Riv. Mat. Univ. Parma, Vol. 9, No. 2, 2018
Ilaria Lucardesi, ^{[a]}
Marco Morandotti, ^{[b]}
Riccardo Scala, ^{[c]}
and
Davide Zucco ^{[b]}
Confinement of dislocations inside a crystal with a prescribed external strain
Pages: 283327
Received: 19 July 2018
Accepted: 2 October 2018
Mathematics Subject Classification (2010): 74E15, (35J25, 74B05, 49J40, 31A05).
Keywords: Dislocations, core radius approach, harmonic functions, divergencemeasure fields.
Authors address:
[a]: Institut Élie Cartan de Lorraine, B.P. 70239, 54506 VandoeuvrelèsNancy, France
[b]: Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy
[c]: Sapienza, Università di Roma, Piazzale Aldo Moro 5, 00185 Roma, Italy
Full Text (PDF)
Abstract:
A system of \(n\) screw dislocations in an isotropic crystal undergoing antiplane shear is studied in the framework of linear elasticity.
Imposing a suitable boundary condition for the strain, namely requesting the nonvanishing of its boundary integral, results in a confinement effect.
More precisely, in the presence of an external strain with circulation equal to \(n\) times the lattice spacing,
it is energetically convenient to have \(n\) distinct dislocations lying inside the crystal.
The result is obtained by formulating the problem via the core radius approach and by studying the asymptotics as the core size vanishes.
An iterative scheme is devised to prove the main result.
This work sets the basis for studying the upscaling problem, i.e., the limit as \(n\to\infty\), which is treated in [17].
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