Solids with non-spherical cavities: Simplified representations of cavity compliance tensors and the overall anisotropy
type: Item
instance of: scholarly article
title: Solids with non-spherical cavities: Simplified representations of cavity compliance tensors and the overall anisotropy
zbMATH Open document ID: 0978.74009
DOI: 10.1016/S0022-5096(98)00073-8
author: Yanyan Li
published in: Journal of the Mechanics and Physics of Solids
publication date: 2002-01-17T00:00:00Z
review text: The authors consider a cavity in an infinite linear elastic solid under the assumption that in the absence of cavity the stress field would be uniform and equal to the stress field at infinity. Under given loads, the authors analyze cavity compliances that determine the contribution of the cavity to the overal strain. In general, the above compliances are characterized by fourth rank tensors \(H\). The authors identify the classes of pore shapes for which the characterization by tensors \(H\) can be reduced, with sufficient accuracy, to the description in terms of second rank symmetric tensors and certain scalar shape factors. These tensors and shape factors are explicitly found in terms of the cavity geometry. It is also shown that in the framework of non-interaction approximation, a solid with pores of certain geometries is orthotropic for any orientational distribution of such pores. In addition, the number of independent moduli is five or even four, in the case of cracks. Finally, the authors show that randomly oriented ellipsoids (overall isotropy) can be approximated, from the point of view of effective moduli, by certain equivalent spheroids.
Mathematics Subject Classification ID: 74B05
Mathematics Subject Classification ID: 74E10
Mathematics Subject Classification ID: 74E35
zbMATH DE Number: 1420151
zbMATH Keywords: non-spherical cavities
zbMATH Keywords: cavity compliance tensors
zbMATH Keywords: anisotropy
zbMATH Keywords: infinite linear elastic solid
zbMATH Keywords: fourth rank tensors
zbMATH Keywords: second rank symmetric tensors
zbMATH Keywords: scalar shape factors
zbMATH Keywords: non-interaction approximation
zbMATH Keywords: randomly oriented ellipsoids
zbMATH Keywords: overall isotropy
zbMATH Keywords: effective moduli
reviewed by: G. Jaiani
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1420151