The upscaling of a system of screw dislocations in a material subject to an external strain is studied. The Gamma-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.
Upscaling of screw dislocations with increasing tangential strain
Marco Morandotti;Davide Zucco
2020-01-01
Abstract
The upscaling of a system of screw dislocations in a material subject to an external strain is studied. The Gamma-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.File | Dimensione | Formato | |
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