Original Paper

Computational Mechanics

, Volume 51, Issue 5, pp 617-627

Crystal plasticity with Jacobian-Free Newton–Krylov

  • K. ChockalingamAffiliated withFuel Modeling and Simulation, Idaho National Laboratory Email author 
  • , M. R. TonksAffiliated withFuel Modeling and Simulation, Idaho National Laboratory
  • , J. D. HalesAffiliated withFuel Modeling and Simulation, Idaho National Laboratory
  • , D. R. GastonAffiliated withFuel Modeling and Simulation, Idaho National Laboratory
  • , P. C. MillettAffiliated withFuel Modeling and Simulation, Idaho National Laboratory
  • , Liangzhe ZhangAffiliated withFuel Modeling and Simulation, Idaho National Laboratory

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Abstract

The objective of this work is to study potential benefits of solving crystal plasticity finite element method (CPFEM) implicit simulations using the Jacobian-Free Newton–Krylov (JFNK) technique. Implicit implementations of CPFEM are usually solved using Newton’s method. However, the inherent non-linearity 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.

Keywords

Crystal plasticity JFNK Nonlinear Implicit methods