CMU Campus
Center for                           Nonlinear Analysis
CNA Home People Seminars Publications Workshops and Conferences CNA Working Groups CNA Comments Form Summer Schools Summer Undergraduate Institute PIRE Cooperation Graduate Topics Courses SIAM Chapter Seminar Positions Contact
Publication 19-CNA-013

Finite Element Approximation of Finite Deformation Dislocation Mechanics

Rajat Arora
Dept. of Civil & Environmental Engineering
Carnegie Mellon University
Pittsburgh, PA 15213
rarora1@andrew.cmu.edu

Xiaohan Zhang
Salesforce.com
Sunnyvale, CA, 94086
xiaohanzhang.cmu@gmail.com

Amit Acharya
Dept. of Civil & Environmental Engineering
Center for Nonlinear Analysis
Carnegie Mellon University
Pittsburgh, PA 15213
acharyaamit@cmu.edu

Abstract: We develop and demonstrate the first general computational tool for finite deformation static and dynamic dislocation mechanics. A finite element formulation of finite deformation (Mesoscale) Field Dislocation Mechanics theory is presented. The model is a minimal enhancement of classical crystal/J2 plasticity that fundamentally accounts for polar/excess dislocations at the mesoscale. It has the ability to compute the static and dynamic finite deformation stress fields of arbitrary (evolving) dislocation distributions in finite bodies of arbitrary shape and elastic anisotropy under general boundary conditions. This capability is used to present a comparison of the static stress fields, at finite and small deformations, for screw and edge dislocations, revealing heretofore unexpected differences. The computational framework is verified against the sharply contrasting predictions of geometrically linear and nonlinear theories for the stress field of a spatially homogeneous dislocation distribution in the body, as well as against other exact results of the theory. Verification tests of the time-dependent numerics are also presented. Size effects in crystal and isotropic versions of the theory are shown to be a natural consequence of the model and are validated against available experimental data. With inertial effects incorporated, the development of an (asymmetric) propagating Mach cone is demonstrated in the finite deformation theory when a dislocation moves at speeds greater than the linear elastic shear wave speed of the material.

Get the paper in its entirety as  19-CNA-013.pdf


«   Back to CNA Publications