Skip to main content

Nematic elastomers: modelling, analysis, and numerical simulations

  • Chapter
Poly-, Quasi- and Rank-One Convexity in Applied Mechanics

Part of the book series: CISM International Centre for Mechanical Sciences ((CISM,volume 516))

Abstract

We review in these notes some of our recent work on modelling the mechanical response of nematic elastomers, both under static and dynamic loadings. Our aim is to compare theoretical results based on mathematical analysis and numerical simulations with the available experimental evidence, in order to examine critically the various accomplishments, and some interesting problems that remain open.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  • P. Bladon, E. M. Terentjev, and M. Warner. Transitions and instabilities in liquid-crystal elastomers. Phys. Rev. E, 47:R3838–R3840, 1993.

    Article  Google Scholar 

  • P. Cesana. Relaxation of multi-well energies in linearized elasticity and applications to nematic elastomers. Submitted, 2009.

    Google Scholar 

  • P. Cesana and A. DeSimone. Strain-order coupling in nematic elastomers: equilibrium configurations. Math. Models Methods Appl. Sci., 19:601–630, 2009.

    Article  MATH  MathSciNet  Google Scholar 

  • S. Conti, A. DeSimone, and G. Dolzmann. Soft elastic response of stretched sheets of nematic elastomers: a numerical study. J. Mech. Phys. Solids, 50:1431–1451, 2002a.

    Article  MATH  MathSciNet  Google Scholar 

  • S. Conti, A. DeSimone, and G. Dolzmann. Semi-soft elasticity and director reorientation in stretched sheets of nematic elastomers. Phys. Rev. E, 66:0617101–0617108, 2002b.

    Article  Google Scholar 

  • A. DeSimone. Energetics of fine domain structures. Ferroelectrics, 222: 275–284, 1999.

    Article  Google Scholar 

  • A. DeSimone and G. Dolzmann. Material instabilities in nematic elastomers. Physica D, 136:175–191, 2000.

    Article  MATH  MathSciNet  Google Scholar 

  • A. DeSimone and G. Dolzmann. Macroscopic response of nematic elastomers via relaxation of a class of SO (3)-invariant energies. Arch. Rat. Mech. Anal., 161:181–204, 2002.

    Article  MATH  MathSciNet  Google Scholar 

  • A. DeSimone and G. Dolzmann. Striping in nematic elastomers: old and new. In: Modeling of Soft Matter (M. C. Calderer, E. Terentjev eds.). Springer, 2005.

    Google Scholar 

  • A. DeSimone and L. Teresi. Elastic energies for nematic elastomers. Eur. Phys. J. E, in press, 2009.

    Google Scholar 

  • A. DeSimone, A. Di Carlo, and L. Teresi. Critical volages and blocking stresses in nematic gels. Eur. Phys. J. E, 24:303–310, 2007.

    Article  Google Scholar 

  • H. Finkelmann and G. Rehage. Liquid crystal side chain polymers. Adv. Polymer Sci., 60/61:99–172, 1984.

    Google Scholar 

  • H. Finkelmann, W. Gleim, H.J. Kock, and G. Rehage. Liquid crystalline polymer network — rubber elastic material with exceptional properties. Makromol. Chem. Suppl., 12:49, 1985.

    Article  Google Scholar 

  • H. Finkelmann, I. Kundler, E. M. Terentjev, and M. Warner. Critical stripe-domain instability of nematic elastomers. J. Phys. II France, 7:1059–1069, 1997.

    Article  Google Scholar 

  • E. Fried and V. Korchagin. Striping of nematic elastomers. Int. J. Solids Structures, 39:3451–3467, 2002.

    Article  MATH  Google Scholar 

  • M. E. Gurtin. Introduction to Continuum Mechanics. Academic Press, 1981.

    Google Scholar 

  • T. Ikeda. Fundamentals of Piezoelectricity. University Press, 1990.

    Google Scholar 

  • I. Kundler and H. Finkelmann. Strain-induced director reorientation in nematic liquid single crystal elastomers. Macromol. Rapid Comm., 16: 679–686, 1995.

    Article  Google Scholar 

  • J. Küpfer and H. Finkelmann. Nematic liquid single-crystal elastomers. Makromol. Chem. Rapid Comm., 12:717–726, 1991.

    Article  Google Scholar 

  • P. Martinoty, P. Stein, H. Finkelmann, H. Pleiner, and H.R. Brand. Mechanical properties of mono domain side chain nematic elastomers. Eur. Phys. J. E, 14:311, 2004.

    Article  Google Scholar 

  • S. Müller. Variational models for microstructure and phase transitions. In: Bethuel, F., Huisken, G., Müller, S., Steffen, K., Hildebrandt, S., Struwe, M. (Eds.), Calculus of Variations and Geometric Evolution Problems, Lectures given at the 2nd Session of the Centro Internazionale Matematico Estivo, Cetraro 1996. Springer, Berlin, 1999.

    Google Scholar 

  • M. Silhavy. Ideally soft nematic elastomers. Networks and Heterogeneous Media, 2:279–311, 2007.

    MATH  MathSciNet  Google Scholar 

  • M. Silhavy. The Mechanics and Thermodynamics of Continuous Media. Springer, 1997.

    Google Scholar 

  • G. C. Verwey, M. Warner, and E. M. Terentjev. Elastic instability and stripe domains in liquid crystalline elastomers. J. Phys. II France, 6: 1273–1290, 1996.

    Article  Google Scholar 

  • M. Warner and E. M. Terentjev. Liquid Crystal Elastomers. Clarendon Press, 2003.

    Google Scholar 

  • J. Weilepp and H. Brand. Director reorientation in nematic-liquid-single-crystal elastomers by external mechanical stress. Europhys. Lett., 34: 495–500, 1996.

    Article  Google Scholar 

  • R. Zentel. Liquid crystal elastomers. Angew. Chem. Adv. Mater., 101:1437, 1989.

    Google Scholar 

  • E. R. Zubarev, S. A. Kuptsov, T. I. Yuranova, R. V. Talroze, and H. Finkelmann. Monodomain liquid crystalline networks: reorientation mechanism from uniform to stripe domains. Liquid Crystals, 26:1531–1540, 1999.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2010 CISM, Udine

About this chapter

Cite this chapter

DeSimone, A. (2010). Nematic elastomers: modelling, analysis, and numerical simulations. In: Schröder, J., Neff, P. (eds) Poly-, Quasi- and Rank-One Convexity in Applied Mechanics. CISM International Centre for Mechanical Sciences, vol 516. Springer, Vienna. https://doi.org/10.1007/978-3-7091-0174-2_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-7091-0174-2_7

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-7091-0173-5

  • Online ISBN: 978-3-7091-0174-2

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics