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Forces on dislocations lines in three dimensions

Banff International Research Station for Mathematical Innovation and Discovery

In this talk we discuss the equilibrium problem for a curved dislocation line in a three-dimensional domain. As the core radius tends to zero, we derive an asymptotic expression to characterize the induced elastic energy. We then obtain the force on the dislocation line as the variation of this expression and identify the highest order terms explicitly. As a main ingredient, we present an explicit asymptotic formula for the induced elastic strain which depends on the curvature of the dislocation line and thus highlights the difference with existing work on straight dislocation lines.

Mathematics; Calculus of variations and optimal control; optimization; Partial differential equations

video/mp4

Author affiliation: Carnegie Mellon University

2019-03-21

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/69003

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/