Elasticity with arbitrarily shaped inhomogeneity
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Elasticity with arbitrarily shaped inhomogeneity. / Mathiesen, Joachim; Procaccia, Itamar; Regev, Ido.
I: Physical Review E, Bind 77, Nr. 2, 026606, 26.02.2008.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - Elasticity with arbitrarily shaped inhomogeneity
AU - Mathiesen, Joachim
AU - Procaccia, Itamar
AU - Regev, Ido
PY - 2008/2/26
Y1 - 2008/2/26
N2 - A classical problem in elasticity theory involves an inhomogeneity embedded in a material of given stress and shear moduli. The inhomogeneity is a region of arbitrary shape whose stress and shear moduli differ from those of the surrounding medium. In this paper we present a semianalytic method for finding the stress tensor for an infinite plate with such an inhomogeneity. The solution involves two conformal maps, one from the inside and the second from the outside of the unit circle to the inside, and respectively outside, of the inhomogeneity. The method provides a solution by matching the conformal maps on the boundary between the inhomogeneity and the surrounding material. This matching converges well only for relatively mild distortions of the unit circle due to reasons which will be discussed in the article. We provide a comparison of the present result to known previous results.
AB - A classical problem in elasticity theory involves an inhomogeneity embedded in a material of given stress and shear moduli. The inhomogeneity is a region of arbitrary shape whose stress and shear moduli differ from those of the surrounding medium. In this paper we present a semianalytic method for finding the stress tensor for an infinite plate with such an inhomogeneity. The solution involves two conformal maps, one from the inside and the second from the outside of the unit circle to the inside, and respectively outside, of the inhomogeneity. The method provides a solution by matching the conformal maps on the boundary between the inhomogeneity and the surrounding material. This matching converges well only for relatively mild distortions of the unit circle due to reasons which will be discussed in the article. We provide a comparison of the present result to known previous results.
UR - http://www.scopus.com/inward/record.url?scp=40549134519&partnerID=8YFLogxK
U2 - 10.1103/PhysRevE.77.026606
DO - 10.1103/PhysRevE.77.026606
M3 - Journal article
AN - SCOPUS:40549134519
VL - 77
JO - Physical Review E
JF - Physical Review E
SN - 2470-0045
IS - 2
M1 - 026606
ER -
ID: 203585814