A general approach to the evaluation of consistent tangent operators for rate-independent elastoplasticity

We present a general approach to the derivation of the explicit expression of tangent operators, consistent with the finite-step integration schemes o f the flow rule, for rate-independent elastoplastic models with mixed harde ning. By exploiting the model of generalized standard material, we show tha t the algorithmic tangent operator can be obtained by inverting a suitable positive definite matrix. Use of the Sherman-Morrison-Woodbury formula allo ws us to reduce to a half the burden associated with such inversion and to derive an expression of the consistent tangent operator prone to computer i mplementation. The application of the proposed approach to the von Mises yi eld criterion with linear kinematic and isotropic hardening shows that the closed-form expression of the operator can be obtained by a straightforward procedure. (C) 1998 Elsevier Science S.A. All rights reserved.