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research
On the variational limits of lattice energies on prestrained elastic bodies
Authors
A Braides
A Rodriguez
+21Â more
A Schloemerkemper
B Dacorogna
B Schmidt
B Schmidt
Ch Ortner
D Caillerie
H Brezis
H Dret Le
H Liang
H Liang
J Bourgain
J Dervaux
M Espanol
M Lewicka
P-S Jouk
R Alicandro
R Alicandro
R Alicandro
R Kupferman
T Mengesha
Y Klein
Publication date
10 August 2014
Publisher
Doi
Cite
View
on
arXiv
Abstract
We study the asymptotic behaviour of the discrete elastic energies in presence of the prestrain metric
G
G
G
, assigned on the continuum reference configuration
Ω
\Omega
Ω
. When the mesh size of the discrete lattice in
Ω
\Omega
Ω
goes to zero, we obtain the variational bounds on the limiting (in the sense of
Γ
\Gamma
Γ
-limit) energy. In case of the nearest-neighbour and next-to-nearest-neibghour interactions, we derive a precise asymptotic formula, and compare it with the non-Euclidean model energy relative to
G
G
G
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Last time updated on 01/04/2019
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