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Journal ArticleDOI

Finite-element modelling of elastic wave propagation and scattering within heterogeneous media

TL;DR: The quantitative agreement is found to be excellent across previously unvisited scattering regimes; it is believed that this is the first quantitative validation of its kind which provides significant support towards the existence of the transitional scattering regime and facilitates future deployment of numerical methods for these problems.
Abstract: The scattering treated here arises when elastic waves propagate within a heterogeneous medium defined by random spatial fluctuation of its elastic properties. Whereas classical analytical studies are based on lower-order scattering assumptions, numerical methods conversely present no such limitations by inherently incorporating multiple scattering. Until now, studies have typically been limited to two or one dimension, however, owing to computational constraints. This article seizes recent advances to realize a finite-element formulation that solves the three-dimensional elastodynamic scattering problem. The developed methodology enables the fundamental behaviour of scattering in terms of attenuation and dispersion to be studied. In particular, the example of elastic waves propagating within polycrystalline materials is adopted, using Voronoi tessellations to randomly generate representative models. The numerically observed scattering is compared against entirely independent but well-established analytical scattering theory. The quantitative agreement is found to be excellent across previously unvisited scattering regimes; it is believed that this is the first quantitative validation of its kind which provides significant support towards the existence of the transitional scattering regime and facilitates future deployment of numerical methods for these problems.
Citations
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Journal ArticleDOI
01 Jul 1949-Nature
TL;DR: In this article, Zener uses the term "anelasticity" to describe the properties of solids, as a result of which stress and strain are not uniquely related.
Abstract: WHEN metals are submitted to stress, the stress/swain relation is generally regarded as consisting of two parts, the elastic region and the region bfsplastiwin which a permanent set remains upon the remova of the stress. In the elastic region the absence of a permanent set does not necessarily imply that the relation between stress and strain is linear of even single-valued. Prof. Zener uses the term ‘anelasticity’ to describe the properties of solids, as a result of which stress and strain are not uniquely related. Examples are the elastic after-effect, the dependence of elastic constants on the method of measurement, and the dissipation of energy during vibration, which is often referred to as the damping capacity or internal friction of a solid. These effects have aroused much interest in recent years, largely owing to Prof. Zener's own work, and a good book on the subject is much to be desired. Elasticity and Anelasticity of Metals By Clarence Zener. Pp. x + 170. (Chicago: University of Chicago Press, London: Cambridge University Press, 1948.) 4 dollars.

235 citations

Journal ArticleDOI
TL;DR: This topical review of micromagnetic modeling gives an overview of this modeling approach and shows how it has contributed to the forefront of current magnetism research.
Abstract: In the last twenty years, numerical modeling has become an indispensable part of magnetism research. It has become a standard tool for both the exploration of new systems and for the interpretation of experimental data. In the last five years, the capabilities of micromagnetic modeling have dramatically increased due to the deployment of graphical processing units (GPU), which have sped up calculations to a factor of 200. This has enabled many studies which were previously unfeasible. In this topical review, we give an overview of this modeling approach and show how it has contributed to the forefront of current magnetism research.

106 citations

Journal ArticleDOI
TL;DR: Grain size distribution is discussed within the context of previous attenuation models valid for arbitrary crystallite symmetries and is anticipated to play an important role in microstructural characterization research associated with ultrasonic scattering.
Abstract: Elastic wave scattering at grain boundaries in polycrystalline media can be quantified to determine microstructural properties. The amplitude drop observed for coherent wave propagation (attenuation) as well as diffuse-field scattering events have been extensively studied. In all cases, the scattering shows a clear dependence on grain size, grain shape, and microstructural texture. Models used to quantify scattering experiments are often developed assuming dependence on a single spatial length scale, usually, mean grain diameter. However, several microscopy studies suggest that most metals have a log normal distribution of grain sizes. In this study, grain size distribution is discussed within the context of previous attenuation models valid for arbitrary crystallite symmetries. Results are presented for titanium using a range of distribution means and widths assuming equiaxed grains and no preferred crystallographic orientation. The longitudinal and shear attenuations are shown to vary with respect to the frequency dependence for varying distribution widths even when the volumetric mean grain size is held constant. Furthermore, the results suggest that grain size estimates based on attenuation can have large errors if the distribution is neglected. This work is anticipated to play an important role in microstructural characterization research associated with ultrasonic scattering.

56 citations

Journal ArticleDOI
TL;DR: A semi-analytical attenuation model, based on an established scattering theory, is presented that accurately accounts for the grain morphology without prior assumptions on grain statistics, and comparisons between simulations and theory show excellent agreement.
Abstract: The influence of a polycrystals' grain structure on elastic wave scattering is studied with analytical and numerical methods in a broad frequency range. A semi-analytical attenuation model, based on an established scattering theory, is presented. This technique accurately accounts for the grain morphology without prior assumptions on grain statistics. This is achieved by incorporating a samples' exact spatial two-point correlation function into the theory. The approach is verified by using a finite element method (FEM) to simulate P-wave propagation in 3D Voronoi crystals with equal mean grain diameter, but different grain shape uniformity. Aluminum and Inconel serve as representatives for weak and strong scattering cubic class materials for simulations and analytical calculations. It was found that the shape of the grains has a strong influence on the attenuation curve progression in the Rayleigh-stochastic transition region, which was attributed to mode conversion scattering. Comparisons between simulations and theory show excellent agreement for both materials. This demonstrates the need for accurately taking the microstructure of heterogeneous materials into account, to get precise analytical predictions for their scattering behaviour. It also demonstrates the impressive accuracy and flexibility of the scattering theory which was used.

