Efficient iteration schemes for anisotropic hyperelasto‐plasticity

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AbstractNumerical 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. Copyright © 2005 John Wiley & Sons, Ltd.