow cylinder subjected to thermal and stress perturbations. Copyright © 2004 John Wiley & Sons, Ltd. [source] Determination of rock mass strength properties by homogenizationINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 13 2001A. Pouya Abstract A method for determining fractured rock mass properties is presented here on the basis of homogenization approach. The rock mass is considered to be a heterogeneous medium composed of intact rock and of fractures. Its constitutive model is studied numerically using finite element method and assimilating the fractures to joint elements (Coste, Comportement Thermo-Hydro-Mécanique des massifs rocheux fracturés. Thèse de Doctorat, Ecole Nationale des Ponts et Chaussées, Paris, 1997). The method has been applied to a granite formation in France. Geological data on different families of fractures have been used for the statistical representation of the fractures. A mesh-generating tool for the medium with high density of fractures has been developed. The mechanical behaviour of the rock mass (elasticity, ultimate strength and hardening law) has been determined assuming linear elasticity and Mohr,Coulomb strength criterion both for the intact rock and the fractures. Evolution of the mechanical strength in different directions has been determined as a function of the mean stress, thanks to various numerical simulations. The mechanical strength appears to be anisotropic due to the preferential orientation of the fractures. The numerical results allowed us to determine an oriented strength criterion for the homogenized rock mass. A 2D constitutive law for the homogenized medium has been deduced from numerical data. A 3D extension of this model is also presented. Copyright © 2001 John Wiley & Sons, Ltd. [source] A new approach to anisotropic, bounding surface plasticity: general formulation and simulations of natural and reconstituted clay behaviourINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 3 2001A. Gajo Abstract It is demonstrated that an efficient framework for the description of a two surface kinematic hardening/bounding surface plasticity model can be devised if the model is conceived in a normalized stress space in which the bounding surface remains of constant size. The hardening of the bounding surface is contained in the transformation laws linking ,real' and ,normalized' stresses while the geometric rules controlling kinematic hardening are considered only in terms of normalized stresses. Within the general framework thus constructed, two particular models are developed in outline. Owing to the proposed anisotropic hardening, these models are shown to have the ability to reproduce the observed characteristics of the progressive destructuration of natural cemented clays and of the plastic anisotropy of reconstituted soils. Copyright © 2001 John Wiley & Sons, Ltd. [source] A stopping criterion for the conjugate gradient algorithm in the framework of anisotropic adaptive finite elementsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 4 2009M. Picasso Abstract We propose a simple stopping criterion for the conjugate gradient (CG) algorithm in the framework of anisotropic, adaptive finite elements for elliptic problems. The goal of the adaptive algorithm is to find a triangulation such that the estimated relative error is close to a given tolerance TOL. We propose to stop the CG algorithm whenever the residual vector has Euclidian norm less than a small fraction of the estimated error. This stopping criterion is based on a posteriori error estimates between the true solution u and the computed solution u (the superscript n stands for the CG iteration number, the subscript h for the typical mesh size) and on heuristics to relate the error between uh and u to the residual vector. Numerical experiments with anisotropic adaptive meshes show that the total number of CG iterations can be divided by 10 without significant discrepancy in the computed results. Copyright © 2008 John Wiley & Sons, Ltd. [source] A hypersingular time-domain BEM for 2D dynamic crack analysis in anisotropic solidsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2009M. Wünsche Abstract A hypersingular time-domain boundary element method (BEM) for transient elastodynamic crack analysis in two-dimensional (2D), homogeneous, anisotropic, and linear elastic solids is presented in this paper. Stationary cracks in both infinite and finite anisotropic solids under impact loading are investigated. On the external boundary of the cracked solid the classical displacement boundary integral equations (BIEs) are used, while the hypersingular traction BIEs are applied to the crack-faces. The temporal discretization is performed by a collocation method, while a Galerkin method is implemented for the spatial discretization. Both temporal and spatial integrations are carried out analytically. Special analytical techniques are developed to directly compute strongly singular and hypersingular integrals. Only the line integrals over an unit circle arising in the elastodynamic fundamental solutions need to be computed numerically by standard Gaussian quadrature. An explicit time-stepping scheme is obtained to compute the unknown boundary data including the crack-opening-displacements (CODs). Special crack-tip elements are adopted to ensure a direct and an accurate computation of the elastodynamic stress intensity factors from the CODs. Several numerical examples are given to show the accuracy and the efficiency of the present hypersingular time-domain BEM. Copyright © 2008 John Wiley & Sons, Ltd. [source] Variational h -adaption in finite deformation elasticity and plasticityINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2007J. Mosler Abstract We ropose a variational h -adaption strategy in which the evolution of the mesh is driven directly by the governing minimum principle. This minimum principle is the principle of minimum potential energy in the case of elastostatics; and a minimum principle for the incremental static problem of elasto-viscoplasticity. In particular, the mesh is refined locally when the resulting energy or incremental pseudo-energy released exceeds a certain threshold value. In order to avoid global recomputes, we estimate the local energy released by mesh refinement by means of a lower bound obtained by relaxing a local patch of elements. This bound can be computed locally, which reduces the complexity of the refinement algorithm to O(N). We also demonstrate how variational h -refinement can be combined with variational r -refinement to obtain a variational hr -refinement algorithm. Because of the strict variational nature of the h -refinement algorithm, the resulting meshes are anisotropic and outperform other refinement strategies based on aspect ratio or other purely geometrical measures of mesh quality. The versatility and rate of convergence of the resulting approach are illustrated by means of selected numerical examples. Copyright © 2007 John Wiley & Sons, Ltd. [source] A variational r -adaption and shape-optimization method for finite-deformation elasticityINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2004P. Thoutireddy Abstract This paper is concerned with the formulation of a variational r -adaption method for finite-deformation elastostatic problems. The distinguishing characteristic of the method is that the variational principle simultaneously supplies the solution, the optimal mesh and, in problems of shape optimization, the equilibrium shapes of the system. This is accomplished by minimizing the energy functional with respect to the nodal field values as well as with respect to the triangulation of the domain of analysis. Energy minimization with respect to the referential nodal positions has the effect of equilibrating the energetic or configurational forces acting on the nodes. We derive general expressions for the configurational forces for isoparametric elements and non-linear, possibly anisotropic, materials under general loading. We illustrate the versatility and convergence characteristics of the method by way of selected numerical tests and applications, including the problem of a semi-infinite crack in linear and non-linear elastic bodies; and the optimization of the shape of elastic inclusions. Copyright © 2004 John Wiley & Sons, Ltd. [source] | |||||||||||||||||||||||||||||||||||||||||||