On the energy of electroelastic fracture
type: Item
instance of: scholarly article
title: On the energy of electroelastic fracture
zbMATH Open document ID: 0832.73063
DOI: 10.1007/BF01003555
published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik
publication date: 1995-08-10T00:00:00Z
review text: In an attempt to give a solution to a controversy existing in the literature for the generalization of the Rice \(J\)-integrals to electroelasticity, the authors reconsider the problem in a more general context. Two formulations of the theory of electroelasticity are proposed, giving rise to two distinct energy release rates, and therefore two distinct \(J\)-integrals. This duality pertains to a general feature of continuum mechanics of electromagnetic media, according to which certain quantities may be regarded as volume source densities or transformed into surface contributions in view of Maxwell's equations. In order to favorize one of the two formulations, the authors investigate a particular fracture problem for which one of the two formulations becomes inadequate. This is the case of electrically conducting cracks propagating through a linear anisotropic dielectric, for which the asymptotic solution for the electric field near the crack-tip was obtained and used to show that the energy balance in one of the two formulations contains a diverging integral. The authors conclude that for this type of fracture problems, only the representation of the (free) electric field action as a surface force can be adopted.
reviewed by: Ahmed Ghaleb
Mathematics Subject Classification ID: 74F15
Mathematics Subject Classification ID: 74R99
zbMATH DE Number: 777680
zbMATH Keywords: crack propagation
zbMATH Keywords: rice \(J\)-integrals
zbMATH Keywords: electrically conducting cracks
zbMATH Keywords: linear anisotropic dielectric
zbMATH Keywords: asymptotic solution
zbMATH Keywords: crack-tip
zbMATH Keywords: surface force
author: Cristian Dascalu
author: Gérard A. Maugin
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 777680