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Riemann–Cartan geometry of nonlinear disclination mechanics

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Abstract.
In the continuous theory of defects in nonlinear elastic solids, it is known that a distribution of disclinations leads, in general, to a non-trivial residual stress field. To study this problem, we consider the particular case of determining the residual stress field of a cylindrically symmetric distribution of parallel wedge disclinations. We first use the tools of differential geometry to construct a Riemannian material manifold in which the body is stress-free. This manifold is metric compatible, has zero torsion, but has non-vanishing curvature. The problem then reduces to embedding this manifold in Euclidean 3-space following the procedure of a classical nonlinear elastic problem. We show that this embedding can be elegantly accomplished by using Cartan’s method of moving frames and compute explicitly the residual stress field for various distributions in the case of a neo-Hookean material.

Keywords: differential geometry, disclinations, geometric elasticity, residual stresses

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Informasi Detail

Judul Seri

Mathematics and Mechanics of Solids

No. Panggil

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Penerbit

London : SAGE Publications Ltd., 2012

Deskripsi Fisik

Mathematics and Mechanics of Solids 18(1): 91–102

Bahasa

English

ISBN/ISSN

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Klasifikasi

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Tipe Isi

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Tipe Media

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Tipe Pembawa

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Edisi

18(1)

Subjek

MATEMATIKA TEKNIK

Info Detail Spesifik

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Pernyataan Tanggungjawab

agus

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