Aufsatz
Does the capacitor analogy model in fracture mechanics of elastic dielectrics constitute an appropriate approximation?
Abstract
The analytical solution of an elliptic dielectric cavity in an infinite dielectric plate is taken as basis to investigate a Griffith crack problem which is obtained by letting the semi-minor axis tend towards zero. In the course of this, an erroneous conformal mapping, commonly employed in literature and correctly reproducing the electric field only in a part of the physical space, is rectified. Interpreting the elliptic interface as faces of a mechanically opened crack which is exposed to an oblique remote electric field, surface charges and electrostatic tractions are calculated. In contrast to the established capacitor analogy model, approximately yielding electric charge densities and Coulombic tractions from displacements and electric potentials in the undeformed crack configuration, the work at hand provides exact solutions accounting for different implications of the crack curvature and for the inclination of the electric field. Crack weight functions are finally used to calculate stress and electric displacement intensity factors. As turns out, the surface charges of the capacitor analogy represent an excellent substitute for the exact electric boundary conditions within a relevant range of parameters, whereas inaccurate Coulombic tractions in the vicinity of crack tips may lead to a significantly overestimated mode I stress intensity factor.
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Gefördert im Rahmen eines Open-Access-Transformationsvertrags mit dem VerlagCitation
@article{doi:10.17170/kobra-2024103111043,
author={Behlen, Lennart and Wallenta, Daniel and Ricoeur, Andreas},
title={Does the capacitor analogy model in fracture mechanics of elastic dielectrics constitute an appropriate approximation?},
journal={Mathematics and Mechanics of Solids},
year={2024}
}
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<resource xsi:schemaLocation="http://datacite.org/schema/kernel-2.2 http://schema.datacite.org/meta/kernel-2.2/metadata.xsd"> 2024-10-31T09:31:13Z 2024-10-31T09:31:13Z 2024-07-26 doi:10.17170/kobra-2024103111043 http://hdl.handle.net/123456789/16131 Gefördert im Rahmen eines Open-Access-Transformationsvertrags mit dem Verlag eng Namensnennung 4.0 International http://creativecommons.org/licenses/by/4.0/ dielectrics semi-permeable crack conformal map Maxwell stress intensity factors crack curvature 600 Does the capacitor analogy model in fracture mechanics of elastic dielectrics constitute an appropriate approximation? Aufsatz The analytical solution of an elliptic dielectric cavity in an infinite dielectric plate is taken as basis to investigate a Griffith crack problem which is obtained by letting the semi-minor axis tend towards zero. In the course of this, an erroneous conformal mapping, commonly employed in literature and correctly reproducing the electric field only in a part of the physical space, is rectified. Interpreting the elliptic interface as faces of a mechanically opened crack which is exposed to an oblique remote electric field, surface charges and electrostatic tractions are calculated. In contrast to the established capacitor analogy model, approximately yielding electric charge densities and Coulombic tractions from displacements and electric potentials in the undeformed crack configuration, the work at hand provides exact solutions accounting for different implications of the crack curvature and for the inclination of the electric field. Crack weight functions are finally used to calculate stress and electric displacement intensity factors. As turns out, the surface charges of the capacitor analogy represent an excellent substitute for the exact electric boundary conditions within a relevant range of parameters, whereas inaccurate Coulombic tractions in the vicinity of crack tips may lead to a significantly overestimated mode I stress intensity factor. open access Behlen, Lennart Wallenta, Daniel Ricoeur, Andreas doi:10.1177/10812865241252368 Dielektrikum Bruchmechanik Riss Konforme Abbildung Maxwellscher Spannungstensor publishedVersion eissn:1741-3028 Issue 11 Mathematics and Mechanics of Solids 2316-2347 Volume 29 </resource>
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