Cesana, Pierluigi (2011) Nematic Elastomers: Gamma-Limits for Large Bodies and Small Particles. SIAM Journal on Mathematical Analysis, 43 (5). pp. 2354-2383. ISSN 0036-1410 http://resolver.caltech.edu/CaltechAUTHORS:20111129-100510290
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We compute the large-body and the small-particle Gamma-limit of a family of energies for nematic elastomers. We work under the assumption of small deformations (linearized kinematics) and consider both compressible and incompressible materials. In the large-body asymptotics, even if we describe the local orientation of the liquid crystal molecules according to the model of perfect order (Frank theory), we prove that we obtain a fully biaxial nematic texture (that of the de Gennes theory) as a by-product of the relaxation phenomenon connected to Gamma-convergence. In the case of small particles, we show that formation of new microstructure is not possible, and we describe the map of minimizers of the Gamma-limit as the phase diagram of the mechanical model.
|Additional Information:||© 2011 Society for Industrial and Applied Mathematics. Received May 17, 2010. Accepted June 21, 2011. Published online October 20, 2011. This work was partially supported by project MTM2009-07662 of the Spanish Ministry of Science and Innovation and by the Department of Energy - National Nuclear Security Administration under award DE-FC5208NA28613 through Caltech’s PSAAP Center for the Predictive Modeling and Simulation of High Energy Density Dynamic Response of Materials. The results contained in this paper have been obtained while the author was a Ph.D. student at Sissa.|
|Subject Keywords:||nematic liquid crystal elastomers, linearized elasticity, Gamma-convergence|
|Classification Code:||AMS Subject Headings: 74B05, 49J45, 49S05, 82D30|
|Official Citation:||Nematic Elastomers: Gamma-Limits for Large Bodies and Small Particles Pierluigi Cesana SIAM J. Math. Anal. 43, pp. 2354-2383|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Ruth Sustaita|
|Deposited On:||29 Nov 2011 18:48|
|Last Modified:||26 Dec 2012 14:27|
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