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Disclinated states in nematic elastomers

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Title: Disclinated states in nematic elastomers
Author(s): Fried, Eliot; Todres, Russell E.
Subject(s): constitutive theory smart materials experimental fluid mechanics granular materials particulate flows phase transitions biological mechanics
Abstract: We present a theory for uniaxial nematic elastomers with variable asphericity. As an application of the theory, we consider the time-independent, isochoric extension of a right circular cylinder. Numerical solutions to the resulting differential equation are obtained for a range of extensions. For sufficiently large extensions, there exists an isotropic core of material surrounding the cylinder axis where the asphericity vanishes and in which the polymeric molecules are shaped as spherical coils. This region, corresponding to a disclination of strength +1 manifesting itself along the axis, is bounded by a narrow transition layer across which the asphericity drops rapidly and attains a nontrivial negative value. The material thereby becomes anisotropic away from the disclination so that the polymeric molecules are shaped as ellipsoidal coils of revolution oblate about the cylinder radius. In accordance with the area of steeply changing asphericity between isotropic and anisotropic regimes, a marked drop in the free-energy density is observed. The boundary of the disclination core is associated with one location of this energy drop. For realistic choices of material parameters, this criterion yields a core on the order of 10^-2 µm, which coincides with observations in conventional liquid-crystal melts. Also occurring at the core boundary, and further confirming its location, are sharp transitions in the behavior of the constitutively determined contribution to the deformational stress and a minimum in the pressure. Furthermore, the constitutively determined contribution to the orientational stress is completely concentrated at the core boundary. The total energy definitively shows an energetic preference for disclinated states.
Issue Date: 2001-10
Publisher: Department of Theoretical and Applied Mechanics (UIUC)
Series/Report: TAM Reports 983
Genre: Technical ReportArticle
Type: Text
Language: English
URI: http://hdl.handle.net/2142/262
ISSN: 0073-5264
Publication Status: published or submitted for publication
Peer Reviewed: is peer reviewed
Date Available in IDEALS: 2007-03-08
Is Version Of: Published as: Eliot Fried and Russell E. Todres. Disclinated states in nematic elastomers. Journal of the Mechanics and Physics of Solids, v 50, n 12, December, 2002, p 2691-2716. DOI: 10.1016/S0022-5096(02)00013-3. Copyright 2002 Elsevier.
 

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  • Theoretical and Applied Mechanics (TAM) Technical Reports
    TAM technical reports include manuscripts intended for publication, theses judged to have general interest, notes prepared for short courses, symposia compiled from outstanding undergraduate projects, and reports prepared for research-sponsoring agencies.

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