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Stress Tensor (stress + tensor)
Selected AbstractsThree-dimensional thermoelastic stresses in off-axis oriented single crystals with hexagonal symmetryCRYSTAL RESEARCH AND TECHNOLOGY, Issue 3 2007K. Böttcher Abstract A three-dimensional (3D) thermoelastic stress analysis is carried out on a single crystal with axisymmetric geometry but with a hexagonal crystallographic symmetry. The crystallographic orientation is off-axis with respect to the cylindrical coordinate system. By applying a Fourier series expansion with respect to the rotational angle , of the cylindrical coordinates, the 3D boundary value problem is reduced to a sequence of 2D ones on the meridian plane, which are solved by the finite-element method. In our example, the off-axis orientation is towards a direction of high symmetry, and therefore only four of the six stress tensor components are non-zero. In the end, the stress tensor is projected onto the slip system of the crystal. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Transport and deformation of droplets in a microdevice using dielectrophoresisELECTROPHORESIS, Issue 4 2007Pushpendra Singh Professor Abstract In microfluidic devices the fluid can be manipulated either as continuous streams or droplets. The latter is particularly attractive as individual droplets can not only move but also split and fuse, thus offering great flexibility for applications such as laboratory-on-a-chip. We consider the transport of liquid drops immersed in a surrounding liquid by means of the dielectrophoretic force generated by electrodes mounted at the bottom of a microdevice. The direct numerical simulation (DNS) approach is used to study the motion of droplets subjected to both hydrodynamic and electrostatic forces. Our technique is based on a finite element scheme using the fundamental equations of motion for both the droplets and surrounding fluid. The interface is tracked by the level set method and the electrostatic forces are computed using the Maxwell stress tensor. The DNS results show that the droplets move, and deform, under the action of nonuniform electric stresses on their surfaces. The deformation increases as the drop moves closer to the electrodes. The extent to which the isolated drops deform depends on the electric Weber number. When the electric Weber number is small, the drops remain spherical; otherwise, the drops stretch. Two droplets, however, that are sufficiently close to each other, can deform and coalesce, even if the electric Weber number is small. This phenomenon does not rely on the magnitude of the electric stresses generated by the bulk electric field, but instead is due to the attractive electrostatic drop,drop interaction overcoming the surface tension force. Experimental results are also presented and found to be in agreement with the DNS results. [source] Numerical comparison between Maxwell stress method and equivalent multipole approach for calculation of the dielectrophoretic force in single-cell trapsELECTROPHORESIS, Issue 11 2005Carlos Rosales Abstract This paper presents detailed numerical calculations of the dielectrophoretic force in traps designed for single-cell trapping. A trap with eight planar electrodes is studied for spherical and ellipsoidal particles using the boundary element method (BEM). Multipolar approximations of orders one to three are compared with the full Maxwell stress tensor (MST) calculation of the electrical force on spherical particles. Ellipsoidal particles are also studied, but in their case only the dipolar approximation is available for comparison with the MST solution. The results show that a small number of multipolar terms need to be considered in order to obtain accurate results for spheres, even in the proximity of the electrodes, and that the full MST calculation is only required in the study of nonspherical particles. [source] Multiaxial fatigue criterion for a high-density polyethylene thermoplasticFATIGUE & FRACTURE OF ENGINEERING MATERIALS AND STRUCTURES, Issue 6 2010A. BERREHILI ABSTRACT The multiaxial fatigue behaviour of a high-density polyethylene was investigated at room temperature and constant frequency. As a consequence of the mode of failure, an end-of-life criterion for fatigue tests is discussed in the first part of the work, in order to define the number of cycles to failure. Based on force controlled fatigue tests under tension, compression and torsion at two stress ratio, a multiaxial fatigue criterion including the stress-ratio effect is proposed for the fatigue design of this polymer. This criterion is based on the maximum and mean values of the second invariant of the stress tensor. [source] A unified continuum representation of post-seismic relaxation mechanisms: semi-analytic models of afterslip, poroelastic rebound and viscoelastic flowGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 3 2010Sylvain Barbot SUMMARY We present a unified continuum mechanics representation of the mechanisms believed to be commonly involved in post-seismic transients such as viscoelasticity, fault creep and poroelasticity. The time-dependent relaxation that follows an earthquake, or any other static stress perturbation, is considered in a framework of a generalized viscoelastoplastic rheology whereby some inelastic strain relaxes a physical quantity in the material. The relaxed quantity is the deviatoric stress in case of