Past Event: Oden Institute Seminar

Riemann-Cartan Geometry of Nonlinear Dislocation Mechanics

Arash Yavari, Civil Engineering & Environmental Engineering, Georgia Institute of Technology

Abstract

In this talk we will show that the mechanics of solids with distributed dislocations can be formulated as a nonlinear elasticity problem provided that the material manifold is chosen appropriately. Choosing a Weitzenböck manifold 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 results of exact calculations of the residual stress fields for several distributed dislocations in incompressible nonlinear elastic solids using Cartan's moving frames. In addition to this, we will clarify the geometric definition of Burgers vector in term of affine development of closed curves in the Weitzenböck material manifold, and will 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 (Applied Mechanics option with minor in Mathematics) from the California Institute of Technology in 2005.