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CNA Seminar/Colloquium/Joint Pitt-CNA Colloquium
Peter Gladbach
Carnegie Melllon University
Title: The phase-field model of dislocations: Interaction between parallel slip planes

Abstract: We investigate the extension of the Peierls-Nabarro model of crystallographic slip to single crystals containing parallel active slip planes, which couples a core energy with long-range elastic interaction.

In the limit as core size and slip plane distance tend to zero, we show that the limit energy, in the sense of Gamma-convergence, is concentrated on dislocations, which are one-dimensional topological crystal defects. Unlike earlier work, the limit energy for multiple planes features interaction between parallel dislocation lines, leading to multiscale microstructure under minimization.

We showcase some multiscale techniques for nonlocal $H^{1/2}$ type energies with logarithmic divergence, such as iterated mollification and ball construction methods as introduced by Jerrard, Sandier, and Serfaty.

Recording: http://mm.math.cmu.edu/recordings/cna/PeterGladbach_small.mp4
Date: Thursday, October 20, 2016
Time: 1:30 pm
Location: Wean Hall 7218
Submitted by:  Ian Tice