Document ESAIM: COCV
DOI: 10.1051/cocv:2008036
Ground states in complex bodies
Paolo Maria Mariano1 and Giuseppe Modica21 DICeA, University of Florence, via Santa Marta 3, 50139 Firenze, Italy; paolo.mariano@unifi.it
2 Dipartimento di Matematica Applicata "G. Sansone", University of Florence, via Santa Marta 3, 50139 Firenze, Italy; giuseppe.modica@unifi.it
Received November 8, 2007. Revised January 17, 2008. Published online May 30, 2008.
Abstract
A unified framework for analyzing the existence of ground states in wide
classes of elastic complex bodies is presented here. The approach makes use
of classical semicontinuity results, Sobolev mappings and Cartesian
currents. Weak diffeomorphisms are used to represent macroscopic
deformations. Sobolev maps and Cartesian currents describe the inner
substructure of the material elements. Balance equations for irregular
minimizers are derived. A contribution to the debate about the role of the
balance of configurational actions follows. After describing a list of
possible applications of the general results collected here, a concrete
discussion of the existence of ground states in thermodynamically stable
quasicrystals is presented at the end.
Mathematics Subject Classification. 74A30, 49J45, 74A60, 49Q15, 74A99
Key words: Cartesian currents, complex bodies, ground states, multifield theories
© EDP Sciences, SMAI 2008