Soft elasticity in smectic elastomers

Abstract

We investigate the soft elastic modes of smectic elastomers, that is shape change without energy cost. We use a microscopic model for their nonlinear elasticity, similar to those used for nematic elastomers. We consider two different phases of smectic elastomer; the biaxial smectic A for a simple illustration, and smectic C phases which are of great practical significance. We show that only one nontrivial trajectory of the director gives soft deformations. We give a geometrical interpretation of this soft elastic mode and give an explicit example.

(An)elastic softening from static grain boundaries and possible effects on seismic wave propagation

“…The nontrivial question is, as often in elasticity, to what extent strain-stress relations remain linear under these conditions. While it is clear that linearity is not obeyed for large stresses for virtually all materials, non-linearities for small stresses exist also for large classes of materials, such as elastomers (Adams and Warner 2005) or ferroic materials (Salje 1992). Once stresses are so small that relevant atomic displacements are smaller than thermal vibrational amplitudes, nonlinearities due to surface relaxations dominate, although it is very hard to measure such effects experimentally.…”

Numerical study of stretched smectic-Aelastomer sheets

“…For elastomers in the smectic-C phase there are several interesting features in the mechanical models, such as spontaneous deformations as observed in nematic elastomers [28,29]. While the set of all deformations that are zero energy (the quasiconvex hull) has been computed [30], the quasiconvex envelope has not, so it is not yet possible to carry out a numerical study as done here for the Sm-A phase.…”

Negative Poisson's ratio and semisoft elasticity of smectic-Cliquid-crystal elastomers

“…There is only one soft mode that satisfies this (up to a global rotation), and it corresponds to a rotation of the director about the layer normal [18,19]. We summarize some of the properties of this soft mode here, as they are crucial in understanding the semisoft response of the elastomer.…”

“…In principle a Sm-C elastomer should have a biaxial shape tensor for the polymer backbone because its shape may be affected by both the director alignment and the layer normal direction. As a first approximation we will treat it as uniaxial here, depending only on the director orientation n. Biaxial soft modes in Sm-A elastomers [18] and the effect of biaxiality in Sm-C soft modes [28] are considered elsewhere. We will also assume that the nematic and smectic order parameters remain fixed throughout the deformation.…”

“…1(a). As a consequence it is predicted to have a soft elastic mode just as in nematic elastomers [18,19]. A more complicated combination of shears is required in Sm-C soft modes.…”