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Boundary Surface (boundary + surface)
Selected AbstractsFree fermions violate the area law for entanglement entropyFORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 7-9 2010R.C. Helling Abstract We show that the entanglement entropy associated to a region grows faster than the area of its boundary surface. This is done by proving a special case of a conjecture due to Widom that yields a surprisingly simple expression for the leading behaviour of the entanglement entropy. [source] Numerical investigation of the effectiveness of a bored pile wall for the minimisation of settlement resulting from tunnel driving.GEOMECHANICS AND TUNNELLING, Issue 6 2009Numerische Untersuchung der Wirkungsweise einer Bohrpfahlwand zur Minimierung der Setzungen infolge Tunnel Soil mechanics; Innovative procedures; Bodenmechanik; Neue Verfahren Abstract Bored pile walls can be constructed between buildings and tunnel alignments to protect sensitive buildings from settlement resulting from tunnelling. The aim of the research work presented here was to evaluate the effectiveness of such a bored pile wall with FE calculations and identify influential parameters. Two methods of predicting settlement were investigated with the programme ABAQUS: The GAP method, where the deformations of the tunnel contour are prescribed, and the stress reduction method, with which the support pressure at the tunnel contour is reduced. The ground is modelled as linear-elastic, ideal-plastic with a Mohr-Coulomb failure criterion as well as with a hypoplastic constitutive law. The contact surface between wall and ground was modelled with complete bonding as well as with a contact law with friction. The simulation results with the stress reduction method and the hypoplastic material model show the best results qualitatively. The predict settlements agree well with empirical methods and centrifuge tests from the literature. The simulations show that the effectiveness of the wall is significantly influenced by the contact properties in the boundary surface. It achieves the best protection effect when frictionless. Zur Abschirmung sensibler Gebäude vor Setzungen infolge Tunnelvortrieb können Bohrpfahlwände zwischen Gebäude und Tunneltrasse eingesetzt werden. Ziel der hier präsentierten Forschungsarbeit war es, die Wirksamkeit einer solchen Bohrpfahlwand mit FE-Berechnungen nachzuvollziehen und Einflussparameter zu identifizieren. Mit dem Programm ABAQUS wurden zwei Möglichkeiten zur Setzungsprognose untersucht: Die GAPMethode, bei der die Verschiebungen der Tunnelkontur vorgegeben werden, und die Spannungsreduktions-Methode, bei welcher der Stützdruck an der Tunnelkontur reduziert wird. Der Boden wurde als linear-elastisch, ideal-plastisch mit Grenzbedingung nach Mohr-Coulomb sowie mit einem hypoplastischen Stoffgesetz modelliert. Die Kontaktfläche zwischen Wand und Boden wurde sowohl mit vollständigem Verbund als auch mit einem Kontaktgesetz mit Reibung modelliert. Die Simulationsergebnisse mit der Spannungsreduktions-Methode und dem hypoplastischen Materialmodell zeigen die qualitativ besten Ergebnisse. Die Setzungsprognosen stimmen gut mit empirischen Ansätzen und Zentrifugenversuchen aus der Literatur überein. Die Simulationen veranschaulichen, dass die Wirksamkeit der Wand maßgeblich von den Kontakteigenschaften in der Grenzfläche beeinflusst wird. Die größte Abschirmwirkung erzielt sie bei Reibungsfreiheit. [source] Numerical studies of shear banding in interface shear tests using a new strain calculation method,INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 12 2007Jianfeng Wang Abstract Strain localization is closely associated with the stress,strain behaviour of an interphase system subject to quasi-static direct interface shear, especially after peak stress state is reached. This behaviour is important because it is closely related to deformations experienced by geotechnical composite structures. This paper presents a study using two-dimensional discrete element method (DEM) simulations on the strain localization of an idealized interphase system composed of densely packed spherical particles in contact with rough manufactured surfaces. The manufactured surface is made up of regular or irregular triangular asperities with varying slopes. A new simple method of strain calculation is used in this study to generate strain field inside a simulated direct interface shear box. This method accounts for particle rotation and captures strain localization features at high resolution. Results show that strain localization begins with the onset of non-linear stress,strain behaviour. A distinct but discontinuous shear band emerges above the rough surface just before the peak stress state, which becomes more expansive and coherent with post-peak strain softening. It is found that the shear bands developed by surfaces with smaller roughness are much thinner than those developed by surfaces with greater roughness. The maximum thickness of the intense shear zone is observed to be about 8,10 median particle diameters. The shear band orientations, which are mainly dominated by the rough boundary surface, are parallel with the zero extension direction, which are horizontally oriented. Published in 2007 by John Wiley & Sons, Ltd. [source] Identification of the boundary surface of an interstellar cloud from a measurement of the photon far-fieldMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 6 2004A. Belleni-Morante Abstract We study an inverse problem for photon