viscoelastic relaxation, the shear stress in case of creep on a fault plane and the trace of the stress tensor in case of poroelastic rebound. In this framework, the instantaneous velocity field satisfies the linear inhomogeneous Navier's equation with sources parametrized as equivalent body forces and surface tractions. We evaluate the velocity field using the Fourier-domain Green's function for an elastic half-space with surface buoyancy boundary condition. The accuracy of the proposed method is demonstrated by comparisons with finite-element simulations of viscoelastic relaxation following strike-slip and dip-slip ruptures for linear and power-law rheologies. We also present comparisons with analytic solutions for afterslip driven by coseismic stress changes. Finally, we demonstrate that the proposed method can be used to model time-dependent poroelastic rebound by adopting a viscoelastic rheology with bulk viscosity and work hardening. The proposed method allows one to model post-seismic transients that involve multiple mechanisms (afterslip, poroelastic rebound, ductile flow) with an account for the effects of gravity, non-linear rheologies and arbitrary spatial variations in inelastic properties of rocks (e.g. the effective viscosity, rate-and-state frictional parameters and poroelastic properties). [source] A structural model for the seismicity of the Arudy (1980) epicentral area (Western Pyrenees, France)GEOPHYSICAL JOURNAL INTERNATIONAL, Issue 1 2007Noalwenn Dubos-Sallée SUMMARY The Western Pyrenees presents a diffuse and moderate (M, 5.7) instrumental seismicity. It nevertheless historically suffered from strong earthquakes (I = IX MSK). The seismic sources of these events are not yet clearly identified. We focus on the Arudy (1980) epicentral area (M= 5.1) and propose here the reactivation of early Cretaceous normal faults of the Iberian margin as a potential source. The late Cretaceous inversion of this basin, first in a left-lateral strike-slip mode and then in a more frontal convergence, resulted in a pop-up geometry. This flower structure attests of the presence of a deep crustal discontinuity. The present-day geodynamic arrangement suggests that this accident is reactivated in a right lateral mode. This reactivation leads to a strain partitioning between the deep discontinuity that accommodates the lateral component of the motion and shallow thrusts, rooted on this discontinuity. These thrusts accommodate the shortening component of the strain. The distribution of the instrumental seismicity fits well the structural model of the Arudy basin. Whatever the compressive regional context, the structural behaviour of the system explains too the extensive stress tensor determined for the Arudy crisis if we interpret it in terms of strain ellipsoid. Indeed numerical modelling has shown that this concomitant activity of strike-slip and thrust faulting results in an extensive component that can rise 50 per cent of the finite strain. We identify too a 25,30 km long potential seismic source for the Arudy area. The size of the structure and its potential reactivation in a strike-slip mode suggest that a maximum earthquake magnitude of ,6.5 could be expected. The extrapolation of this model at the scale of the Western Pyrenees allows to propose other potential sources for major regional historical earthquakes. [source] Inversion of earthquake focal mechanisms to obtain the seismotectonic stress IV,a new method free of choice among nodal planesGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 3 2002Jacques Angelier Summary A new method is presented, to obtain the stress state that best accounts for a set of double couple focal mechanisms of earthquakes. This method is based on the slip shear stress component (SSSC) criterion. The sum of the SSSC values is maximized as a function of four unknowns that describe the reduced stress tensor, including the orientations of the principal stress axes and the ratio between the principal stress differences. This new method combines two advantages. First, no choice between the nodal planes of each focal mechanism is needed, because of the intrinsic properties of the SSSC. Secondly, the runtime is negligible regardless of the size of the data set, because the inverse problem is solved by analytical means so that the numerical aspects are reduced to a minimum. For these reasons, the SSSC-based inversion is easily included in a variety of processes for separating or refining the data. A typical set of focal mechanisms of earthquakes in Taiwan is processed to illustrate the application and potential of the new method. [source] On the capillary stress tensor in wet granular materialsINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 10 2009L. Scholtès Abstract This paper presents a micromechanical study of unsaturated granular media in the pendular regime, based on numerical experiments using the discrete element method, compared with a microstructural elastoplastic model. Water effects are taken into account by adding capillary menisci at contacts and their consequences in terms of force and water volume are studied. Simulations of triaxial compression tests are used to investigate both macro and micro-effects of a partial saturation. The results provided by the two methods appear to be in good agreement, reproducing the major trends of a partially saturated granular assembly, such as the increase in the shear strength and the