Loading [MathJax]/jax/output/SVG/jax.js
Search Advanced

Networks and Heterogeneous Media

2007, Volume 2, Issue 2: 279-311. doi: 10.3934/nhm.2007.2.279
Previous Article Next Article

Ideally soft nematic elastomers

  • 1.
    Dipartimento di Matematica, Università di Pisa, Largo Bruno Pontecorvo 5, 56127 Pisa
  • Received: 01 March 2006 Revised: 01 January 2007

  • Primary: 35B27.

  • The paper examines a class of energies of nematic elastomers that exhibit ideally soft behavior. These are generalizations of the neo-classical energy function proposed by Bladon, Terentjev & Warner [7]. The effective energy (quasiconvexification) of is calculated for a large subclass of considered energies. Within the subclass, the rank 1 convex, quasiconvex, and polyconvex envelopes coincide and reduce to the largest function below that satisfies the Baker–Ericksen inequalities. Compressible cases are included. The effective energy displays three regimes: one fluid-like, one partially fluid-like and one hard, as established by DeSimone & Dolzmann [20] for the energy function of Bladon, Terentjev & Warner. Ideally soft deformation modes are shown to arise.

    Citation: M. Silhavý. Ideally soft nematic elastomers[J]. Networks and Heterogeneous Media, 2007, 2(2): 279-311. doi: 10.3934/nhm.2007.2.279

    Related Papers:

    [1] M. Silhavý . Ideally soft nematic elastomers. Networks and Heterogeneous Media, 2007, 2(2): 279-311. doi: 10.3934/nhm.2007.2.279
    [2] Marco Cicalese, Antonio DeSimone, Caterina Ida Zeppieri . Discrete-to-continuum limits for strain-alignment-coupled systems: Magnetostrictive solids, ferroelectric crystals and nematic elastomers. Networks and Heterogeneous Media, 2009, 4(4): 667-708. doi: 10.3934/nhm.2009.4.667
    [3] Andrea Braides, Margherita Solci, Enrico Vitali . A derivation of linear elastic energies from pair-interaction atomistic systems. Networks and Heterogeneous Media, 2007, 2(3): 551-567. doi: 10.3934/nhm.2007.2.551
    [4] Leandro M. Del Pezzo, Nicolás Frevenza, Julio D. Rossi . Convex and quasiconvex functions in metric graphs. Networks and Heterogeneous Media, 2021, 16(4): 591-607. doi: 10.3934/nhm.2021019
    [5] Grigory Panasenko, Ruxandra Stavre . Asymptotic analysis of the Stokes flow with variable viscosity in a thin elastic channel. Networks and Heterogeneous Media, 2010, 5(4): 783-812. doi: 10.3934/nhm.2010.5.783
    [6] Julian Braun, Bernd Schmidt . On the passage from atomistic systems to nonlinear elasticity theory for general multi-body potentials with p-growth. Networks and Heterogeneous Media, 2013, 8(4): 879-912. doi: 10.3934/nhm.2013.8.879
    [7] Antoine Gloria Cermics . A direct approach to numerical homogenization in finite elasticity. Networks and Heterogeneous Media, 2006, 1(1): 109-141. doi: 10.3934/nhm.2006.1.109
    [8] V. V. Zhikov, S. E. Pastukhova . Korn inequalities on thin periodic structures. Networks and Heterogeneous Media, 2009, 4(1): 153-175. doi: 10.3934/nhm.2009.4.153
    [9] Hervé Le Dret, Annie Raoult . Homogenization of hexagonal lattices. Networks and Heterogeneous Media, 2013, 8(2): 541-572. doi: 10.3934/nhm.2013.8.541
    [10] Maksym Berezhnyi, Evgen Khruslov . Non-standard dynamics of elastic composites. Networks and Heterogeneous Media, 2011, 6(1): 89-109. doi: 10.3934/nhm.2011.6.89
  • The paper examines a class of energies of nematic elastomers that exhibit ideally soft behavior. These are generalizations of the neo-classical energy function proposed by Bladon, Terentjev & Warner [7]. The effective energy (quasiconvexification) of is calculated for a large subclass of considered energies. Within the subclass, the rank 1 convex, quasiconvex, and polyconvex envelopes coincide and reduce to the largest function below that satisfies the Baker–Ericksen inequalities. Compressible cases are included. The effective energy displays three regimes: one fluid-like, one partially fluid-like and one hard, as established by DeSimone & Dolzmann [20] for the energy function of Bladon, Terentjev & Warner. Ideally soft deformation modes are shown to arise.


