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

We present a general approach to the derivation of the explicit expression of tangent operators, consistent with the finite-step integration schemes of the flow rule, for rate-independent elastoplastic models with mixed hardening. By exploiting the model of generalized standard material, we show that the algorithmic tangent operator can be obtained by inverting a suitable positive definite matrix. Use of the Sherman-Morrison-Woodbury formula allows 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 implementation. The application of the proposed approach to the von Mises yield criterion with linear kinematic and isotropic hardening shows that the closed-form expression of the operator can be obtained by a straightforward procedure.