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Integration of nonlinear mixed hardening models

Mohammad Rezaiee‐Pajand (Department of Civil Engineering, Ferdowsi University of Mashhad, Mashhad, Iran)
Cyrus Nasirai (Department of Civil Engineering, Islamic Azad University – Mashhad Branch, Mashhad, Iran)
Mehrzad Sharifian (Department of Civil Engineering, Ferdowsi University of Mashhad, Mashhad, Iran)

Multidiscipline Modeling in Materials and Structures

ISSN: 1573-6105

Article publication date: 27 September 2011




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.

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.


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.



Rezaiee‐Pajand, M., Nasirai, C. and Sharifian, M. (2011), "Integration of nonlinear mixed hardening models", Multidiscipline Modeling in Materials and Structures, Vol. 7 No. 3, pp. 266-305.



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Copyright © 2011, Emerald Group Publishing Limited

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