Semisoft elasticity and director reorientation in stretched sheets of nematic elastomers

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 66, Issue 6, 2002, Pages 8-

  Conti, Sergio ^a   DeSimone, Antonio ^a   Dolzmann, Georg ^b  

^a MAX PLANCK INSTITUTE FOR MATHEMATICS IN THE SCIENCES   (Germany)

^b Bldg 142   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

NEMATIC ELASTOMERS; PERIODIC FUNCTIONS OF PERIOD; REORIENTATION; SEMISOFT ELASTICITY;

CROSSLINKING; CRYSTAL STRUCTURE; DEFORMATION; ELASTICITY; FUNCTIONS; LIQUID CRYSTAL POLYMERS; MICROSCOPIC EXAMINATION; MICROSTRUCTURE; NEMATIC LIQUID CRYSTALS; OSCILLATIONS; PLASTIC FILMS; STRETCHING;

ELASTOMERS;

ARTICLE;

EID: 41349119548     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.66.061710     Document Type: Article

References (32)

1. E.M. Terentjev, J. Phys.: Condens. Matter 11, R239 (1999).
2. M. Warner, J. Mech. Phys. Solids 47, 1355 (1999).
3. T.C. Lubensky, R. Mukhopadhyay, L. Radzihovsky, and X. Xing, Phys. Rev. E 66, 011702 (2002).
4. M. Warner and E.M. Terentjev, Prog. Polym. Sci. 21, 853 (1996).
5. A.R. Tajbakhsh and E.M. Terentjev, Eur. Phys. J. E 6, 181 (2001).
6. M. Hébert, R. Kant, and P.-G. de Gennes, J. Phys. I 7, 909 (1997).
7. S.M. Clarke, A.R. Tajbakhsh, E.M. Terentjev, and M. Warner, Phys. Rev. Lett. 86, 4044 (2001).
8. G.C. Verwey, M. Warner, and E.M. Terentjev, J. Phys. II 6, 1273 (1996).
9. N. Uchida, Phys. Rev. E 62, 5119 (2000).
10. S.M. Clarke, E.M. Terentjev, I. Kundler, and H. Finkelmann, Macromolecules 31, 4862 (1998).
11. H. Finkelmann, E. Nishikawa, G.G. Pereira, and M. Warner, Phys. Rev. Lett. 87, 015501 (2001).
12. J. Küpfer and H. Finkelmann, Makromol. Chem., Rapid Commun. 12, 717 (1991).
13. J. Kundler and H. Finkelmann, Macromol. Rapid Commun. 16, 679 (1995).
14. L. Golubović and T.C. Lubensky, Phys. Rev. Lett. 63, 1082 (1989).
15. P. Bladon, E.M. Terentjev, and M. Warner, Phys. Rev. E 47, R3838 (1993).
16. E.R. Zubarev, S.A. Kuptsov, T.I. Yuranova, R.V. Talroze, and H. Finkelmann, Liq. Cryst. 26, 1531 (1999).
17. A. DeSimone and G. Dolzmann, Arch. Ration. Mech. Anal. 161, 181 (2002).
18. S. Conti, A. DeSimone, and G. Dolzmann, J. Mech. Phys. Solids 50, 1431 (2002).
19. S. Conti, A. DeSimone, G. Dolzmann, S. Müller, and F. Otto, in Trends in Nonlinear Analysis, edited by M. Kirkilionis, S. Krömker, R. Rannacher, and F. Tomi (Springer, Heidelberg, 2002).
20. M. Šilhavý (unpublished).
21. Our reference configuration differs from the initial configuration by the uniaxial deformation (Formula presented) where (Formula presented) VWT instead used the initial configuration as reference. Their deformation gradient (Formula presented) is related to ours by (Formula presented) This also affects the definition of aspect ratio (see 30).
22. S. Müller, in Calculus of Variations and Geometric Evolution Problems, Springer Lecture Notes in Mathematics Vol. 1713, edited by F. Bethuel et al. (Springer, Berlin, 1999), pp. 85–210.
23. J. Weilepp and H.R. Brand, Europhys. Lett. 34, 495 (1996)
24. Europhys. Lett.J. WeileppH.R. Brandsee also 37, 495 (1997);
25. Europhys. Lett.J. WeileppH.R. Brand37, 499 (1997).
26. H. Finkelmann, I. Kundler, E.M. Terentjev, and M. Warner, J. Phys. II 7, 1059 (1997).
27. N. Uchida and A. Onuki, Europhys. Lett. 45, 341 (1999).
28. E. Fried and V. Korchagin, Int. J. Solids Struct. 39, 3451 (2002).
29. To compare our formulas with VWT 8, note that their r corresponds to our (Formula presented) and their (Formula presented) to our (Formula presented)
30. Jensen’s inequality states that if f is convex, then the average of (Formula presented) is greater than or equal to (Formula presented) where (Formula presented) is the average of u.
31. The normal cannot be changed from (Formula presented) since in the optimality argument of Eqs. (151617) the two components of the energy (13) could be treated separately.
32. We define the aspect ratio r as the ratio between the length of the sample in the x and in the y directions in the reference configuration. The initial configuration differs from the reference configuration by the uniaxial stretch mentioned in 21, so that the ratio between its x and y dimensions is (Formula presented)