Continuum Mechanical and Computational Aspects of Material Behavior

Fried, Eliot ; Gurtin, Morton E.

Eliot Fried/University of Illinois at Urbana-Champaign (United States)

关键词: Differential Equations;    Free Energy;    36 Materials Science;    Numerical Solution Nematic Elastomers;    Elastomers;   

DOI  :  10.2172/822056
RP-ID  :  DOE/ER/25439-1
RP-ID  :  FG02-01ER25439
RP-ID  :  822056

美国|英语

来源: UNT Digital Library

【 摘 要 】

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.