Numerical implementation of constitutive integration for rate-independent elastoplasticity

In this paper, constitutive integration for rate-independent, small deformation elastoplasticity is studied. Smooth yield surfaces and work/strain hardening are assumed. Both associative or non-associative flow rules are considered. An Euler backward algorithm is applied for constitutive integration. Tangent moduli that are consistent with the Euler backward algorithm, i.e. a so-called consistent tangent operator, are derived. Emphasis is placed on numerical implementation of the Eular backward algorithm into finite element codes using such a consistent tangent operator. In particular, a commercial code ANSYS is considered. Numerical examples, including materials sensitive and insensitive to hydrostatic stress, are used for the verification of the implementation. A comparison of the algorithmic performance to an explicit Euler forward algorithm is given and the superiority of the Euler backward algorithm is demonstrated.The work described in the present paper has been sponsored by The Research Council of Norway, The North Calotte Education and Research Council, Statoil and Norsk Hydro.