Title: Homogenization of edge dislocations via de-Rham currents
Abstract: Edge dislocations are material defects: atomic discrepancies in a material lattice structure. In this talk, we present a geometric model for edge-dislocations using (layering) 1-forms and their singular counterparts, de-Rham currents. Isolated edge-dislocations are represented by 1-forms which are smooth and closed outside a singularity segment. A smooth distribution of dislocations is represented by a (globally) smooth non-closed 1-form. We prove an homogenization result for edge dislocations; every smooth distribution of dislocations is a limit (in the sense of currents) of arrays of isolated dislocations. We also define the notion of singular torsion and study its relation to the defect structure and homogenization process.
This is a joint work with Raz Kupferman.