hardening with suction. Moreover, a capillary stress tensor is exhibited from capillary forces by using homogenization techniques. Both macroscopic and microscopic considerations emphasize an induced anisotropy of the capillary stress tensor in relation with the pore fluid distribution inside the material. Insofar as the tensorial nature of this fluid fabric implies shear effects on the solid phase associated with suction, a comparison has been made with the standard equivalent pore pressure assumption. It is shown that water effects induce microstructural phenomena that cannot be considered at the macro level, particularly when dealing with material history. Thus, the study points out that unsaturated soil stress definitions should include, besides the macroscopic stresses such as the total stress, the microscopic interparticle stresses such as the ones resulting from capillary forces, in order to interpret more precisely the implications of the pore fluid on the mechanical behaviour of granular materials. Copyright © 2009 John Wiley & Sons, Ltd. [source] Analysis of the solid phase stress tensor in multiphase porous mediaINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 4 2007William G. Gray Abstract Conservation equations for mass, momentum, energy, and entropy are formulated for the phases and interfaces of a three-phase system consisting of a solid and two immiscible fluids. The microscale equations are averaged to the macroscale by integration over a representative elementary volume. Thermodynamic statements for each of the phases and interface entities are also formulated at the microscale and then averaged to the macroscale. This departure from most uses of thermodynamics in macroscale analysis ensures consistency between models and parameters at the two scales. The expressions for the macroscale rates of change of internal energy are obtained by differentiating the derived forms for energy and making use of averaging theorems. These thermodynamic expressions, along with the conservation equations, serve as constraints on the entropy inequality. A linearization of the resulting equations is employed to investigate the theoretical origins of the Biot coefficient that relates the hydrostatic part of the total stress tensor to the normal force applied at the solid surface by the pore fluids. The results here are placed in the context of other formulations and expressions that appear in the literature. Copyright © 2006 John Wiley & Sons, Ltd. [source] Shearing flows of a dry granular material,hypoplastic constitutive theory and numerical simulationsINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 14 2006Chung Fang Abstract In the present study, the Goodman,Cowin theory is extended to incorporate plastic features to construct an elasto-visco-plastic constitutive model for flowing dry granular materials. A thermodynamic analysis, based on the Müller,Liu entropy principle, is performed to derive the equilibrium expressions of the constitutive variables. Non-equilibrium responses are proposed by use of a quasi-linear theory, in particular a hypoplastic-type relation is introduced to model the internal friction and plastic effects. It is illustrated that the Goodman,Cowin theory can appropriately be extended to include frictional effects into the evolution equation of the volume fraction (i.e. the so-called balance of equilibrated force) and the equilibrium expression of the Cauchy stress tensor. The implemented model is applied to investigate conventional steady isothermal granular flows with incompressible grains, namely simple plane shear, inclined gravity-driven and vertical channel-flows, respectively. Numerical results show that the hypoplastic effect plays a significant role in the behaviour of a flowing granular material. The obtained profiles of the velocity and the volume fraction with hypoplastic features are usually sharper and the shear-thinning effect is more significant than that without such plastic effects. This points at the possible wide applicability of the present model in the fields of granular materials and soil mechanics. In addition, the present paper also provides a framework for a possible extension of the hypoplastic theories which can be further undertaken. Copyright © 2006 John Wiley & Sons, Ltd. [source] A critical state model for sands dependent on stress and densityINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 4 2004Y.P. Yao Abstract An elastoplastic model for sands is presented in this paper, which can describe stress,strain behaviour dependent on mean effective stress level and void ratio. The main features of the proposed model are: (a) a new state parameter, which is dependent on the initial void ratio and initial mean stress, is proposed and applied to the yield function in order to predict the plastic deformation for very loose sands; and (b) another new state parameter, which is used to determine the peak strength and describe the critical state behaviour of sands during shearing, is proposed in order to predict simply negative/positive dilatancy and the hardening/softening behaviour of medium or dense sands. In addition, the proposed model can also predict the stress,strain behaviour of sands under three-dimensional stress conditions by using a transformed stress tensor instead of ordinary stress tensor. Copyright © 2004 John Wiley & Sons, Ltd. [source] Influence of particle shape and angularity on the