Efficient iteration schemes for anisotropic hyperelasto-plasticity

Numerical issues arising when integrating hyperelasto-plastic constitutive equations with elastic anisotropy, stemming from anisotropic damage, and plastic anisotropy as represented by kinematic hardening are discussed. In particular, solution algorithms for the corresponding non-linear system of equations due to implicit integration algorithms are addressed. It is shown that algorithms like staggered iteration and quasi-Newton techniques are superior to a pure Newton technique when the cpu time is compared. However, the drawback of the staggered and the quasi-Newton technique is that rather small time steps must be taken to ensure convergence, which can be of importance when applying complex constitutive models in a finite element programme