Spherically layered inclusions in a homogeneous elastic medium
type: Item
instance of: scholarly article
title: Spherically layered inclusions in a homogeneous elastic medium
zbMATH Open document ID: 0624.73017
DOI: 10.1016/0021-8928(86)90013-4
author: S. K. Kanaun
author: L. T. Kudryavtseva
published in: Journal of Applied Mathematics and Mechanics
publication date: 1986-01-01T00:00:00Z
review text: A three-dimensional homogeneous and isotropic elastic medium is considered that contains an isolated inhomogeneity (inclusion) in the shape of a sphere. It is assumed that the elastic moduli of the medium within the sphere depend only on the distance r to the centre of the inclusion. It is shown that in the case of a constant external field the problem of the equilibrium of a medium with an inhomogeneity reduces to a system of ordinary differential equations in three scalar functions of the variable r. An inhomogeneity with a piecewise-constant dependence of the elastic moduli on r (a spherically layered inclusion) is examined in detail. In this case, an effective calculational algorithm is proposed to construct the solution of the problem. The solution of the problem of one inclusion is then utilized to determine the effective elastic moduli of a medium with a random set of spherically layered inclusions and the estimates of the stress concentration at individual inhomogeneities. The method of an effective (selfconsistent) field is used to take account of interaction between the inclusions.
Mathematics Subject Classification ID: 74E05
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 74G70
Mathematics Subject Classification ID: 74A40
Mathematics Subject Classification ID: 45E99
zbMATH DE Number: 4014128
zbMATH Keywords: three-dimensional homogeneous
zbMATH Keywords: isotropic elastic medium
zbMATH Keywords: isolated inhomogeneity
zbMATH Keywords: constant external field
zbMATH Keywords: system of ordinary differential equations
zbMATH Keywords: three scalar functions
zbMATH Keywords: effective calculational algorithm
zbMATH Keywords: effective elastic moduli
zbMATH Keywords: random set of spherically layered inclusions
zbMATH Keywords: method of an effective (selfconsistent) field
MaRDI profile type: Publication
full work available at URL: 0021-8928(86)90013-4
OpenAlex ID: W2036649085
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description: scientific article; zbMATH DE number 4014128