Parameter Identification Methods for Hyperelastic and Hyper-Viscoelastic Models

In this paper, the Ogden model is employed to characterize the hyperelastic properties of rubber, and on the basis of a pattern search algorithm and the Levenberg-Marquardt algorithm, a professional method that can realize the comprehensive fitting of the uniaxial tension, biaxial tension, planar tension, and simple shear experimental data of hyperelastic materials was developed. The experiment data from Treloar (1944) was fitted very well, and the determined parameters by using this method were proven correct and practical in the numerical verification in ANSYS. Then, the constitutive model of the hyper-viscoelastic materials combining the Ogden model with the generalized Maxwell model was explained in detail, and the parameter identification method was also proposed by using the pattern search method. Then, three groups of relaxation tests of uniaxial tension and four groups of simple shear tests with different loading velocities were conducted to obtain the corresponding virtual experiment data. After discussing the constraints and initial setting values for the undetermined parameters, these virtual data of different loading histories were respectively employed to identify the parameters in the hyper-elastic model, and the accuracy and the reliability of the estimated parameters were also verified in ANSYS.