A strain energy function for large deformations of compressible elastomers

Elastomers are typically considered incompressible or slightly compressible. However, we present simple tension and bulk tests showing that, under large deformations, these materials can undergo significant volume changes. A review of the literature reveals the lack of an accurate hyperelastic model for finite volumetric deformations of elastomers. Therefore, we propose a new volumetric strain energy density (SED) that overcomes the limitations of the current models. The main advantages of the proposed SED are: (1) accurate description of the response of rubbers for both small and large volumetric deformations; (2) ability to reproduce diverse behaviors during volume shrinkage and expansion; (3) adaptability to other compressible materials, such as soft tissues, foams and hydrogels. Using the deviatoric- volumetric split of the strain energy, the proposed volumetric SED is combined with a suitable deviatoric part selected from the literature. The parameters of the combined SED are calibrated by fitting the model to the experimental data from simple tension and bulk tests. As a result, an accurate description of the response of elastomers under both shape and volume deformations is provided. The proposed SED can be implemented in numerical codes to capture the effects of volumetric deformations on the equilibrium solutions for various stress states.