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The purpose of this paper is to present a new effective integration method for cyclic plasticity models.

By defining an integrating factor and an augmented stress vector, the system of differential equations of the constitutive model is converted into a nonlinear dynamical system, which could be solved by an exponential map algorithm.

The numerical tests show the robustness and high efficiency of the proposed integration scheme.

The von‐Mises yield criterion in the regime of small deformation is assumed. In addition, the model obeys a general nonlinear kinematic hardening and an exponential isotropic hardening.

Integrating the constitutive equations in order to update the material state is one of the most important steps in a nonlinear finite element analysis. The accuracy of the integration method could directly influence the result of the elastoplastic analyses.

The paper deals with integrating the constitutive equations in a nonlinear finite element analysis. This subject could be interesting for the academy as well as industry. The proposed exponential‐based integration method is more efficient than the classical strategies.

This paper aims to provide a more rapid stress updating algorithm for von‐Mises plasticity with mixed‐hardening and to compare it with the previous works.

An augmented stress vector is defined. This can convert the original nonlinear differential equation system to a quasi‐linear one. Then the dynamical system can be solved with an exponential map approach in a semi‐implicit manner.

The presented stress updating algorithm gives very accurate results and it has a quadratic convergence rate.

Von‐Mises plasticity in a small strain regime is considered. Furthermore, the material is supposed to have linear hardening.

Stress updating is the heart of a nonlinear finite element analysis due to the large consumption of computation time. The efficiency and accuracy of the calculations of nonlinear finite element analysis are strongly influenced by the efficiency and accuracy of stress updating schemes.

The paper offers a new stress updating strategy based on exponential maps. This may be used as a routine in a nonlinear finite element analysis software to enhance its performance.