649 research outputs found
Characterization of soft stripe-domain deformations in Sm-C and Sm-C* liquid-crystal elastomers
The neoclassical model of Sm-C (and Sm-C*) elastomers developed by Warner and Adams predicts a class of âsoftâ (zero energy) deformations. We find and describe the full set of stripe domainsâlaminate structures in which the laminates alternate between two different deformationsâthat can form between pairs of these soft deformations. All the stripe domains fall into two classes, one in which the smectic layers are not bent at the interfaces, but for whichâin the Sm-C* caseâthe interfaces are charged, and one in which the smectic layers are bent but the interfaces are never charged. Striped deformations significantly enhance the softness of the macroscopic elastic response
Exactly isochoric deformations of soft solids
Many materials of contemporary interest, such as gels, biological tissues and
elastomers, are easily deformed but essentially incompressible. Traditional
linear theory of elasticity implements incompressibility only to first order
and thus permits some volume changes, which become problematically large even
at very small strains. Using a mixed coordinate transformation originally due
to Gauss, we enforce the constraint of isochoric deformations exactly to
develop a linear theory with perfect volume conservation that remains valid
until strains become geometrically large. We demonstrate the utility of this
approach by calculating the response of an infinite soft isochoric solid to a
point force that leads to a nonlinear generalization of the Kelvin solution.
Our approach naturally generalizes to a range of problems involving
deformations of soft solids and interfaces in 2 dimensional and axisymmetric
geometries, which we exemplify by determining the solution to a distributed
load that mimics muscular contraction within the bulk of a soft solid
Supersoft elasticity in polydomain nematic elastomers
We consider the equilibrium stress-strain behavior of polydomain liquid crystal elastomers (PLCEs). We show that there is a fundamental difference between PLCEs cross-linked in the high temperature isotropic and low temperature aligned states. PLCEs cross-linked in the isotropic state then cooled to an aligned state will exhibit extremely soft elasticity (confirmed by recent experiments) and ordered director patterns characteristic of textured deformations. PLCEs cross-linked in the aligned state will be mechanically much harder and characterized by disclination textures
Plateau-Rayleigh instability in solids is a simple phase separation
A long elastic cylinder, with radius a and shear-modulus ÎŒ, becomes unstable given sufficient surface tension Îł. We show this instability can be simply understood by considering the energy, E(λ), of such a cylinder subject to a homogenous longitudinal stretch λ. Although E(λ) has a unique minimum, if surface tension is sufficient [ÎâĄÎł/(aÎŒ)>â32] it loses convexity in a finite region. We use a Maxwell construction to show that, if stretched into this region, the cylinder will phase-separate into two segments with different stretches λ1 and λ2. Our model thus explains why the instability has infinite wavelength and allows us to calculate the instability's subcritical hysteresis loop (as a function of imposed stretch), showing that instability proceeds with constant amplitude and at constant (positive) tension as the cylinder is stretched between λ1 and λ2. We use full nonlinear finite-element calculations to verify these predictions and to characterize the interface between the two phases. Near Î=â32 the length of such an interface diverges, introducing a new length scale and allowing us to construct a one-dimensional effective theory. This treatment yields an analytic expression for the interface itself, revealing that its characteristic length grows as lwallâŒa/âÎââ32.C.X. thanks the China Scholarship Council and the EPSRC for funding
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