Discrete-to-continuum limits for strain-alignment-coupled systems:
Magnetostrictive solids, ferroelectric crystals and nematic
Marco Cicalese - Dipartimento di Matematica e Applicazioni "R. Caccioppoli”, Università di Napoli Federico II, Via Cintia, 80126 Napoli, Italy (email)
Abstract: 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.
Keywords: $\Gamma$-convergence, discrete systems, linear elasticity, liquid
crystals, magnetostrictive solids, ferroelectric crystals, nematic
Received: January 2009; Revised: June 2009; Available Online: October 2009.
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