Upscaling of screw dislocations with increasing tangential strain
Ilaria LucardesiUniversité de Lorraine, Vandœuvre-lès-Nancy, France
Marco MorandottiPolitecnico di Torino, Italy
Riccardo ScalaUniversità di Siena, Italy
Davide ZuccoUniversità di Torino, Italy
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. 421–445DOI 10.4171/RLM/898