  • This article has been cited by:

    1. Alain Goriely, L Angela Mihai, Liquid crystal elastomers wrinkling, 2021, 34, 0951-7715, 5599, 10.1088/1361-6544/ac09c1
    2. L Angela Mihai, Alain Goriely, Likely striping in stochastic nematic elastomers, 2020, 25, 1081-2865, 1851, 10.1177/1081286520914958
    3. Carlos Mora-Corral, Marcos Oliva, Relaxation of nonlinear elastic energies involving the deformed configuration and applications to nematic elastomers, 2019, 25, 1292-8119, 19, 10.1051/cocv/2018005
    4. Virginia Agostiniani, Antonio DeSimone, Ogden-type energies for nematic elastomers, 2012, 47, 00207462, 402, 10.1016/j.ijnonlinmec.2011.10.001
    5. Sergio Conti, Georg Dolzmann, Relaxation of a model energy for the cubic to tetragonal phase transformation in two dimensions, 2014, 24, 0218-2025, 2929, 10.1142/S0218202514500419
    6. Sergio Conti, Georg Dolzmann, Relaxation in crystal plasticity with three active slip systems, 2016, 28, 0935-1175, 1477, 10.1007/s00161-015-0490-x
    7. Pierluigi Cesana, Antonio DeSimone, Quasiconvex envelopes of energies for nematic elastomers in the small strain regime and applications, 2011, 59, 00225096, 787, 10.1016/j.jmps.2011.01.007
    8. Sergio Conti, Georg Dolzmann, On the Theory of Relaxation in Nonlinear Elasticity with Constraints on the Determinant, 2015, 217, 0003-9527, 413, 10.1007/s00205-014-0835-9
    9. Sergio Conti, Georg Dolzmann, An adaptive relaxation algorithm for multiscale problems and application to nematic elastomers, 2018, 113, 00225096, 126, 10.1016/j.jmps.2018.02.001
    10. Antonio DeSimone, 2010, Chapter 7, 978-3-7091-0173-5, 241, 10.1007/978-3-7091-0174-2_7
    11. G. Dolzmann, Microstructure and effective behavior of materials, 2013, 93, 00442267, 4, 10.1002/zamm.201200128
    12. A. DeSimone, L. Teresi, Elastic energies for nematic elastomers, 2009, 29, 1292-8941, 191, 10.1140/epje/i2009-10467-9
    13. L. Angela Mihai, 2022, Chapter 6, 978-3-031-06691-7, 183, 10.1007/978-3-031-06692-4_6
    14. Georg Dolzmann, 2010, Chapter 5, 978-90-481-9194-9, 65, 10.1007/978-90-481-9195-6_5
    15. Florian Behr, Georg Dolzmann, Klaus Hackl, Ghina Jezdan, Analytical and numerical relaxation results for models in soil mechanics, 2023, 35, 0935-1175, 2019, 10.1007/s00161-023-01225-9
  • Reader Comments
  • © 2007 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索
Networks and Heterogeneous Media
1.2 1.8

Metrics

Article views(3519) PDF downloads(137) Cited by(15)

Preview PDF
Download XML
Export Citation
Article outline
Abstract

Other Articles By Authors

Related pages

Tools

Copyright © AIMS Press

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog