A canonical form return mapping algorithm for rate independent plasticity

Keavey, M. A.

Abstract

A canonical form for the representation of elastic predictor radial return plasticity algorithms is presented which is deceptive in its simplicity. Iterative application of the corrector is in a form used universally in the solution of ordinary differential equations and substitution of different yield functions and state variable evolution equations is trivial. The consistency condition is maintained by an additional constraint equation via what is, in effect, a Lagrange multiplier. A consistent material Jacobian may be obtained automatically by applying partial elimination to the same set of equations. The process is numerical and requires no additional algebraic manipulation. To demonstrate the validity of such a simple technique, existing, apparently more complex, formulations are derived through the simple expedient of static condensation. As a practical example of the application of the method, a standard von Mises plasticity model is implemented and results are presented for two standard benchmarks that test quadratic convergence for large increments. Copyright © 2001 John Wiley and Sons, Ltd.

• Journal Article Type: Article
• Publication Date: Feb 28, 2002
• Journal: International Journal for Numerical Methods in Engineering
• Print ISSN: 0029-5981
• Electronic ISSN: 1097-0207
• Publisher: Wiley
• Peer Reviewed: Not Peer Reviewed
• Volume: 53
• Issue: 6
• Pages: 1491-1510
• DOI: https://doi.org/10.1002/nme.350
• Keywords: plasticity, return mapping algorithms, constitutive equations
• Public URL: https://uwe-repository.worktribe.com/output/1079344
• Publisher URL: http://dx.doi.org/10.1002/nme.350
• Additional Information: Additional Information : Provides automatic and accurate calculation of material Jacobian for implicit finite element codes allowing straightforward implementation of complex constitutive models where Jacobian previously had to be derived by hand. Prompted invitation to become visiting research fellow in Dept. of Materials Engineering, Open University, contact Prof L Edwards. Based on previous research supported by British Energy (Barnwood, Glos contacts P J Bouchard, Dr R A Ainsworth) and Magnox Electric Berkeley, contact Dr P J Flewitt). Immediate application is simulation of the welding process with annealing and solid state phase transformation in ferritic steels, of interest to the European nuclear industry.