A scheme of automatic stress-updating on yield surfaces for a class of elastoplastic models

•A return-free integration is proposed for a large class of elastoplastic models. The return-free integration updates stress points on the yield surface automatically.•The return-free capability is guaranteed by the theory of Lie algebra and Lie group.•The accuracy of the return-free integration is demonstrated numerically.

For a large class of elastoplastic models, the present paper proposes an integration scheme which updates stress points on yield surfaces automatically. Associated plastic flow models with the rules of kinematic, isotropic, and distortional hardening/softening are contained in the model class. The underlying structure of the class of elastoplastic models is exposed and utilized to develop the return-free integration scheme that keeps the stress points on the yield surfaces without any extra enforcement. The return-free capability of the integration scheme is underpinned by the theory of Lie group and Lie algebra. Numerical demonstrations show that the stress points are updated on the yield surfaces automatically and exactly within the machinery round-off error.