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Maseeh Colloquium: Riemann-Cartan Geometry and the Nonlinear Mechanics of Distributed Dislocations
Friday, March 1, 2013 - 3:15pm

The Maseeh Mathematics and Statistics Colloquium Series* 

Arash Yavari, Ph.D.
School of Civil and Environmental Engineering, Georgia Institute of Technology

Riemann-Cartan Geometry and the Nonlinear Mechanics of Distributed Dislocations

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.

Friday, March 1st, 2013 at 3:15pm 
Urban Center room 204
(Refreshments served at 2:45 in presentation room)

* 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.