Woodruff School of Mechanical Engineering
Riemann-Cartan Geometry of Nonlinear Dislocation Mechanics
Dr. Arash Yavari
School of Civil and Environmental Engineering, Georgia Tech
Thursday, April 12, 2012 at 11:00:00 AM
MRDC Building, Room 4211
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.
Dr. Yavari is an Associate Professor in the School of Civil and Environmental Engineering at the Georgia Institute of Technology. He received his B.S. in Civil Engineering from Sharif University of Technology, Tehran, Iran in 1997. He continued his studies at the George Washington University where he obtained an M.S. in Mechanical Engineering in 2000. He then moved to Pasadena, CA and obtained his Ph.D. in Mechanical Engineering (with minor in Mathematics) from the California Institute of Technology in 2005.