The remarkable nature of radially symmetric deformation of spherically uniform linear anisotropic elastic solids
type: Item
instance of: scholarly article
title: The remarkable nature of radially symmetric deformation of spherically uniform linear anisotropic elastic solids
zbMATH Open document ID: 0946.74014
DOI: 10.1023/A:1007516218827
published in: Journal of Elasticity
publication date: 2000-10-17T00:00:00Z
review text: The author investigates the stresses state in the interior of a sphere of radius \(r\), subjected to a uniform pressure on its surface. The sphere is made of a spherically uniform linear anisotropic elastic material. It is shown that the existence of infinite stress at \(r=0\) does not depend on the traction \(\sigma_0\) at the surface, but depends only on a non-dimensional material parameter \(k\), a function of elastic constants of the material. For a certain range of \(k\), the author shows that a cavitation (if \(\sigma_0>0)\) or a black hole (for \(\sigma_0<0)\) occurs at the centre of the sphere. Finally, the author studies various particular cases of anisotropy, for instance the triclinic anisotropy, as well as various relations between the elastic constants of the material.
Mathematics Subject Classification ID: 74E10
Mathematics Subject Classification ID: 74B10
Mathematics Subject Classification ID: 74G70
zbMATH DE Number: 1359831
zbMATH Keywords: stress singularity
zbMATH Keywords: sphere
zbMATH Keywords: spherically uniform linear anisotropic elastic material
zbMATH Keywords: elastic constants
zbMATH Keywords: cavitation
zbMATH Keywords: triclinic anisotropy
author: Ting, T. C. T.
reviewed by: Petre P. Teodorescu
MaRDI profile type: Publication
full work available at URL: a:1007516218827
OpenAlex ID: W2194603298
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description: scientific article; zbMATH DE number 1359831