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Deformation Field (deformation + field)

Distribution by Scientific Domains

Earth and Environmental Science	45%
Engineering	27%

Selected Abstracts

Deformation Field around the Stress Induced Crack Area in Sandstone by the Digital Speckle Correlation Method

ACTA GEOLOGICA SINICA (ENGLISH EDITION), Issue 3 2009
Yonghong ZHAO
Abstract: The deformation field around sub-cracks was calculated using the digital speckle correlation method. First, the uni-axial compression tests on sandstone samples containing a pre-fabricated fracture were made. Photomicrographs showing the characteristics of the sub-crack development were taken using a scanning electron microscope (SEM). From these photomicrographs, the real-time images showing the initiation, growth and coalescence of sub-cracks and micro-cracks in the sandstone specimens were obtained and the effects of loading level as well as grain boundaries on the development of cracks were analyzed. Second, the intensity images of the sandstone specimen surface were captured from the observations of the SEM corresponding to different loading levels. Then correlation computation was carried out for the sequential pairs of intensity images to evaluate the displacement components, as well as the strain field. The results show that the deformation varies in different areas separated by sub-cracks during rock damage processes. [source]

Direct Visualization of Deformation in Volumes

COMPUTER GRAPHICS FORUM, Issue 3 2009
Stef Busking
Abstract Deformation is a topic of interest in many disciplines. In particular in medical research, deformations of surfaces and even entire volumetric structures are of interest. Clear visualization of such deformations can lead to important insight into growth processes and progression of disease. We present new techniques for direct focus+context visualization of deformation fields representing transformations between pairs of volumetric datasets. Typically, such fields are computed by performing a non-rigid registration between two data volumes. Our visualization is based on direct volume rendering and uses the GPU to compute and interactively visualize features of these deformation fields in real-time. We integrate visualization of the deformation field with visualization of the scalar volume affected by the deformations. Furthermore, we present a novel use of texturing in volume rendered visualizations to show additional properties of the vector field on surfaces in the volume. [source]

Multiscale estimation of GPS velocity fields

GEOPHYSICAL JOURNAL INTERNATIONAL, Issue 2 2009
Carl Tape
SUMMARY We present a spherical wavelet-based multiscale approach for estimating a spatial velocity field on the sphere from a set of irregularly spaced geodetic displacement observations. Because the adopted spherical wavelets are analytically differentiable, spatial gradient tensor quantities such as dilatation rate, strain rate and rotation rate can be directly computed using the same coefficients. In a series of synthetic and real examples, we illustrate the benefit of the multiscale approach, in particular, the inherent ability of the method to localize a given deformation field in space and scale as well as to detect outliers in the set of observations. This approach has the added benefit of being able to locally match the smallest resolved process to the local spatial density of observations, thereby both maximizing the amount of derived information while also allowing the comparison of derived quantities at the same scale but in different regions. We also consider the vertical component of the velocity field in our synthetic and real examples, showing that in some cases the spatial gradients of the vertical velocity field may constitute a significant part of the deformation. This formulation may be easily applied either regionally or globally and is ideally suited as the spatial parametrization used in any automatic time-dependent geodetic transient detector. [source]

Surface deformation due to loading of a layered elastic half-space: a rapid numerical kernel based on a circular loading element

