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SUMMARY:Explicit integral representations of the relaxation of non-local e
 nergies for  structured deformations - Jose Matias (Instituto Superior Té
 cnico\, Lisboa)
DTSTART:20190619T141000Z
DTEND:20190619T145000Z
UID:TALK126535@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:The theory of structured deformations in the SBV setting devel
 oped by Chocki &amp\; Fonseca [1]<br>only takes into account the linear de
 pendance on jumps along the approximating sequences. Following a<br>model 
 from Del Piero &amp\; Owen [2] that captures the non-linear dependence on 
 jumps\, the present approach<br>to relaxation of non-local energies rests 
 on two limiting processes: start from a submacroscopical level<br>where we
  have a weighted average of disarrangements within neighborhoods of fixed 
 size r &gt\; 0 and pass to<br>the macrolevel\, permitting disarrangements 
 to diffuse through such a neighborhood. This limiting process<br>determine
 s a structured deformation as well as the non-local dependence of the ener
 gy density of such a<br>structured deformation. Pass to the limit as r ! 0
 \, to obtain purely local bulk and interfacial energy<br>densities for the
  structured deformation identified in the first step.<br>This is a joint w
 ork with<br>Marco Morandotti\, Dipartimento di Scienze Matematiche &ldquo\
 ;G. L. Lagrange&rdquo\;\, Politecnico di Torino\,<br>David R. Owen\, Depar
 tment of Mathematical Sciences\, Carnegie Mellon University\,<br>Elvira Za
 ppale\, Dipartimento di Ingegneria Industriale\, Universit&agrave\; degli 
 Studi di Salerno.<br>References<br>[1] R. Choksi and I. Fonseca: Bulk and 
 interfacial energy densities for structured deformations of continua. Arch
 . Rational<br>Mech. Anal. 138 (1997)\, 37-103.<br>[2] G. Del Piero and D. 
 R. Owen: Structured Deformations: Part Two. Quaderni<br><br>
LOCATION:Seminar Room 2\, Newton Institute
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