Abstract

In this study, the Virtual Fields Method (VFM) is applied to identify constitutive parameters of hyperelastic models from a heterogeneous test. Digital image correlation (DIC) was used to estimate the displacement and strain fields required by the identification procedure. Two different hyperelastic models were considered: the Mooney model and the Ogden model. Applying the VFM to the Mooney model leads to a linear system that involves the hyperelastic parameters thanks to the linearity of the stress with respect to these parameters. In the case of the Ogden model, the stress is a nonlinear function of the hyperelastic parameters and a suitable procedure should be used to determine virtual fields leading to the best identification. This complicates the identification and affects its robustness. This is the reason why the sensitivity-based virtual field approach recently proposed in case of anisotropic plasticity by Marek et al. (Comput Mech 60(3):409–431, 2017) has been successfully implemented to be applied in case of hyperelasticity. Results obtained clearly highlight the benefits of such an inverse identification approach in case of non-linear systems.

Highlights

  • The constitutive parameters of hyperelastic models are generally identified from several homogeneous tests, typically uniaxial tension (UT), pure shear (PS) and equibiaxial tension (EQT)

  • When the system becomes non-linear, typically for the Odgen model [8], a statistical analysis can be carried out for optimizing the choice of the virtual fields. This complicates the identification procedure and affects its robustness. This is the reason why we applied here to hyperelasticity the sensitivity-based virtual field approach recently proposed in case of anisotropic plasticity by [1]

  • The data obtained experimentally were used in the identification of the constitutive parameters for random and sensitivity-based virtual displacement fields

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Summary

Introduction

The constitutive parameters of hyperelastic models are generally identified from several homogeneous tests, typically uniaxial tension (UT), pure shear (PS) and equibiaxial tension (EQT). Among the different identification methodologies available, the Virtual Field Method (VFM) has been successfully applied to hyperelasticity in [3]. When the system becomes non-linear, typically for the Odgen model [8], a statistical analysis can be carried out for optimizing the choice of the virtual fields. This complicates the identification procedure and affects its robustness. This is the reason why we applied here to hyperelasticity the sensitivity-based virtual field approach recently proposed in case of anisotropic plasticity by [1]

Methods
Results
Conclusion

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