TY - JOUR
T1 - Exact Constructions in the (Non-linear) Planar Theory of Elasticity
T2 - From Elastic Crystals to Nematic Elastomers
AU - Cesana, Pierluigi
AU - Della Porta, Francesco
AU - Rüland, Angkana
AU - Zillinger, Christian
AU - Zwicknagl, Barbara
N1 - Funding Information:
P.C. is supported by JSPS Grant-in-Aid for Young Scientists (B) 16K21213 and partially by JSPS Innovative Area Grant 19H05131. P.C. holds an honorary appointment at La Trobe University and is a member of GNAMPA. C.Z. acknowledges a travel grant from the Simon’s foundation. B.Z. would like to thank Sergio Conti for helpful discussions, and acknowledges support by the Berliner Chancengleichheitsprogramm and by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through SFB 1060 “The Mathematics of Emergent Effects” (Project 211504053).
Funding Information:
P.C. is supported by JSPS Grant-in-Aid for Young Scientists (B) 16K21213 and partially by JSPS Innovative Area Grant 19H05131. P.C. holds an honorary appointment at La Trobe University and is a member of GNAMPA. C.Z. acknowledges a travel grant from the Simon’s foundation. B.Z. would like to thank Sergio Conti for helpful discussions, and acknowledges support by the Berliner Chancengleichheitsprogramm and by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through SFB 1060 “The Mathematics of Emergent Effects” (Project 211504053).
Publisher Copyright:
© 2020, Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2020/7/1
Y1 - 2020/7/1
N2 - In this article we deduce necessary and sufficient conditions for the presence of “Conti-type”, highly symmetric, exactly stress-free constructions in the geometrically non-linear, planar n-well problem, generalising results of Conti et al. (Proc R Soc A 473(2203):20170235, 2017). Passing to the limit n→ ∞, this allows us to treat solid crystals and nematic elastomer differential inclusions simultaneously. In particular, we recover and generalise (non-linear) planar tripole star type deformations which were experimentally observed in Kitano and Kifune (Ultramicroscopy 39(1–4):279–286, 1991), Manolikas and Amelinckx (Physica Status Solidi (A) 60(2):607–617, 1980; Physica Status Solidi (A) 61(1):179–188, 1980). Furthermore, we discuss the corresponding geometrically linearised problem.
AB - In this article we deduce necessary and sufficient conditions for the presence of “Conti-type”, highly symmetric, exactly stress-free constructions in the geometrically non-linear, planar n-well problem, generalising results of Conti et al. (Proc R Soc A 473(2203):20170235, 2017). Passing to the limit n→ ∞, this allows us to treat solid crystals and nematic elastomer differential inclusions simultaneously. In particular, we recover and generalise (non-linear) planar tripole star type deformations which were experimentally observed in Kitano and Kifune (Ultramicroscopy 39(1–4):279–286, 1991), Manolikas and Amelinckx (Physica Status Solidi (A) 60(2):607–617, 1980; Physica Status Solidi (A) 61(1):179–188, 1980). Furthermore, we discuss the corresponding geometrically linearised problem.
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U2 - 10.1007/s00205-020-01511-9
DO - 10.1007/s00205-020-01511-9
M3 - Article
AN - SCOPUS:85083495228
SN - 0003-9527
VL - 237
SP - 383
EP - 445
JO - Archive for Rational Mechanics and Analysis
JF - Archive for Rational Mechanics and Analysis
IS - 1
ER -