Bayesian model selection of hyperelastic models for simple and pure shear at large deformations

Abstract

Hyperelastic materials are extensively employed in a wide range of applications. Although there are well-established models for describing the mechanical behavior of the hyperelastic materials, relatively few papers have attempted to rank different models. This paper aims to identify parameters of some constitutive models for pure and simple shear of an incompressible isotropic hyperelastic material under large deformations, and also aims to propose a strategy to rank different models. The constitutive models considered in the present analysis are the following: Mooney–Rivlin, Yeoh, Ogden (1 and 2 terms), Lopez-Pamies (1 and 2 terms), and Gent. In the first part of the paper, the Bayesian framework is applied for the identification of the parameters of the models, where experimental data are used to update the prior probabilistic model of the unknown parameters. The Maximum a Posteriori Estimate is obtained, and the error between the model prediction and the experimental data is computed to rank the models. In the second part of the paper, the Bayesian framework is again employed, but now as an strategy for model selection. Instead of ranking the models using the error between the model prediction and the experimental result, more ingredients, such as the Ockham factor, are taken into account for the model selection. The results indicate that all models and experimental results for pure shear are in good agreement, but Mooney–Rivlin, Gent and Yeoh models were not able to well describe the available experimental data from simple shear. The best model for pure shear is Mooney–Rivlin and the best model for simple shear is Ogden (2 terms), considering the available experimental data and the criteria proposed in the present paper.