A universal relation in torsion for a mixture of solid and fluid
type: Item
instance of: scholarly article
title: A universal relation in torsion for a mixture of solid and fluid
zbMATH Open document ID: 0564.73048
DOI: 10.1007/BF00041990
published in: Journal of Elasticity
publication date: 1985-01-01T00:00:00Z
review text: In his study of combined finite extension and torsion of a nonlinear, incompressible, isotropic elastic circular cylinder, \textit{R. S. Rivlin} [Philos. Trans. R. Soc. Lond., A 242, 173-195 (1949; Zbl 0035.415)] established a relation for the torsional stiffness which depends only on the axial force, the axial extension ratio and the radius of the undeformed cylinder, in the case of small twist. The relationship did not depend on the structure of the stored energy function and is hence a ''universal relation''. In this paper, we extend Rivlin's result to the case of combined extension and torsion of a cylindrical mixture of a nonlinear elastic solid and fluid.
Mathematics Subject Classification ID: 74B20
Mathematics Subject Classification ID: 74F10
Mathematics Subject Classification ID: 74K15
zbMATH DE Number: 3900275
zbMATH Keywords: extended result of Rivlin
zbMATH Keywords: theory of interacting continua
zbMATH Keywords: no restriction on fluid content of mixture
zbMATH Keywords: state of cylinder range from completely dry to fully saturated
zbMATH Keywords: solid and fluid constituents are at rest
zbMATH Keywords: fluid can be nonhomogeneously dispersed throughout the mixture
zbMATH Keywords: concentration gradients
zbMATH Keywords: combined extension and torsion
zbMATH Keywords: cylindrical mixture of a nonlinear elastic solid and fluid
author: Mukesh V. Gandhi
author: K. R. Rajagopal
author: Alan S. Wineman
MaRDI profile type: Publication
cites work: Large elastic deformations of isotropic materials VI. Further results in the theory of torsion, shear and flexure
cites work: A theory of mixtures with a long range spatial interaction
cites work: CONTINUUM THEORIES OF MIXTURES: BASIC THEORY AND HISTORICAL DEVELOPMENT
cites work: Incompressible mixtures of Newtonian fluids
cites work: Applications of the theory of interacting continua to the diffusion of a fluid through a nonlinear elastic media
cites work: The mechanics of rubber elasticity
cites work: ON BASIC EQUATIONS FOR MIXTURES
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description: scientific article; zbMATH DE number 3900275