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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.

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.

The numerical studies demonstrate the high precision and robustness of the suggested algorithm.

The perfect von-Mises plasticity together with Lemaitre damage model is considered within the realm of small deformations.

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.

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.

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.

Women Entrepreneurship has received increasing attention over the past decade. In particular, a new area dealing with women entrepreneurs in the developing societies. The aim of this study is how is women entrepreneurship in developing economies? More specifically, we are excavating various questions at the individual and institutional level. The results of this study contribute to understanding the importance of the context on women entrepreneurs’ activities. Additionally, it systematically provides a comprehensive framework at multilevel analyses to cover all aspects of women entrepreneurship in developing countries. Ultimately, knowing women entrepreneurship in developing countries helps policymakers provide a firm ground for self-employment of women.