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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
40/2001

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

Sergio Conti, Antonio DeSimone and Georg Dolzmann

Abstract

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, Terentjev and Warner [Phys. Rev. E 47 (1993), 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) small-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.

Received:
Aug 31, 2001
Published:
Aug 31, 2001
Keywords:
microstructures, phase transformations, rubber material, energy methods, finite elements

Related publications

inJournal
2002 Repository Open Access
Sergio Conti, Antonio DeSimone and Georg Dolzmann

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

In: Journal of the mechanics and physics of solids, 50 (2002) 7, pp. 1431-1451