A comparative study of invariant-based hyperelastic models for silicone elastomers under biaxial deformation with the virtual fields method

Abstract

Silicone elastomers have been widely used for biomedical applications. A variety of hyperelastic models have been proposed to describe this type of materials in the past few decades. The assessment of the quality of the proposed models is mostly based on stress-strain data obtained from uniform deformation, but very little work has been done to investigate model performances with heterogeneous deformation fields and full-field characterization methods. In this study, thirteen hyperelastic models are evaluated using the virtual fields method combined with full-field deformation data obtained from biaxial tests. The quality of these models is assessed by their capabilities to predict the mechanical responses of silicone elastomers, and the influences of the first and second invariants on modeling of elastomers are investigated through comparative studies between models. The results indicate that for elastomers under finite biaxial deformation, Yeoh model performs the best among selected models; the first invariant plays an important role in constitutive modeling; the second invariant does not have obvious influence on improving the fitting performance. This study provides a full-field method to calibrate and compare hyperelastic models of silicone elastomers under biaxial loading conditions.

Keywords: Biaxial testing; Full-field measurement; Hyperelastic models; Material parameter identification; Model comparison; Virtual fields method.