behaviour of granular materials: a numerical analysisINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 14 2003C. Nouguier-Lehon Abstract This paper analyses the influence of grain shape and angularity on the behaviour of granular materials from a two-dimensional analysis by means of a discrete element method (Contact Dynamics). Different shapes of grains have been studied (circular, isotropic polygonal and elongated polygonal shapes) as well as different initial states (density) and directions of loading with respect to the initial fabric. Simulations of biaxial tests clearly show that the behaviour of samples with isotropic particles can be dissociated from that of samples with anisotropic particles. Indeed, for isotropic particles, angularity just tends to strengthen the behaviour of samples and slow down either local or global phenomena. One of the main results concerns the existence of a critical state for isotropic grains characterized by an angle of friction at the critical state, a critical void ratio and also a critical anisotropy. This critical state seems meaningless for elongated grains and the behaviour of samples generated with such particles is highly dependent on the direction of loading with respect to the initial fabric. The study of local variables related to fabric and particle orientation gives more information. In particular, the coincidence of the principal axes of the fabric tensor with those of the stress tensor is sudden for isotropic particles. On the contrary, this process is gradually initiated for elongated particles. Copyright © 2003 John Wiley & Sons, Ltd. [source] Multiscale modeling of impact on heterogeneous viscoelastic solids containing evolving microcracksINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2010Flavio V. Souza Abstract Multiscale computational techniques play a major role in solving problems related to viscoelastic composites due to the complexities inherent to these materials. In this paper, a numerical procedure for multiscale modeling of impact on heterogeneous viscoelastic solids containing evolving microcracks is proposed in which the (global scale) homogenized viscoelastic incremental constitutive equations have the same form as the local-scale viscoelastic incremental constitutive equations, but the homogenized tangent constitutive tensor and the homogenized incremental history-dependent stress tensor at the global scale depend on the amount of damage accumulated at the local scale. Furthermore, the developed technique allows the computation of the full anisotropic incremental constitutive tensor of viscoelastic solids containing evolving cracks (and other kinds of heterogeneities) by solving the micromechanical problem only once at each material point and each time step. The procedure is basically developed by relating the local-scale displacement field to the global-scale strain tensor and using first-order homogenization techniques. The finite element formulation is developed and some example problems are presented in order to verify the approach and demonstrate the model capabilities. Copyright © 2009 John Wiley & Sons, Ltd. [source] Energy,momentum consistent finite element discretization of dynamic finite viscoelasticityINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 11 2010M. Groß Abstract This paper is concerned with energy,momentum consistent time discretizations of dynamic finite viscoelasticity. Energy consistency means that the total energy is conserved or dissipated by the fully discretized system in agreement with the laws of thermodynamics. The discretization is energy,momentum consistent if also momentum maps are conserved when group motions are superimposed to deformations. The performed approximation is based on a three-field formulation, in which the deformation field, the velocity field and a strain-like viscous internal variable field are treated as independent quantities. The new non-linear viscous evolution equation satisfies a non-negative viscous dissipation not only in the continuous case, but also in the fully discretized system. The initial boundary value problem is discretized by using finite elements in space and time. Thereby, the temporal approximation is performed prior to the spatial approximation in order to preserve the stress objectivity for finite rotation increments (incremental objectivity). Although the present approach makes possible to design schemes of arbitrary order, the focus is on finite elements relying on linear Lagrange polynomials for the sake of clearness. The discrete energy,momentum consistency is based on the collocation property and an enhanced second Piola,Kirchhoff stress tensor. The obtained coupled non-linear algebraic equations are consistently linearized. The corresponding iterative solution procedure is associated with newly proposed convergence criteria, which take the discrete energy consistency into account. The iterative solution procedure is therefore not complicated by different scalings in the independent variables, since the motion of the element is taken into account for solving the viscous evolution equation. Representative numerical simulations with various boundary conditions show the superior stability of the new time-integration algorithm in comparison with the ordinary midpoint rule. Both the quasi-rigid deformations during a free flight, and large deformations arising in a dynamic tensile test are considered. Copyright © 2009 John Wiley & Sons, Ltd. [source] A uniform nodal strain tetrahedron with isochoric stabilizationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2009M. W. Gee Abstract A stabilized node-based uniform strain tetrahedral element is presented and analyzed for finite deformation elasticity. The element is based on linear interpolation of a classical displacement-based tetrahedral element formulation but applies nodal averaging of the deformation gradient to improve mechanical behavior, especially in the regime of near-incompressibility where classical linear tetrahedral elements perform very poorly. This uniform strain approach adopted here exhibits spurious modes as has been previously reported in the literature. We present a new type of stabilization exploiting the circumstance that the instability in the formulation is related to the isochoric strain energy contribution only and we therefore present a stabilization based on an isochoric,volumetric splitting of the stress tensor. We demonstrate that by stabilizing the isochoric energy contributions only, reintroduction of volumetric locking through the stabilization can be avoided. The isochoric,volumetric splitting can be applied for all types of materials with only minor restrictions and leads to a formulation that demonstrates impressive performance in examples provided. Copyright © 2008 John Wiley & Sons, Ltd. [source] A second-order homogenization procedure for multi-scale analysis based on micropolar kinematicsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 12 2007Ragnar Larsson Abstract The paper presents a higher order homogenization scheme based on non-linear micropolar kinematics representing the macroscopic variation within a representative volume element (RVE) of the material. On the microstructural level the micro,macro kinematical coupling is introduced as a second-order Taylor series expansion of the macro displacement field, and the microstructural displacement variation is gathered in a fluctuation term. This approach relates strongly to second gradient continuum formulations, presented by, e.g. Kouznetsova et al. (Int. J. Numer. Meth. Engng 2002; 54:1235,1260), thus establishing a link between second gradient and micropolar theories. The major difference of the present approach as compared to second gradient formulations is that an additional constraint is placed on the higher order deformation gradient in terms of the micropolar stretch. The driving vehicle for the derivation of the homogenized macroscopic stress measures is the Hill,Mandel condition, postulating the equivalence of microscopic and macroscopic (homogenized) virtual work. Thereby, the resulting homogenization procedure yields not only a stress tensor, conjugated to the micropolar stretch tensor, but also the couple stress tensor, conjugated to the micropolar curvature tensor. The paper is concluded by a couple of numerical examples demonstrating the size effects imposed by the homogenization of stresses based on the micropolar kinematics. Copyright © 2006 John Wiley & Sons, Ltd. [source] Remarks on tension instability of Eulerian and Lagrangian corrected smooth particle hydrodynamics (CSPH) methodsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 11 2001Javier Bonet Abstract The paper discusses the problem of tension instability of particle-based methods such as smooth particle hydrodynamics (SPH) or corrected SPH (CSPH). It is shown that tension instability is a property of a continuum where the stress tensor is isotropic and the value of the pressure is a function of the density or volume ratio. The paper will show that, for this material model, the non-linear continuum equations fail to satisfy the stability condition in the presence of tension. Consequently, any discretization of this continuum will result in negative eigenvalues in the tangent stiffness matrix that will lead to instabilities in the time integration process. An important exception is the 1-D case where the continuum becomes stable but SPH or CSPH can still exhibit negative eigenvalues. The paper will show that these negative eigenvalues can be eliminated if a Lagrangian formulation is used whereby all derivatives are referred to a fixed reference configuration. The resulting formulation maintains the momentum preservation properties of its Eulerian equivalent. Finally a simple 1-D wave propagation example will be used to demonstrate that a stable solution can be obtained using Lagrangian CSPH without the need for any artificial viscosity. Copyright © 2001 John Wiley & Sons, Ltd. [source] Large eddy simulations of turbulent swirling flows in a dump combustor: a sensitivity studyINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 2 2005P. Wang Abstract Large eddy simulations (LES) of confined turbulent swirling flows in a model dump combustor are carried out. The simulations are based on a high-order finite difference method on a Cartesian grid, with the sub-grid scale stress tensor modelled using a scale-similarity model. The aims of this work are to study the physics of the flow and to evaluate the performance of LES method for simulation of the major features of turbulent swirling flows,the vortex breakdown, the highly anisotropic and fast-decaying turbulence structure. Influences of inflow/outflow conditions, combustor geometry, inlet swirl profile and Reynolds numbers on the vortex breakdown and turbulence structures are investigated. At