On the basic theorems in linear elastostatics for bodies containing edge cracks
type: Item
instance of: scholarly article
title: On the basic theorems in linear elastostatics for bodies containing edge cracks
zbMATH Open document ID: 0553.73086
DOI: 10.1016/0020-7225(84)90040-5
author: Remigio Russo
published in: International Journal of Engineering Science
publication date: 1984-01-01T00:00:00Z
review text: The paper deals with an extension of the basic theorems of linear elastostatics for bodies containing edge cracks. In previous papers in this direction [e.g. \textit{K. B. Howell}, J. Elasticity 10, 407-427 (1980; Zbl 0459.73005)] it is proved that in order for work and energy theorem to hold [\textit{M. E. Gurtin} in Encyclopedia of physics, Vol. VIa/2, S. Flügge (ed.) (1972; Zbl 0277.73001); pp. 1-294], it is sufficient that the elastic tensor \({\mathcal C}\) is positive definite and the displacement field \({\mathfrak u}\) is bounded. As a consequence, uniqueness and Betti's theorem still hold under the same assumptions. The present paper extends the above mentioned results to the case in which \({\mathfrak u}\) can grow at the crack edge and \({\mathcal C}\) is not necessarily positive definite.
Mathematics Subject Classification ID: 74R05
Mathematics Subject Classification ID: 74G30
Mathematics Subject Classification ID: 74H25
Mathematics Subject Classification ID: 74B99
Mathematics Subject Classification ID: 74H99
zbMATH DE Number: 3882015
zbMATH Keywords: extension of the basic theorems
zbMATH Keywords: linear elastostatics
zbMATH Keywords: bodies containing edge cracks
reviewed by: K. S. Parihar
MaRDI profile type: Publication
full work available at URL: 0020-7225(84)90040-5
OpenAlex ID: W2078410325
cites work: Uniqueness in linear elastostatics for problems involving unbounded bodies
cites work: On the uniqueness of viscous fluid motions
description: scientific article; zbMATH DE number 3882015