Calculus of Variations and Geometric Measure Theory

M. Cicalese - A. DeSimone - C. I. Zeppieri

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

created by cicalese on 18 Feb 2008
modified on 08 Mar 2010


Published Paper

Inserted: 18 feb 2008
Last Updated: 8 mar 2010

Journal: Networks and Heterogeneous Media
Volume: 4
Number: 4
Pages: 667-708
Year: 2009


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, nematic elastomers, magnetostrictive solids, ferroelectric crystals