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.
DOI : 10.1051/cocv/2014022
Mots-clés : Nematic elastomers, polyconvexity, invertibility
@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/
and , 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
, Convexity conditions and existence theorems in nonlinear elasticity. Arch. Ration. Mech. Anal. 63 (1976) 337–403. | DOI | MR | Zbl
, 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
and , 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
and , Elastic energies for nematic elastomers. Eur. Phys. J. E 29 (2009) 191–204. | DOI
and , 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
and , 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
and , Fracture surfaces and the regularity of inverses for deformations. Arch. Ration. Mech. Anal. 201 (2011) 575–629. | DOI | MR | Zbl
, and , 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).
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