# Events

Maseeh Colloquium: Riemann-Cartan Geometry and the Nonlinear Mechanics of Distributed Dislocations

Friday, March 1, 2013 - 3:15pm

Maseeh Colloquium: Riemann-Cartan Geometry and the Nonlinear Mechanics of Distributed Dislocations

Friday, March 1, 2013 - 3:15pm

presents

Arash Yavari, Ph.D.

School of Civil and Environmental Engineering, Georgia Institute of Technology

Riemann-Cartan Geometry and the Nonlinear Mechanics of Distributed Dislocations

ABSTRACT

In this seminar we will show that the nonlinear mechanics of solids with distributed dislocations can be formulated as a nonlinear elasticity problem provided that the material manifold – where the body is stress-free − is chosen appropriately. Choosing a Weitzenböck manifold (a manifold with a flat and metric-compatible affine connection that has torsion) with torsion tensor identified with the given dislocation density tensor the body would be stress-free in the material manifold by construction. For classical nonlinear elastic solids in order to calculate stresses one needs to know the changes of the relative distances, i.e. a metric in the material manifold is needed. For distributed dislocations this metric is the metric compatible with the Weitzenböck connection. We will present exact solutions for the residual stress field of several distributed dislocation problems in incompressible nonlinear elastic solids using Cartan's method of moving frames. We will also discuss zero-stress dislocation distributions in nonlinear dislocation mechanics.

* Sponsored by the Maseeh Mathematics and Statistics Colloquium Series Fund and the Fariborz Maseeh Department of Mathematics & Statistics, PSU. This event is free and open to the public.