Quasiconvex envelopes of energies for nematic elastomers in the small strain regime and applications

Journal of the Mechanics and Physics of Solids

Volumn 59, Issue 4, 2011, Pages 787-803

  Cesana, Pierluigi ^a,b,c   Desimone, Antonio ^a  

^a SISSA   (Italy)

^b BCAM BASQUE CENTER FOR APPLIED MATHEMATICS   (Spain)

^c CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Hyperelasticity; Nematic elastomers; Quasiconvexity; Relaxation

Indexed keywords

ANALYTICAL FORMULAS; ENERGY DENSITY; EXPERIMENTAL INVESTIGATIONS; EXPLICIT FORMULA; HYPER-ELASTICITY; NEMATIC ELASTOMERS; PLANE STRAIN CONDITION; PURE SHEAR; QUASICONVEX ENVELOPE; QUASICONVEXITY; RELAXATION; SMALL STRAINS; STRESS-STRAIN RESPONSE;

ELASTICITY; PLASTICS;

ELASTOMERS;

EID: 79952361963     PISSN: 00225096     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmps.2011.01.007     Document Type: Article

References (27)

1. E. Acerbi, and N. Fusco Semicontinuity problems in the calculus of variations Arch. Ration. Mech. Anal. 86 1984 125 145
2. Agostiniani, V., DeSimone, A. Gamma-convergence of energies for nematic elastomers in the small strain limit. Continuum Mech. Thermodyn., in press, doi: 10.1007/s00161-011-0180-2.
3. K. Bhattacharya Microstructure of Martensite 2003 Oxford University Press Oxford
4. J.S. Biggins, E.M. Terentjev, and M. Warner Semisoft elastic response of nematic elastomers to complex deformations Phys. Rev. E 78 2008 041704.1041704.9
5. P. Bladon, E.M. Terentjev, and M. Warner Transitions and instabilities in liquid-crystal elastomers Phys. Rev. E 47 1993 R3838 R3840
6. A. Braides Relaxation of functionals with constraints on the divergence Ann. Univ. Ferrara - Sez. VII - Sc. Mat. XXXIII 1987 157 177
7. P. Cesana Relaxation of multi-well energies in linearized elasticity and applications to nematic elastomers Arch. Ration. Mech. Anal. 197 2010 903 923
8. P. Cesana, and A. DeSimone Strain-order coupling in nematic elastomers: equilibrium configurations Math. Models Methods Appl. Sci. 19 2009 601 630
9. S. Conti, A. DeSimone, and G. Dolzmann Soft elastic response of stretched sheets of nematic elastomers: a numerical study J. Mech. Phys. Solids 50 2002 1431 1451 (Pubitemid 34551827)
10. S. Conti, A. DeSimone, and G. Dolzmann Semi-soft elasticity and director reorientation in stretched sheets of nematic elastomers Phys. Rev. E 60 2002 61710-161710-8
11. Dacorogna, B., 2008. Direct Methods in the Calculus of Variations, second ed. Springer.
12. A. DeSimone Energetics of fine domain structures Ferroelectrics 222 1999 275 284 (Pubitemid 129660157)
13. A. DeSimone Electro-mechanical response of nematic elastomers: an introduction R.W. Ogden, D.J. Steigmann, Mechanics and Electrodynamics of Magneto- and Electro-elastic Materials, CISM Courses and Lectures vol. 527 2011 Springer Verlag 231 266
14. A. DeSimone, and G. Dolzmann Macroscopic response of nematic elastomers via relaxation of a class of SO(3)-invariant energies Arch. Ration. Mech. Anal. 161 2002 181 204 (Pubitemid 36185875)
15. A. DeSimone, and L. Teresi Elastic energies for nematic elastomers Eur. Phys. J. E 29 2009 191 204
16. H. Finkelmann, I. Kundler, E.M. Terentjev, and M. Warner Critical stripe-domain instability of nematic elastomers J. Phys. II France 7 1997 1059 1069
17. A. Fukunaga, K. Urayama, T. Takigawa, A. DeSimone, and L. Teresi Dynamics of electro-opto-mechanical effects in swollen nematic elastomers Macromolecules 41 2008 9389 9396
18. I. Kundler, and H. Finkelmann Strain-induced director reorientation in nematic liquid single crystal elastomers Macromol. Rapid Comm. 16 1995 679 686
19. J. Kpfer, and H. Finkelmann Liquid crystal elastomers: influence of the orientational distribution of the crosslinks on the phase behaviour and reorientation processes Macromol. Chem. Phys. 195 1994 1353 1367
20. S. Mller Variational methods for microstructure and phase transitions F. Bethuel, G. Huisken, S. Mller, K. Steffen, S. Hildebrandt, M. Strwe, Proceedings of the C.I.M.E. Summer School "Calculus of Variation and Geometric Evolution Problems" Cetraro 1996, Lecture Notes in Mathematics vol. 1713 1999 Springer
21. R.W. Ogden Non-linear Elastic Deformations 1997 Dover Publications
22. A. Petelin, and M. Copic Observation of a soft mode of elastic instability in liquid crystal elastomers Phys. Rev. Lett. 103 2009 077801-1077801-4
23. D. Rogez, G. Francius, H. Finkelmann, and P. Martinoty Shear mechanical anisotropy of side chain liquid-crystal elastomers: influence of sample preparation Eur. Phys. J. E 20 2006 369 378 (Pubitemid 44386796)
24. M. Silhavy Ideally soft nematic elastomers Networks Heterogeneous Media 2 2007 279 311
25. Treloar, L.R.G., 1975. The Physics of Rubber Elasticity, third ed. Oxford University Press.
26. G.C. Verwey, M. Warner, and E. Terentjev Elastic instability and stripe domains in liquid crystalline elastomers J. Phys. II France 6 1996 1273 1290 (Pubitemid 126796092)
27. Warner, M., Terentjev, E.M., 2007. Liquid Crystal Elastomers, revised ed. Clarendon Press, Oxford.