Numerical computation of algorithmic (consistent) tangent moduli in large-strain computational inelasticity

An algorithm for the numerical computation of so-called algorithmic or consistent tangent moduli in finite inelasticity is presented. These moduli determine the sensitivity of algorithmic expressions for stresses with respect to the change in total deformation. They serve as iteration operators by application of Newton-type solvers for the iterative solution of non-linear initial-boundary-value problems in finite inelasticity. The underlying concept of the numerical computation is a perturbation technique based on a forward difference approximation which reduces the computation of the tangent moduli to a multiple stress computation. The algorithmic procedure is material-independent and surprisingly simple. It is outlined for a Lagrangian, as well as an Eulerian geometric setting and applied to model problems of finite elasticity and finite elastoplasticity.