Continuum Mechanical and Computational Aspects of Material Behavior

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The authors develop a theory for uniaxial nematic elastomers with variable asphericity. As an application of the theory, they consider the time-independent, isochoric radial expansion of a right circular cylinder. Numerical solutions to the resulting differential equation are obtained for a range of radial expansions. For all expansions considered, there exists an isotropic core of material surrounding the cylinder axis where the asphericity vanishes and in which the polymeric chains are shaped as spherical coils. This region, corresponding to a disclination of strength + 1 along the axis, is bounded by a narrow transition layer across which the asphericity increases ... continued below

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874 KB pages

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Fried, Eliot & Gurtin, Morton E. March 14, 2004.

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Description

The authors develop a theory for uniaxial nematic elastomers with variable asphericity. As an application of the theory, they consider the time-independent, isochoric radial expansion of a right circular cylinder. Numerical solutions to the resulting differential equation are obtained for a range of radial expansions. For all expansions considered, there exists an isotropic core of material surrounding the cylinder axis where the asphericity vanishes and in which the polymeric chains are shaped as spherical coils. This region, corresponding to a disclination of strength + 1 along the axis, is bounded by a narrow transition layer across which the asphericity increases rapidly and attains a non-trivial positive value. The material thereby becomes anisotropic away from the disclination so that the polymeric chains are shaped as ellipsoidal coils of revolution prolate about 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 the location of this energy drop. For realistic choices of material parameters, this criterion yields a core on the order of 10{sup -2} {micro}m, 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 contributions to the deformational stress and a change in the pressure. Furthermore, the constitutively determined contribution to the orientational stress is completely concentrated at the core boundary. The total energy shows a definitive preference for disclinated states.

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874 KB pages

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OSTI as DE00822056

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  • Other Information: PBD: 14 Mar 2004

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  • Report No.: DOE/ER/25439-1
  • Grant Number: FG02-01ER25439
  • DOI: 10.2172/822056 | External Link
  • Office of Scientific & Technical Information Report Number: 822056
  • Archival Resource Key: ark:/67531/metadc781626

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  • March 14, 2004

Added to The UNT Digital Library

  • Dec. 3, 2015, 9:30 a.m.

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  • June 10, 2016, 6:19 p.m.

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Fried, Eliot & Gurtin, Morton E. Continuum Mechanical and Computational Aspects of Material Behavior, report, March 14, 2004; United States. (digital.library.unt.edu/ark:/67531/metadc781626/: accessed October 17, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.