Eur. Phys. J. E (2012) 35: 2
https://doi.org/10.1140/epje/i2012-12002-5

Regular Article

Biaxially stretched nematic liquid crystalline elastomers

¹ ITE, Polytechnic University of Valencia, Valencia, Spain
² ICTP, (CSIC), Madrid, Spain

^* e-mail: rdiazc@ter.upv.es

Received: 20 September 2011
Accepted: 22 December 2011
Published online: 18 January 2012

Abstract

The biaxial stretching of sheets of liquid crystalline neo-Hookean elastomer has been studied in the isotropic case. The results suggest two types of laminate structures in the process of quasiconvexification of the free energy, a fact that implies the appearance of several shear terms in the deformation gradient matrix. More that one decomposition of the deformation gradient is possible, which is consistent with a bifurcation in the undeformed configuration ( = 1) . This situation is similar to the well-known Rivlin’s problem of the triaxial symmetric traction of a neo-Hookean cube. The problem can easily be generalized for an anisotropic material by introducing a semisoft term in the free-energy expression. In this case, the horizontal plateau corresponding to the minimal energy, characteristic of the soft elasticity, disappears, and only an equilibrium condition is obtained.