Algorithmic tangent stiffness in elastoplasticity and elastoviscoplasticity: A geometric insight

The algorithmic, or consistent, tangent stiffness was introduced to improve the asymptotic convergence rate of the iterative correction algorithm for the evolutive analysis of elastoplastic structures. The original approach is based on a formulation of the elastoplastic law in terms of a plastic multiplier with an analysis which, in general, requires an operator inversion. A geometric description of the method, based on hypersurface theory, is proposed here to provide a clear picture of the algorithmic properties. An estimate of the tangent stiffness associated with finite step elastoplastic and elastoviscoplastic constitutive models is given. It is based on the properties of the projection operator on the elastic domain and avoids operator inversions retaining the beneficial properties of the original one.