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Purpose The purpose of this paper is to suggest a robust hybrid method for updating the stress and plastic internal variables in plasticity considering damage mechanics. Design/methodology/approach By benefiting the properties of the well-known explicit and implicit integrations, a new mixed method is derived. In fact, the advantages of the mentioned techniques are used to achieve an efficient integration. Findings The numerical studies demonstrate the high precision and robustness of the suggested algorithm. Research limitations The perfect von-Mises plasticity together with Lemaitre damage model is considered within the realm of small deformations. Practical implications Updating stress and plastic internal variables are of utmost importance in elastoplastic analyses of structures. The accuracy and efficiency of stress-updating methods significantly affect the final outcomes of nonlinear analyses. Originality/value The idea which is used to derive the hybrid method leads to an efficient integration method for updating the constitutive equations of the damage mechanics.

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