very high swirl levels, the influence of the outflow conditions and the outlet geometry is fairly significant, not only at downstream near the outlet, but also at far upstream. At low Reynolds numbers, the onset of vortex breakdown is fairly sensitive to the change of Reynolds number; however, at high Reynolds numbers it is rather insensitive to the Reynolds number. Comparisons of LES results with experimental data are made. The LES results are shown to be in reasonably good agreement with the experimental data if appropriate inflow and outflow boundary conditions are imposed. Copyright © 2004 John Wiley & Sons, Ltd. [source] On the Lp,Lq maximal regularity for Stokes equations with Robin boundary condition in a bounded domainMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 3 2007Rieko Shimada Abstract We obtain the Lp,Lq maximal regularity of the Stokes equations with Robin boundary condition in a bounded domain in ,n (n,2). The Robin condition consists of two conditions: v , u=0 and ,u+,(T(u, p)v , ,T(u, p)v, v,v)=h on the boundary of the domain with ,, ,,0 and ,+,=1, where u and p denote a velocity vector and a pressure, T(u, p) the stress tensor for the Stokes flow and v the unit outer normal to the boundary of the domain. It presents the slip condition when ,=1 and non-slip one when ,=1, respectively. The slip condition is appropriate for problems that involve free boundaries. Copyright © 2006 John Wiley & Sons, Ltd. [source] Asymptotic analysis of elastic curved rodsMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 1 2007Rostislav Vodák Abstract We consider a sequence of curved rods which consist of isotropic material and which are clamped on the lower base or on both bases. We study the asymptotic behaviour of the stress tensor and displacement under the assumptions of linearized elasticity when the cross-sectional diameter of the rods tends to zero and the body force is given in the particular form. The analysis covers the case of a non-smooth limit line of centroids. We show how the body force and the choice of the approximating curved rods can affect the strong convergence and the limit form of the stress tensor for the curved rods clamped on both bases. Copyright © 2006 John Wiley & Sons, Ltd. [source] Testing the locality of transport in self-gravitating accretion discsMONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 2 2004G. Lodato ABSTRACT In this paper, we examine the issue of characterizing the transport associated with gravitational instabilities in relatively cold discs, discussing in particular the conditions under which it can be described within a local, viscous framework. We present the results of global, three-dimensional, smoothed particle hydrodynamics simulations of self-gravitating accretion discs, in which the disc is cooled using a simple parametrization for the cooling function. Our simulations show that the disc settles in a ,self-regulated' state, where the axisymmetric stability parameter Q, 1 and where transport and energy dissipation are dominated by self-gravity. We have computed the gravitational stress tensor and compared our results with expectations based on a local theory of transport. We find that, as long as the disc mass is smaller than 0.25M, and the aspect ratio H/R, 0.1, transport is determined locally, thus allowing for a viscous treatment of the disc evolution. [source] Lagrangian simulation of wind transport in the urban environmentTHE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 643 2009Dr J. D. Wilson Abstract Fluid element trajectories are computed in inhomogeneous urban-like flows, the needed wind statistics being furnished by a Reynolds-averaged Navier,Stokes (RANS) model that explicitly resolves obstacles. Performance is assessed against pre-existing measurements in flows ranging from the horizontally uniform atmospheric surface layer (no buildings), through regular obstacle arrays in a water-channel wall shear layer, to full-scale observations at street scale in an urban core (the Oklahoma City tracer dispersion experiment Joint Urban 2003). Agreement with observations is encouraging, e.g. for an Oklahoma City tracer trial in which sixteen detectors reported non-zero concentration, modelled concentration lies within a factor of two of the corresponding observation in nine cases (FAC2 = 56%). Although forward and backward simulations offer comparable fidelity relative to the data, interestingly they differ (by a margin far exceeding statistical uncertainty) wherever trajectories from source to receptor traverse regions of abrupt change in the Reynolds stress tensor. Copyright © 2009 Royal Meteorological Society [source] Charge density and electrostatic potential analyses in paracetamolACTA CRYSTALLOGRAPHICA SECTION B, Issue 3 2009Nouzha Bouhmaida The electron density of monoclinic paracetamol was derived from high-resolution X-ray diffraction at 100,K. The Hansen,Coppens multipole model was used to refine the experimental electron density. The topologies of the electron density and the electrostatic potential were carefully analyzed. Numerical and analytical procedures were used to derive the charges integrated over the atomic basins. The highest charge magnitude (,1.2,e) was found for the N atom of the paracetamol molecule, which is in agreement with the observed nucleophilic attack occurring in the biological media. The electric field generated by the paracetamol molecule was used to