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complex bodies

ESAIM: Control, Optimisation and Calculus of Variations (1)

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Ground states in complex bodies
Paolo Maria Mariano, Giuseppe Modica
Journal:

ESAIM: Control, Optimisation and Calculus of Variations / Volume 15 / Issue 2 / April 2009

Published online by Cambridge University Press:

30 May 2008, pp. 377-402

Print publication:

April 2009
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A unified framework for analyzing the existence of ground states in wideclasses of elastic complex bodies is presented here. The approach makes useof classical semicontinuity results, Sobolev mappings and Cartesiancurrents. Weak diffeomorphisms are used to represent macroscopicdeformations. Sobolev maps and Cartesian currents describe the innersubstructure of the material elements. Balance equations for irregularminimizers are derived. A contribution to the debate about the role of thebalance of configurational actions follows. After describing a list ofpossible applications of the general results collected here, a concretediscussion of the existence of ground states in thermodynamically stablequasicrystals is presented at the end.