transport in a host medium (e.g. an interstellar cloud), that occupies a bounded and strictly convex region ,,R3. Under the assumption that the cross-sections and the sources are known, we identify the boundary surface , = ,,(within a suitable family F of surfaces), provided that one value of the photon number density is measured at some given location far from ,. Copyright © 2004 John Wiley & Sons, Ltd. [source] Explicit solutions for the instantaneous undrained contraction of hollow cylinders and spheres in porous elastoplastic mediumINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 3 2002A. Giraud Abstract In this article we present closed-form solutions for the undrained variations in stress, pore pressure, deformation and displacement inside hollow cylinders and hollow spheres subjected to uniform mechanical pressure instantaneously applied to their external and internal boundary surfaces. The material is assumed to be a saturated porous medium obeying a Mohr,Coulomb model failure criterion, exhibiting dilatant plastic deformation according to a non-associated flow rule which accounts for isotropically strain hardening or softening. The instantaneous response of a porous medium submitted to an instantaneous loading is undrained, i.e. without any fluid mass exchange. The short-term equilibrium problem to be solved is now formally identical to a problem of elastoplasticity where the constitutive equations involve the undrained elastic moduli and particular equivalent plastic parameters. The response of the model is presented (i) for extension and compression undrained triaxial tests, and (ii) for unloading problems of hollow cylinders and spheres through the use of appropriately developed closed-form solutions. Numerical results are presented for a plastic clay stone with strain hardening and an argilite with strain softening. The effects of plastic dilation, of the strain softening law and also of geometry of the cavity on the behaviour of the porous medium have been underlined. Analytical solutions provide valuable benchmarks enabling various numerical methods in undrained conditions with a finite boundary to be verified. Copyright © 2002 John Wiley & Sons, Ltd. [source] A method for representing boundaries in discrete element modelling,part I: Geometry and contact detectionINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 12 2001M. Kremmer Abstract The discrete element method for analysis of the dynamic behaviour of discontinuous media is well established. However, its application to engineering problems is still limited to simplified representations of structural boundaries and their kinematics. In this paper a method is developed for representing three-dimensional boundaries of arbitrary geometry and for modelling the interaction between boundary objects and particles within the discrete element modelling framework. The approach, which we term the finite wall method, uses planar triangular elements to approximate the boundary surface topology. Any number of wall elements can be used to model the shape of the structure. A contact detection scheme is presented for boundary surfaces and spheres based on a series of vector projections to reduce the problem dimensionally. The algorithm employs spatial sporting to obtain the set of potential contacts between spheres and wall elements prior to contact resolution. In a further stage, all possible contact conditions including contact with surfaces, edges and corners are explicitly determined. Part I of this two-part series of papers describes the finite wall method for representation of surface geometry and fully elaborates the method for detecting and resolving contact between boundary wall elements and spheres. In Part II the finite wall method is extended to apply kinematics to linearly independent boundary objects using combinations of translational and rotational motion. An approach is developed for coupling the DEM with the FEM for the purpose of optimising the design of structures which are dynamically interacting with particulate media. Copyright © 2001 John Wiley & Sons, Ltd. [source] A method for representing boundaries in discrete element modelling,part II: KinematicsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 12 2001M. Kremmer Abstract The application of the DEM to engineering problems involving the dynamic behaviour of discontinuous media has necessitated the introduction of moving boundary surfaces. In this paper a method is presented for modelling three-dimensional moving boundary surfaces within the discrete element framework. The surfaces of boundary objects are discretized into triangular planar surfaces using the finite wall method. Wall elements are grouped and each group is associated with a single discrete boundary object which may move independently. Movement comprises any combination of translation and rotation of wall element groups, subject to a given acceleration and velocity during a calculation cycle. The scheme is explicit due to rigidity of the wall elements which are stationary fixed in position and orientation over a time step. Any in-plane velocity is handled as a contact point velocity within a calculation cycle. The kinematic conditions at each calculation cycle may be pre-defined or returned from a separate calculation of rigid body motion of the boundary object. The method provides a means for coupling sphere-based particle dynamics with rigid body dynamics and structural analysis of boundary components. Copyright © 2001 John Wiley & Sons, Ltd. [source] | ||||||||||