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A canonical form return mapping algorithm for rate independent plasticity
Author(s) -
Keavey M. A.
Publication year - 2001
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.350
Subject(s) - mathematics , jacobian matrix and determinant , lagrange multiplier , algorithm , canonical form , ordinary differential equation , rate of convergence , simple (philosophy) , constraint algorithm , state variable , mathematical optimization , differential equation , computer science , mathematical analysis , pure mathematics , channel (broadcasting) , computer network , philosophy , physics , epistemology , thermodynamics
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 & Sons, Ltd.