A canonical form return mapping algorithm for rate independent plasticity

Abstract

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.