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Complex nonlinear unloading behavior following plastic deformation on metals has been observed by researchers. However, a constant chord modulus has been used by most of the researchers to describe the unloading behavior. In this study, a new hypoelastic model is proposed in order to describe this complex nonlinear behavior. The elastic modulus is assumed to be the initial Young’s modulus at the beginning of each loading reversal and is exponentially decreased with the elastic deformation and finally saturates to a particular value at the start of plastic deformation. The model can be easily utilized in any plasticity constitutive law. Furthermore, its numerical implementation is fairly straightforward. As an example, a simple constitutive law was developed using the von-Mises yield function, isotropic hardening law and the proposed hypoelastic model. This constitutive law was implemented into ABAQUS commercial package via a user material subroutine UMAT. A comparison between the experimental response of DP980 and its simulated response showed that the model is able to describe the material response fairly well.

Keywords: constitutive law, Nonlinear Unloading Behavior, Elastic Modulus Variation, Hypoelastic Model

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