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Networks and Heterogeneous Media

2009, Volume 4, Issue 4: 667-708. doi: 10.3934/nhm.2009.4.667
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Discrete-to-continuum limits for strain-alignment-coupled systems: Magnetostrictive solids, ferroelectric crystals and nematic elastomers

  • 1.
    Dipartimento di Matematica e Applicazioni "R. Caccioppoli”, Università di Napoli Federico II, Via Cintia, 80126 Napoli
  • 2.
    SISSA-International School for Advanced Studies, Via Beirut 2-4, 34014 Trieste
  • Received: 01 January 2009 Revised: 01 June 2009

  • Primary: 49J45, 49M25; Secondary: 74B05, 76A15, 82D45, 82D40.

  • In the framework of linear elasticity, we study the limit of a class of discrete free energies modeling strain-alignment-coupled systems by a rigorous coarse-graining procedure, as the number of molecules diverges. We focus on three paradigmatic examples: magnetostrictive solids, ferroelectric crystals and nematic elastomers, obtaining in the limit three continuum models consistent with those commonly employed in the current literature. We also derive the correspondent macroscopic energies in the presence of displacement boundary conditions and of various kinds of applied external fields.

    Citation: Marco Cicalese, Antonio DeSimone, Caterina Ida Zeppieri. Discrete-to-continuum limits for strain-alignment-coupled systems:Magnetostrictive solids, ferroelectric crystals and nematicelastomers[J]. Networks and Heterogeneous Media, 2009, 4(4): 667-708. doi: 10.3934/nhm.2009.4.667

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  • In the framework of linear elasticity, we study the limit of a class of discrete free energies modeling strain-alignment-coupled systems by a rigorous coarse-graining procedure, as the number of molecules diverges. We focus on three paradigmatic examples: magnetostrictive solids, ferroelectric crystals and nematic elastomers, obtaining in the limit three continuum models consistent with those commonly employed in the current literature. We also derive the correspondent macroscopic energies in the presence of displacement boundary conditions and of various kinds of applied external fields.


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    5. Pierluigi Cesana, Nematic Elastomers: Gamma-Limits for Large Bodies and Small Particles, 2011, 43, 0036-1410, 2354, 10.1137/100795619
    6. Pierluigi Cesana, Relaxation of Multiwell Energies in Linearized Elasticity and Applications to Nematic Elastomers, 2010, 197, 0003-9527, 903, 10.1007/s00205-009-0283-0
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  • © 2009 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)
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