Construction of Isotropic Compressible Hyperelastic Constitutive Models Based Solely on Uniaxial Tests

Constructing constitutive models for compressible soft materials is essential for accurately describing their highly nonlinear, large deformation mechanical behavior and volumetric deformation. However, most existing constitutive models rely on predefined assumptions about the form of the strain energy function. Constructing compressible hyperelastic constitutive models is particularly challenging because, beyond the uniaxial test, it typically requires additional more sophisticated and more costly experiments, such as biaxial, pure shear, and hydrostatic tests. In this paper, we propose an approach to constructing an isotropic compressible hyperelastic constitutive model without assuming a predefined form of the strain energy function. Instead, we derive the strain energy function directly from experimental data. Our method requires only uniaxial tests, significantly simplifying the experimental requirements and costs. This approach is achieved by utilizing the deviatoric-volumetric decomposition of the strain energy function coupled with an interpolation scheme. To validate our proposed approach, we compare our model against traditional compressible constitutive models and well-known experimental data on incompressible rubbers. Additionally, we perform experiments on compressible rubbers, including foamed silicone and foamed EPDM (ethylene propylene diene monomer), for further validation. It is found that our model perfectly predicts the uniaxial test data and accurately predicts mechanical behavior under various other loading conditions. Finally, we discuss strategies for enhancing model accuracy and its ability to decouple uniaxial behavior from compressibility. This decoupling feature is crucial for accurately capturing the distinct mechanical responses associated with different deformation modes, thereby improving the predictive capability of the constitutive model.