calculate the atomic charges using the divergence theorem. This was simultaneously applied to estimate the total electrostatic force exerted on each atom of the molecule by using the Maxwell stress tensor. The interaction electrostatic energy of dimers of paracetamol in the crystal lattice was also estimated. [source] Tensor visualizations in computational geomechanicsINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 10 2002Boris Jeremi Abstract We present a novel technique for visualizing tensors in three dimensional (3D) space. Of particular interest is the visualization of stress tensors resulting from 3D numerical simulations in computational geomechanics. To this end we present three different approaches to visualizing tensors in 3D space, namely hedgehogs, hyperstreamlines and hyperstreamsurfaces. We also present a number of examples related to stress distributions in 3D solids subjected to single and load couples. In addition, we present stress visualizations resulting from single-pile and pile-group computations. The main objective of this work is to investigate various techniques for visualizing general Cartesian tensors of rank 2 and it's application to geomechanics problems. Copyright © 2002 John Wiley & Sons, Ltd. [source] Elastic strain and stress determination by Rietveld refinement: generalized treatment for textured polycrystals for all Laue classesJOURNAL OF APPLIED CRYSTALLOGRAPHY, Issue 2 2001N. C. Popa A novel approach to model diffraction line shifts caused by elastic residual or applied stresses in textured polycrystals is proposed. The model yields the complete strain and stress tensors as a function of crystallite orientation, as well as the average values of the macroscopic strain and stress tensors. It is particularly suitable for implementation in Rietveld refinement programs. The requirements on refinable parameters for all crystal Laue classes are given. The effects of sample symmetry are also included and the conditions for strain invariance to both the sample symmetries (texture and stress/strain) are discussed. [source] Flow of particles suspended in a sheared viscous fluid: Effects of finite inertia and inelastic collisionsAICHE JOURNAL, Issue 10 2010Micheline Abbas Abstract We investigate in this article the macroscopic behavior of sheared suspensions of spherical particles. The effects of the fluid inertia, the Brownian diffusion, and the gravity are neglected. We highlight the influence of the solid-phase inertia on the macroscopic behavior of the suspension, considering moderate to high Stokes numbers. Typically, this study is concerned with solid particles O (100 ,m) suspended in a gas with a concentration varying from 5% to 30%. A hard-sphere collision model (with elastic or inelasic rebounds) coupled with the particle Lagrangian tracking is used to simulate the suspension dynamics in an unbounded periodic domain. We first consider the behavior of the suspension with perfect elastic collisions. The suspension properties reveal a strong dependence on the particle inertia and concentration. Increasing the Stokes number from 1 to 10 induces an enhancement of the particle agitation by three orders of magnitude and an evolution of the probability density function of the fluctuating velocity from a highly peaked (close to the Dirac function) to a Maxwellian shape. This sharp transition in the velocity distribution function is related to the time scale which controls the overall dynamics of the suspension flow. The particle relaxation (resp. collision) time scale dominates the particulate phase behavior in the weakly (resp. highly) agitated suspensions. The numerical results are compared with the prediction of two statistical models based on the kinetic theory for granular flows adapted to moderately inertial regimes. The suspensions have a Newtonian behavior when they are highly agitated similarly to rapid granular flows. However, the stress tensors are highly anisotropic in weakly agitated suspensions as a difference of normal stresses arises. Finally, we discuss the effect of energy dissipation due to inelastic collisions on the statistical quantities. We also tested the influence of a simple modeling of local hydrodynamic interactions during the collision by using a restitution coefficient which depends on the local impact velocities. © 2010 American Institute of Chemical Engineers AIChE J, 2010 [source] Polarized Raman scattering studies of nonpolar a -plane GaN films grown on r -plane sapphire substrates by MOCVDPHYSICA STATUS SOLIDI (A) APPLICATIONS AND MATERIALS SCIENCE, Issue 15 2006Haiyong Gao Abstract Nonpolar (110) a -plane GaN thin films were grown on r -plane (102) sapphire substrates by low-pressure metal organic chemical vapor deposition (MOCVD). The stress characteristics of the a -plane GaN films were investigated by means of polarized Raman scattering spectra in backscattering configurations. The experimental results show that there are strong anisotropic in-plane stresses within the epitaxial a -plane GaN films by calculating the corresponding stress tensors. The temperature dependence of Raman scattering spectra was studied in the range from 100 K to 550 K. The measurements reveal that the Raman phonon frequencies decrease with increasing temperature. The temperature at which nonpolar a -plane GaN films are strain free is discussed. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] | ||||||||||||||||||||||