Purpose – The purpose of this paper is to present a new effective integration method for cyclic plasticity models. Design/methodology/approach – 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. Findings – The numerical tests show the robustness and high efficiency of the proposed integration scheme. Research limitations/implications – 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. Practical implications – 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. Originality/value – 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.

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