Frank energy for nematic elastomers: a nonlinear model
ESAIM: Control, Optimisation and Calculus of Variations, Tome 21 (2015) no. 2, pp. 372-377.

We discuss the well-posedness of a new nonlinear model for nematic elastomers. The main novelty in our work is that the Frank energy penalizes spatial variations of the nematic director in the deformed, rather than in the reference configuration, as it is natural in the case of large deformations.

Reçu le :
DOI : 10.1051/cocv/2014022
Classification : 74B20, 74G65
Mots clés : Nematic elastomers, polyconvexity, invertibility
Barchiesi, Marco 1 ; DeSimone, Antonio 2

1 Universitàdegli Studi di Napoli “Federico II”, Via Cintia, 80126 Napoli, Italy.
2 SISSA-International School for Advanced Studies, Via Bonomea 265, 34136 Trieste, Italy.
@article{COCV_2015__21_2_372_0,
     author = {Barchiesi, Marco and DeSimone, Antonio},
     title = {Frank energy for nematic elastomers: a nonlinear model},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {372--377},
     publisher = {EDP-Sciences},
     volume = {21},
     number = {2},
     year = {2015},
     doi = {10.1051/cocv/2014022},
     mrnumber = {3348403},
     zbl = {1311.74020},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1051/cocv/2014022/}
}
TY  - JOUR
AU  - Barchiesi, Marco
AU  - DeSimone, Antonio
TI  - Frank energy for nematic elastomers: a nonlinear model
JO  - ESAIM: Control, Optimisation and Calculus of Variations
PY  - 2015
SP  - 372
EP  - 377
VL  - 21
IS  - 2
PB  - EDP-Sciences
UR  - http://archive.numdam.org/articles/10.1051/cocv/2014022/
DO  - 10.1051/cocv/2014022
LA  - en
ID  - COCV_2015__21_2_372_0
ER  - 
%0 Journal Article
%A Barchiesi, Marco
%A DeSimone, Antonio
%T Frank energy for nematic elastomers: a nonlinear model
%J ESAIM: Control, Optimisation and Calculus of Variations
%D 2015
%P 372-377
%V 21
%N 2
%I EDP-Sciences
%U http://archive.numdam.org/articles/10.1051/cocv/2014022/
%R 10.1051/cocv/2014022
%G en
%F COCV_2015__21_2_372_0
Barchiesi, Marco; DeSimone, Antonio. Frank energy for nematic elastomers: a nonlinear model. ESAIM: Control, Optimisation and Calculus of Variations, Tome 21 (2015) no. 2, pp. 372-377. doi : 10.1051/cocv/2014022. http://archive.numdam.org/articles/10.1051/cocv/2014022/

V. Agostiniani and A. Desimone, Ogden-type energies for nematic elastomers. Int. J. Nonlin. Mech. 47 (2012) 402–412. | DOI

V. Agostiniani, G. Dal Maso and A. DeSimone, Attainment results for nematic elastomers. Proc. Roy. Soc. Edinb. A, in press (2013). | MR

L. Ambrosio and P. Tilli, Topics on analysis in metric spaces. In vol. 25 of Oxford lecture series in mathematics and its applications. Oxford University Press, New York (2004). | MR | Zbl

J.M. Ball, Convexity conditions and existence theorems in nonlinear elasticity. Arch. Ration. Mech. Anal. 63 (1976) 337–403. | DOI | MR | Zbl

J.M. Ball, Global invertibility of Sobolev functions and the interpenetration of matter. Proc. Roy. Soc. Edinb. 88A (1981) 315–328. | DOI | MR | Zbl

M.C. Calderer, C.A. Garavito and C. Luo, Liquid crystal elastomers and phase transitions in rod networks. Preprint arXiv:1303.6220 (2013). | MR

P. Cesana and A. Desimone, Strain-order coupling in nematic elastomers: equilibrium configurations. Math. Models Methods Appl. Sci. 19 (2009) 601–630. | DOI | MR | Zbl

P.G. Ciarlet, Mathematical elasticity. I. Three-dimensional elasticity. Vol. 20 of Stud. Math. Appl. North-Holland Publishing Co., Amsterdam (1988). | MR | Zbl

B. Dacorogna, Direct methods in the calculus of variations. Vol. 78 of Appl. Math. Sci., 2nd ed. Springer, Berlin (2008). | MR | Zbl

A. Desimone and L. Teresi, Elastic energies for nematic elastomers. Eur. Phys. J. E 29 (2009) 191–204. | DOI

I. Fonseca and W. Gangbo, Local invertibility of Sobolev functions. SIAM J. Math. Anal. 26 (1995) 280–304. | DOI | MR | Zbl

V.M. Gol’dshtein and Y.G. Reshetnyak, Quasiconformal mapping and Sobolev spaces, vol. 54. Kluwer Academic Publishers, Dordrecht, Germany (1990). | MR | Zbl

D. Henao and C. Mora-Corral, Invertibility and weak continuity of the determinant for the modelling of cavitation and fracture in nonlinear elasticity. Arch. Ration. Mech. Anal. 197 (2010) 619–655. | DOI | MR | Zbl

D. Henao and C. Mora-Corral, Fracture surfaces and the regularity of inverses for BV deformations. Arch. Ration. Mech. Anal. 201 (2011) 575–629. | DOI | MR | Zbl

S. Müller, Q. Tang and B.S. Yan, On a new class of elastic deformations not allowing for cavitation. Ann. Inst. Henri Poincaré, Anal. Non Linéaire 11 (1994) 217–243. | DOI | Numdam | MR | Zbl

M. Warner and E.M. Terentjev, Liquid Crystal Elastomers. Clarendon Press, Oxford (2003).

Cité par Sources :