Dynamics of dielectric breakdown paths

Boksiner, Jeffrey; Leath, P. L.

doi:10.1103/physreve.67.066610

Cited by 10 publications

(5 citation statements)

References 16 publications

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“…15 Formally, these shear bands are closely related to other types of minimal breakdown manifolds in heterogeneous media ͑mechanical systems, as well as nonlinear electrical networks͒. [16][17][18] However, nonlinear EMAs which address plasticity rely on a quasiequilibrium hypothesis, which means that the characteristic time of an individual "breakdown" ͑or slip͒ event is longer than that of wave propagation through the medium 19 ͑in nonlinear dielectrics, such conditions are met, as well as in the reversible diode network experiment 20 ͒. Plastic deformation being a strongly irreversible process, applications of such EMAs to plasticity should therefore be restricted to incipient deformation in an incremental framework.…”

Section: Introductionmentioning

confidence: 99%

Effective-medium theory for infinite-contrast two-dimensionally periodic linear composites with strongly anisotropic matrix behavior: Dilute limit and crossover behavior

et al. 2008

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Follow this and additional works at: http://repository.upenn.edu/meam_papers Part of the Mechanical Engineering CommonsSuggested Citation: F. Willot, Y. Pellegrini, M.I. Idiart and P.P. Castañeda. (2008). "Effective-medium theory for infinite-contrast two-dimensionally periodic linear composites with strongly anisotropic matrix behavior: Dilute limit and crossover behavior. Effective-medium theory for infinite-contrast two-dimensionally periodic linear composites with strongly anisotropic matrix behavior: Dilute limit and crossover behavior AbstractThe overall behavior of a two-dimensional lattice of voids embedded in an anisotropic elastic matrix is investigated in the limit of vanishing porosity f. An effective-medium model (of the Clausius-Mossoti type), which accounts for elastic interactions between neighboring voids, is compared to fast Fourier transform numerical solutions and, in the limits of infinite anisotropy, to exact results. A crossover between regular and singular dilute regimes is found, driven by a characteristic length which depends on f and on the anisotropy strength. The singular regime, where the leading dilute correction to the elastic moduli is an O(f 1/2 ), is related to strain localization and to change in character-from elliptic to hyperbolic-of the governing equations. The overall behavior of a two-dimensional lattice of voids embedded in an anisotropic elastic matrix is investigated in the limit of vanishing porosity f. An effective-medium model ͑of the Clausius-Mossoti type͒, which accounts for elastic interactions between neighboring voids, is compared to fast Fourier transform numerical solutions and, in the limits of infinite anisotropy, to exact results. A crossover between regular and singular dilute regimes is found, driven by a characteristic length which depends on f and on the anisotropy strength. The singular regime, where the leading dilute correction to the elastic moduli is an O͑f 1/2 ͒, is related to strain localization and to change in character-from elliptic to hyperbolic-of the governing equations. Disciplines Engineering | Mechanical Engineering

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Section: Introductionmentioning

confidence: 99%

Effective-medium theory for infinite-contrast two-dimensionally periodic linear composites with strongly anisotropic matrix behavior: Dilute limit and crossover behavior

et al. 2008

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“…A model for the forming was proposed based on the creation of a network of conducting filaments by the applied electric field. [18][19][20] The model predicts a bifurcated structure starting on the initial filament and broadens toward the other side, independent of the used parameters. This model describes qualitatively our data in the initial forming step, as seen in Fig.…”

mentioning

confidence: 94%

Spatial distribution of oxygen vacancies in Cr-doped SrTiO3 during an electric-field-driven insulator-to-metal transition

Andreasson

Janousch

Staub

et al. 2009

Applied Physics Letters

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Spatially resolved x-ray fluorescence maps are presented that show the introduction and the evolution of oxygen vacancies in chromium-doped strontium titanate during an electric-field-driven insulator-to-metal transition. The vacancies are introduced at the anode and diffuse through the crystal toward the cathode. The spatial distribution of vacancies is explained by a model describing the electrical breakdown as a percolation process. Strong differences in the vacancy distribution were found when the transition took place in air and in a hydrogen-enriched atmosphere. In air, the vacancies disappeared from the surface, whereas in the reducing hydrogen atmosphere, they remained at the surface.

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“…Several other models are similar in nature in that they use networks of circuit components to model breakdown. These network models use fuse-like components that are destroyed when subjected to high fields [Joshi et al 2002;Boksiner and Leath 2003;Quiña et al 2008]. In addition to simulation methods, a simple relation between breakdown strength and a material's elastic properties can be derived, giving a rough estimate of electromechanical breakdown strength [Zebouchi and Malec 1998].…”

Section: Introductionmentioning

confidence: 99%

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2015

J. Mech. Mater. Struct.

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This special issue contains contributions that were invited on the occasion of the Peridynamic Theory symposium held at the 17th U.S. National Congress on Theoretical and Applied Mechanics (USNCTAM) at Michigan State University in June, 2014.One theme of these papers is exploiting the potential of peridynamics in contemporary technology, particularly by including multiple physical effects and applying it to nanoscale mechanics. The paper by Turner, Val Bloemen Waanders, and Parks develops an inverse method to determine heterogeneous nonlocal material properties from experimental data, including digital image correlation (DIC). Wildman and Gazonas couple peridynamic mechanics with a model for electrical conduction and Joule heating to simulate fracture caused by high voltage dielectric breakdown. Application of peridynamics to friction and wear at the nanoscale is demonstrated in the paper by Ebrahim, Steigmann, and Komvopoulos.Another general theme of the special issue is making peridynamic mechanics more practical as a general analysis tool for applications involving fracture. The paper by Mitchell, Silling, and Littlewood describes a new material model within peridynamics that helps avoid difficulties due to the nonlocal nature of the theory in treating free surfaces. With the goal of applying peridynamics only within a small subregion of a large structure where damage is expected, Silling, Littlewood, and Seleson investigate techniques for varying the peridynamic horizon within a model, including application to local-nonlocal coupling. In a related paper elsewhere in this journal (

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Dynamics of dielectric breakdown paths

Cited by 10 publications

References 16 publications

Effective-medium theory for infinite-contrast two-dimensionally periodic linear composites with strongly anisotropic matrix behavior: Dilute limit and crossover behavior

Effective-medium theory for infinite-contrast two-dimensionally periodic linear composites with strongly anisotropic matrix behavior: Dilute limit and crossover behavior

Spatial distribution of oxygen vacancies in Cr-doped SrTiO3 during an electric-field-driven insulator-to-metal transition

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