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 stress es with respect to the change in total deformation. They serve as iter ation operators by application of Newton-type solvers for the iterativ e solution of non-linear initial-boundary-value problems in finite ine lasticity. The underlying concept of the numerical computation is a pe rturbation technique based on a forward difference approximation which reduces the computation of the tangent moduli to a multiple stress co mputation. The algorithmic procedure is material-independent and surpr isingly simple. It is outlined for a Lagrangian, as well as an Euleria n geometric setting and applied to model problems of finite elasticity and finite elastoplasticity.