GEOPHYSICAL JOURNAL INTERNATIONAL, Issue 1 2007
E. Pan
SUMMARY This study is motivated by a desire to develop a fast numerical algorithm for computing the surface deformation field induced by surface pressure loading on a layered, isotropic, elastic half-space. The approach that we pursue here is based on a circular loading element. That is, an arbitrary surface pressure field applied within a finite surface domain will be represented by a large number of circular loading elements, all with the same radius, in which the applied downwards pressure (normal stress) is piecewise uniform: that is, the load within each individual circle is laterally uniform. The key practical requirement associated with this approach is that we need to be able to solve for the displacement field due to a single circular load, at very large numbers of points (or ,stations'), at very low computational cost. This elemental problem is axisymmetric, and so the displacement vector field consists of radial and vertical components both of which are functions only of the radial coordinate r. We achieve high computational speeds using a novel two-stage approach that we call the sparse evaluation and massive interpolation (SEMI) method. First, we use a high accuracy but computationally expensive method to compute the displacement vectors at a limited number of r values (called control points or knots), and then we use a variety of fast interpolation methods to determine the displacements at much larger numbers of intervening points. The accurate solutions achieved at the control points are framed in terms of cylindrical vector functions, Hankel transforms and propagator matrices. Adaptive Gauss quadrature is used to handle the oscillatory nature of the integrands in an optimal manner. To extend these exact solutions via interpolation we divide the r -axis into three zones, and employ a different interpolation algorithm in each zone. The magnitude of the errors associated with the interpolation is controlled by the number, M, of control points. For M= 54, the maximum RMS relative error associated with the SEMI method is less than 0.2 per cent, and it is possible to evaluate the displacement field at 100 000 stations about 1200 times faster than if the direct (exact) solution was evaluated at each station; for M= 99 which corresponds to a maximum RMS relative error less than 0.03 per cent, the SEMI method is about 700 times faster than the direct solution. [source]

Contemporary kinematics of the southern Aegean and the Mediterranean Ridge

GEOPHYSICAL JOURNAL INTERNATIONAL, Issue 3 2004
Corné Kreemer
SUMMARY This study focuses on the kinematics of the southern Aegean and the Mediterranean Ridge (MR). A quantification of the deformation of the MR is essential for both evaluating physical models of accretionary wedges in general and for obtaining a self-consistent model of the surface deformation over the entire Nubia,Eurasia (NU,EU) plate boundary zone in the eastern Mediterranean. Previous kinematic studies have not properly considered the deformation field south of the Hellenic arc. Although this study focuses on the deformation field of the MR, we also discuss the kinematics of the southern Aegean, because the geometry and movement of the Hellenic arc determine to a large extent the kinematic boundary conditions for kinematic studies of the MR. We calculate a continuous velocity and strain rate field by interpolating model velocities that are fitted in a least-squares sense to published Global Positioning System (GPS) velocities. In the interpolation, we use information from a detailed data set of onshore and offshore active faulting to place constraints on the expected style and direction of the model strain rate field. In addition, we use the orientations of tracks left by seamounts travelling into the wedge to further constrain the offshore deformation pattern. Our model results highlight the presence of active shear partitioning within the Mediterranean ridge. High compressional strain rates between the ridge crest and the deformation front accommodate approximately 60,70 per cent of the total motion over the wedge, and the outward growth rate of the frontal thrust is , 4 mm yr,1. Strain partitioning within the wedge leads to 19,23 mm yr,1 of dextral motion at the wedge,backstop contact of the western MR, whereas the Pliny and Strabo trenches in the eastern MR accommodate 21,23 mm yr,1 of sinistral motion. The backstop of the western MR is kinematically part of the southern Aegean, which moves as a single block [the Aegean block (AE)] at 33,34 mm yr,1 in the direction of S24°W ± 1° towards stable Nubia (NU). Our model confirms that there is a clear divergence between the western and eastern Hellenic arc and we argue for a causal relation between the outward motion of the arc and the gradient in the regional geoid anomaly. Our results suggest that a significant driving source of the surface velocity field lies south of the Hellenic arc and only for the southeastern Aegean could there be some effect as a result of gravitational collapse associated with density differences within the overriding plate. [source]

Energy,momentum consistent finite element discretization of dynamic finite viscoelasticity

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 11 2010
M. 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]

Modeling three-dimensional crack propagation,A comparison of crack path tracking strategies

