Crystal plasticity with JacobianFree Newton–Krylov
 K. Chockalingam,
 M. R. Tonks,
 J. D. Hales,
 D. R. Gaston,
 P. C. Millett,
 Liangzhe Zhang
 … show all 6 hide
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The objective of this work is to study potential benefits of solving crystal plasticity finite element method (CPFEM) implicit simulations using the JacobianFree Newton–Krylov (JFNK) technique. Implicit implementations of CPFEM are usually solved using Newton’s method. However, the inherent nonlinearity in the flow rule model that characterizes the crystal slip system deformation on occasions would require considerable effort to form the exact analytical Jacobian needed by Newton’s method. In this paper we present an alternative using JFNK. As it does not require an exact Jacobian, JFNK can potentially decrease development time. JFNK approximates the effect of the Jacobian through finite differences of the residual vector, allowing modified formulations to be studied with relative ease. We show that the JFNK solution is identical to that obtained using Newton’s method and produces quadratic convergence. We also find that preconditioning the JFNK solution with the elastic tensor provides the best computational efficiency.
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 Title
 Crystal plasticity with JacobianFree Newton–Krylov
 Journal

Computational Mechanics
Volume 51, Issue 5 , pp 617627
 Cover Date
 20130501
 DOI
 10.1007/s0046601207417
 Print ISSN
 01787675
 Online ISSN
 14320924
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 Crystal plasticity
 JFNK
 Nonlinear
 Implicit methods
 Industry Sectors
 Authors

 K. Chockalingam ^{(1)}
 M. R. Tonks ^{(1)}
 J. D. Hales ^{(1)}
 D. R. Gaston ^{(1)}
 P. C. Millett ^{(1)}
 Liangzhe Zhang ^{(1)}
 Author Affiliations

 1. Fuel Modeling and Simulation, Idaho National Laboratory, P.O. Box 1625, Idaho Falls, ID, 834153840, USA