Upscaling of screw dislocations with increasing tangential strain
Ilaria Lucardesi
Université de Lorraine, Vandœuvre-lès-Nancy, FranceMarco Morandotti
Politecnico di Torino, ItalyRiccardo Scala
Università di Siena, ItalyDavide Zucco
Università di Torino, Italy
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Abstract
The upscaling of a system of screw dislocations in a material subject to an external strain is studied. The -limit of a suitable rescaling of the renormalized energy is characterized in the space of probability measures. This corresponds to a discrete-to-continuum limit of the dislocations, which, as a byproduct, provides information on their distribution when the circulation of the tangential component of the external strain becomes larger and larger. Specifically, for particular choices of the limiting external strain, dislocations are shown to concentrate at the boundary of the material and to distribute as the limiting external strain.
Cite this article
Ilaria Lucardesi, Marco Morandotti, Riccardo Scala, Davide Zucco, Upscaling of screw dislocations with increasing tangential strain. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 31 (2020), no. 2, pp. 421–445
DOI 10.4171/RLM/898