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 9 2008
P. Jäger
Abstract The development of a new finite element technique for the simulation of discontinuous failure phenomena in three dimensions is the key objective of this study. In contrast to the widely used extended finite element technique, we apply a purely deformation-based strategy based on an independent interpolation of the deformation field on both sides of the discontinuity. This method has been applied successfully for two-dimensional crack propagation problems in the past. However, when it comes to three-dimensional failure phenomena, it faces the same difficulties as the extended finite element method. Unlike in two dimensions, the characterization for the three-dimensional failure surface is non-unique and the tracking of the discrete crack can be performed in several conceptually different ways. In this work, we review the four most common three-dimensional crack tracking strategies. We perform a systematic comparison in terms of standard algorithmic quality measures such as mesh independency, efficiency, robustness, stability and computational cost. Moreover, we discuss more specific issues such as crack path continuity and integratability in commercial finite element packages. The features of the suggested crack tracking algorithms will be elaborated by means of characteristic benchmark problems in failure analysis. Copyright © 2008 John Wiley & Sons, Ltd. [source]

Analysis of SR thermal load studied by FEA

PHYSICA STATUS SOLIDI (A) APPLICATIONS AND MATERIALS SCIENCE, Issue 8 2007

Abstract This work deals with analysis of the thermal effects and inherent mechanical deformations under absorption of the X-ray beam heat. The work is motivated by recent research concentrated on the development of optics for high-flux synchrotron radiation sources. We present the analyses of the static thermal load effects on the surface deformation field for a monocrystalline silicon target, which is the basic material for crystal X-ray optics. The surface and bulk thermal load induces the gradient of temperature and mechanical deformations of the target that are affecting the reflection and diffraction properties of the target. The paper presents the finite-element analyses (FEA) and simulation results of mechanical deformation of flat and slotted silicon targets. The hints for improved target geometry and physical limits for an actual cooling system can be obtained from the presented analyses. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

Local and non-local ductile damage and failure modelling at large deformation with applications to engineering

PROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2003
Bob Svendsen Prof. Dr.
The numerical analysis of ductile damage and failure in engineering materials is often based on the micromechanical model of Gurson [1]. Numerical studies in the context of the finite-element method demonstrate that, as with other such types of local damage models, the numerical simulation of the initiation and propagation of damage zones is strongly mesh-dependent and thus unreliable. The numerical problems concern the global load-displacement response as well as the onset, size and orientation of damage zones. From a mathematical point of view, this problem is caused by the loss of ellipticity of the set of partial di.erential equations determining the (rate of) deformation field. One possible way to overcome these problems with and shortcomings of the local modelling is the application of so-called non-local damage models. In particular, these are based on the introduction of a gradient type evolution equation of the damage variable regarding the spatial distribution of damage. In this work, we investigate the (material) stability behaviour of local Gurson-based damage modelling and a gradient-extension of this modelling at large deformation in order to be able to model the width and other physical aspects of the localization of the damage and failure process in metallic materials. [source]

Entropy sources in a dynamical core atmosphere model

THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 614 2006
Tim Woollings
Abstract Numerical atmosphere models are not generally constructed to ensure accurate treatment of entropy, but little is known about the significance of the resulting errors. This paper examines the entropy changes during a baroclinic wave simulation in a typical dynamical core model, specifically a ,-coordinate spectral model, which includes scale-selective dissipation terms in the form of a numerical hyperdiffusion. Lagrangian entropy conservation is found to be badly represented, with numerical transport errors resulting in cross-isentrope mass fluxes which are of the same size as those associated with some real diabatic processes. In a global average, the total entropy increases at a rate of just 0.5 mW m,2K,1. This, however, is seen to be the residual of two opposing numerical effects which are several times larger, namely the destruction of entropy by dispersion and Gibbs errors, and its creation by diffusion. The entropy generated by diffusion is shown to be remarkably insensitive to the details of the diffusion scheme. This leads us to hypothesize that the entropy source from diffusion is determined by the rate at which small scales are generated by the deformation field of the large-scale flow so that, while the diffusion mechanism is clearly unrealistic, the magnitude of the entropy source is, we argue, representative of that generated by physical dissipative processes in the real atmosphere. Even in this simple model it is not possible to quantify precisely the different entropy sources and sinks which combine to give the overall entropy change. However, we can say that if there is a systematic spurious entropy source in this model, then it is small, i.e. of size 0.5 mW m,2K,1 or smaller. Copyright © 2006 Royal Meteorological Society [source]