Normal-stress differences and the detection of disclinations in nematic elastomers

We use a continuum model to investigate the isochoric radial expansion of a right circular cylindrical specimen composed of a nematic elastomer that is cross-linked in a uniaxial state and then annealed. Numerical solutions show that, above a certain radial expansion, the material has a definitive energetic preference for a state involving a disclination of strength +1 along the cylinder axis. Surrounding such a disclination is a core with radial dimension on the order of 10^-2 ??m, which coincides with observations in conventional liquid-crystal melts. Examination of the normal-stress differences shows that the first of these differences depends non-monotonically on the extent of radial expansion and possesses a local minimum at the point where a disclination becomes energetically preferred. This suggests a practical experimental method for testing the predictions of our model.published or submitted for publicationis peer reviewe

Mind the gap: The shape of the free surface of a rubber-like material in proximity to a rigid contactor

Extending Andreussi and Gurtin???s (1977) pioneering work on the wrinkling of a free surface, we investigate the wrinkling stability of an incompressible elastic-like half-space whose surface is proximate to a contactor. Assuming a plane-strain deformation and accounting for both surface prestress and curvature-dependence of the surface free-energy density, we impose balances of forces and torques both in the bulk and on the surface. From the resulting linearized bulk and superficial equations, we derive a quintic dimensionless dispersion relation and perform a parametric study to see when stable or unstable behavior of the free surface is manifested. In contrast to the quadratic dispersion relation of Andreussi and Gurtin (1977), we obtain a quintic dispersion relation. An anlysis of this dispersion relation shows that the combined effects associated with surface pre-stress, curvature-dependence of the surface free-energy density, and the interactions between the surface and the proximate contactor lead always to an increased number linearly stable wrinkled configurations.published or submitted for publicationis peer reviewe

Disclinated states in nematic elastomers

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 ??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 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.published or submitted for publicationis peer reviewe

Biaxial disclinated states in nematic elastomers

We use a continuum model to investigate the isochoric axial contraction and expansion of a right circular cylindrical specimen composed of a nematic elastomer that is cross-linked in a uniaxial state and then annealed. We build on previous work by relaxing the constraint that the molecular conformation be spherical or uniaxial, allowing instead for biaxiality. The material exhibits an energetic preference for states involving a disclination of strength +1 along the cylinder axis surrounded by a region in which the conformation of the polymer chains is indeed biaxial. We show that such states represent minimizers of the total free-energy. Also, the reactive pressure necessary to enforce the constraint of material incompressibility within the disclination core is found to be reduced by an order of magnitude when the conformation is biaxial rather than uniaxial. A bifurcation analysis is used to analytically determine the thresholds of axial expansion and contraction at which the material prefers a disclinated state. These thresholds are found to be consistent with numerical predictions. Finally, the stability of the solutions for the studied parameters is also investigated.published or submitted for publicationis peer reviewe

On the Shape of the Free Surface of a Rubber-Like Material in Proximity to a Rigid Contactor

79 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2005.Motivated by recent experimental research on thin elastic films by Moench and Herminghaus and by Shenoy and Sharma, we build on Andreussi and Gurtin's pioneering work on the wrinkling of a free surface with residual stress and investigate the wrinkling of residually stressed solid films subjected to van der Waals or other types of interaction from a proximate contactor. We consider an incompressible rubber-like film of infinite depth, account for the influence of the contactor and both residual surface stress and curvature on the surface free-energy density, and impose force balance both in the bulk and on the surface. From the resulting linearized bulk and superficial equations, we derive a quintic dimensionless dispersion relation and perform a parametric study to see when linearly stable or unstable behavior of the film surface is manifested. Compared with the quadratic dispersion relation of Andreussi and Gurtin, the present model always yields more linearly stable wrinkled configurations possible for the film. Thus, for experimental or design applications, the addition of the contactor and inclusion of surface curvature effects may be advantageous.U of I OnlyRestricted to the U of I community idenfinitely during batch ingest of legacy ETD

On the Shape of the Free Surface of a Rubber-Like Material in Proximity to a Rigid Contactor

79 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2005.Motivated by recent experimental research on thin elastic films by Moench and Herminghaus and by Shenoy and Sharma, we build on Andreussi and Gurtin's pioneering work on the wrinkling of a free surface with residual stress and investigate the wrinkling of residually stressed solid films subjected to van der Waals or other types of interaction from a proximate contactor. We consider an incompressible rubber-like film of infinite depth, account for the influence of the contactor and both residual surface stress and curvature on the surface free-energy density, and impose force balance both in the bulk and on the surface. From the resulting linearized bulk and superficial equations, we derive a quintic dimensionless dispersion relation and perform a parametric study to see when linearly stable or unstable behavior of the film surface is manifested. Compared with the quadratic dispersion relation of Andreussi and Gurtin, the present model always yields more linearly stable wrinkled configurations possible for the film. Thus, for experimental or design applications, the addition of the contactor and inclusion of surface curvature effects may be advantageous.U of I OnlyRestricted to the U of I community idenfinitely during batch ingest of legacy ETD

Prediction of disclinations in nematic elastomers

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. Away from the disclination, the material is anisotropic, and the polymeric molecules are shaped as ellipsoidal coils of revolution oblate about the radial direction. Along 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(−2) μm, which coincides with observations in conventional liquid crystal melts. Finally, we find that the total energy definitively shows a preference for disclinated states