Soft elastic response of stretched sheets of nematic elastomers: a numerical study

Stretching experiments on sheets of nematic elastomers have revealed soft deformation modes and formation of microstructure in parts of the sample. Both phenomena are manifestations of the existence of a symmetry-breaking phase transformation from a random, isotropic phase to an aligned, nematic phase. The microscopic energy proposed by Bladon et al. (Phys. Rev. E 47 (1993), R 3838) to model this transition delivers a continuum of symmetry-related zero-energy states, which can be combined in different ways to achieve a variety of zero-energy macroscopic deformations. We replace the microscopic energy with a macroscopic effective energy, the so-called quasiconvexification. This procedure yields a coarse-grained description of the physics of the system, with (energetically optimal) fine-scale oscillations of the state variables correctly accounted for in the energetics, but averaged out in the kinematics. Knowledge of the quasiconvexified energy enables us to compute efficiently with finite elements, and to simulate numerically stretching experiments on sheets of nematic elastomers. Our numerical experiments show that up to a critical, geometry-dependent stretch, no reaction force arises. At larger stretches, a force is transmitted through parts of the sheet and, although fine phase mixtures disappear from most of the sample, microstructures survive in some pockets. We reconstruct from the computed deformation gradients a possible composition of the microstructure, thereby resolving the local orientation of the nematic director.