Discrete-to-continuum limits for strain-alignment-coupled systems: Magnetostrictive solids, ferroelectric crystals and nematic elastomers | Zendy

Marco Cicalese | Zendy; Antonio DeSimone | Zendy; Caterina Ida Zeppieri | Zendy

Open Access

Discrete-to-continuum limits for strain-alignment-coupled systems: Magnetostrictive solids, ferroelectric crystals and nematic elastomers

Author(s) -

Marco Cicalese,

Antonio DeSimone,

Caterina Ida Zeppieri

Publication year - 2009

Publication title -

networks and heterogeneous media

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.732

H-Index - 34

eISSN - 1556-181X

pISSN - 1556-1801

DOI - 10.3934/nhm.2009.4.667

Subject(s) - liquid crystal , elasticity (physics) , elastomer , magnetostriction , limit (mathematics) , ferroelectricity , materials science , ferromagnetism , displacement (psychology) , classical mechanics , condensed matter physics , linear elasticity , physics , mathematical analysis , mathematics , quantum mechanics , thermodynamics , magnetic field , finite element method , composite material , psychology , dielectric , psychotherapist

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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