38 citations

Journal ArticleDOI
TL;DR: In this paper, an explicit relation between spatial two-point correlation function (TPCF) and volumetric (or three-dimensional) grain size distribution for aggregates of statistically equiaxed grains was established.

17 citations

References
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Book
26 Jun 1995
TL;DR: The Finite Element Method as mentioned in this paper is a method for linear analysis in solid and structural mechanics, and it has been used in many applications, such as heat transfer, field problems, and Incompressible Fluid Flows.
Abstract: 1. An Introduction to the Use of Finite Element Procedures. 2. Vectors, Matrices and Tensors. 3. Some Basic Concepts of Engineering Analysis and an Introduction to the Finite Element Methods. 4. Formulation of the Finite Element Method -- Linear Analysis in Solid and Structural Mechanics. 5. Formulation and Calculation of Isoparametric Finite Element Matrices. 6. Finite Element Nonlinear Analysis in Solid and Structural Mechanics. 7. Finite Element Analysis of Heat Transfer, Field Problems, and Incompressible Fluid Flows. 8. Solution of Equilibrium Equations in State Analysis. 9. Solution of Equilibrium Equations in Dynamic Analysis. 10. Preliminaries to the Solution of Eigenproblems. 11. Solution Methods for Eigenproblems. 12. Implementation of the Finite Element Method. References. Index.

8,068 citations

Journal ArticleDOI
TL;DR: Gmsh as mentioned in this paper is an open-source 3D finite element grid generator with a build-in CAD engine and post-processor that provides a fast, light and user-friendly meshing tool with parametric input and advanced visualization capabilities.
Abstract: Gmsh is an open-source 3-D finite element grid generator with a build-in CAD engine and post-processor. Its design goal is to provide a fast, light and user-friendly meshing tool with parametric input and advanced visualization capabilities. This paper presents the overall philosophy, the main design choices and some of the original algorithms implemented in Gmsh. Copyright (C) 2009 John Wiley & Sons, Ltd.

5,322 citations

Book
01 Jan 1973
TL;DR: In this article, the authors apply the material developed in the Volume One to various boundary value problems (reflection and refraction at plane surfaces, composite media, waveguides and resonators).
Abstract: This work, part of a two-volume set, applies the material developed in the Volume One to various boundary value problems (reflection and refraction at plane surfaces, composite media, waveguides and resonators). The text also covers topics such as perturbation and variational methods.

5,211 citations

Journal ArticleDOI
TL;DR: In this paper, the authors present a Gebrauch bestimmt ausschließlich für den persönlichen, nicht kommerziellen Gebrauchs, which is a rechtschutzbestimmter gebrauch, and gilt vorbehaltlich der folgenden Einschränkungen.
Abstract: ----------------------------------------------------Nutzungsbedingungen DigiZeitschriften e.V. gewährt ein nicht exklusives, nicht übertragbares, persönliches und beschränktes Recht auf Nutzung dieses Dokuments. Dieses Dokument ist ausschließlich für den persönlichen, nicht kommerziellen Gebrauch bestimmt. Das Copyright bleibt bei den Herausgebern oder sonstigen Rechteinhabern. Als Nutzer sind Sie sind nicht dazu berechtigt, eine Lizenz zu übertragen, zu transferieren oder an Dritte weiter zu geben. Die Nutzung stellt keine Übertragung des Eigentumsrechts an diesem Dokument dar und gilt vorbehaltlich der folgenden Einschränkungen: Sie müssen auf sämtlichen Kopien dieses Dokuments alle Urheberrechtshinweise und sonstigen Hinweise auf gesetzlichen Schutz beibehalten; und Sie dürfen dieses Dokument nicht in irgend einer Weise abändern, noch dürfen Sie dieses Dokument für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, aufführen, vertreiben oder anderweitig nutzen; es sei denn, es liegt Ihnen eine schriftliche Genehmigung von DigiZeitschriften e.V. und vom Herausgeber oder sonstigen Rechteinhaber vor. Mit dem Gebrauch von DigiZeitschriften e.V. und der Verwendung dieses Dokuments erkennen Sie die Nutzungsbedingungen an.

3,675 citations

Journal ArticleDOI
TL;DR: This review attempts to illuminate the state of the art of FWI by building accurate starting models with automatic procedures and/or recording low frequencies, and improving computational efficiency by data-compression techniquestomake3DelasticFWIfeasible.
Abstract: Full-waveform inversion FWI is a challenging data-fitting procedure based on full-wavefield modeling to extract quantitative information from seismograms. High-resolution imaging at half the propagated wavelength is expected. Recent advances in high-performance computing and multifold/multicomponent wide-aperture and wide-azimuth acquisitions make 3D acoustic FWI feasible today. Key ingredients of FWI are an efficient forward-modeling engine and a local differential approach, in which the gradient and the Hessian operators are efficiently estimated. Local optimization does not, however, prevent convergence of the misfit function toward local minima because of the limited accuracy of the starting model, the lack of low frequencies, the presence of noise, and the approximate modeling of the wave-physics complexity. Different hierarchical multiscale strategiesaredesignedtomitigatethenonlinearityandill-posedness of FWI by incorporating progressively shorter wavelengths in the parameter space. Synthetic and real-data case studies address reconstructing various parameters, from VP and VS velocities to density, anisotropy, and attenuation. This review attempts to illuminate the state of the art of FWI. Crucial jumps, however, remain necessary to make it as popular as migration techniques. The challenges can be categorized as 1 building accurate starting models with automatic procedures and/or recording low frequencies, 2 defining new minimization criteria to mitigate the sensitivity of FWI to amplitude errors and increasing the robustness of FWI when multiple parameter classes are estimated, and 3 improving computational efficiency by data-compression techniquestomake3DelasticFWIfeasible.

2,981 citations