Does the capacitor analogy model in fracture mechanics of elastic dielectrics constitute an appropriate approximation?

Behlen, Lennart; Wallenta, Daniel; Ricoeur, Andreas

dc.date.accessioned	2024-10-31T09:31:13Z
dc.date.available	2024-10-31T09:31:13Z
dc.date.issued	2024-07-26
dc.identifier	doi:10.17170/kobra-2024103111043
dc.identifier.uri	http://hdl.handle.net/123456789/16131
dc.description.sponsorship	Gefördert im Rahmen eines Open-Access-Transformationsvertrags mit dem Verlag	ger
dc.language.iso	eng
dc.rights	Namensnennung 4.0 International	*
dc.rights.uri	http://creativecommons.org/licenses/by/4.0/	*
dc.subject	dielectrics	eng
dc.subject	semi-permeable crack	eng
dc.subject	conformal map	eng
dc.subject	Maxwell stress	eng
dc.subject	intensity factors	eng
dc.subject	crack curvature	eng
dc.subject.ddc	600
dc.title	Does the capacitor analogy model in fracture mechanics of elastic dielectrics constitute an appropriate approximation?	eng
dc.type	Aufsatz
dcterms.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.	eng
dcterms.accessRights	open access
dcterms.creator	Behlen, Lennart
dcterms.creator	Wallenta, Daniel
dcterms.creator	Ricoeur, Andreas
dc.relation.doi	doi:10.1177/10812865241252368
dc.subject.swd	Dielektrikum	ger
dc.subject.swd	Bruchmechanik	ger
dc.subject.swd	Riss	ger
dc.subject.swd	Konforme Abbildung	ger
dc.subject.swd	Maxwellscher Spannungstensor	ger
dc.type.version	publishedVersion
dcterms.source.identifier	eissn:1741-3028
dcterms.source.issue	Issue 11
dcterms.source.journal	Mathematics and Mechanics of Solids	eng
dcterms.source.pageinfo	2316-2347
dcterms.source.volume	Volume 29