Novel strategies for parameter fitting procedure of the Ogden hyperfoam model under shear condition

Abstract

The Ogden hyperfoam model has been widely used to characterize the hyperelastic deformation of elastomeric foams. To capture the shear response, shear stress–strain data obtained from simple shear tests are traditionally used, along with uniaxial compression data, to fit the model parameters. The adequacy of the shear stress–strain data for the parameter fitting of the Ogden hyperfoam model to describe the true shear response is investigated in this study. The normal stress, perpendicular to the shear surface induced by the Poynting effect of simple shear, is tested and compared with the predicted values of the model fitted using the traditional strategy. A noticeable deviation between the values of normal stress indicates that the traditional strategy cannot give precise model parameters for the Ogden hyperfoam model to describe the real shear response. Three novel strategies for the parameter fitting procedure of the Ogden hyperfoam model are proposed. Besides the nominal stress of uniaxial compression and the shear stress of simple shear, normal stress perpendicular to the shear plane, or zero-side normal traction constraint on the inclined surface, or both normal stress and zero-side normal traction constraint are used to construct the error functions for new strategies. Model parameters for the third-order Ogden hyperfoam model are obtained by minimizing the error functions. The performances of the novel strategies are demonstrated by comparing the fitted material responses with experimental data. The results indicate that the prediction accuracy of the model is directly proportional to the number of constraints used in the parameter fitting procedure. The novel strategy based on additional constraints of normal stress and zero-side normal traction is suggested. This strategy is expected to improve the shear response prediction performance of the Ogden hyperfoam model and aid in the establishment of constitutive models for elastomeric foams.