A new micro-macro transition for hyperelastic materials

Many classic hyperelastic models fail to predict the stress responses of soft materials in complex loading conditions with parameters calibrated through one simple test. To address this fundamental issue, we propose a new micro-macro transition for the microstructural hyperelasticity modeling, which is further integrated into the full network framework. With a Gaussian chain distribution, this new mapping scheme yields an explicit one-parameter hyperelastic model in terms of principal stretches. This new linear model achieves remarkable success in capturing the stress responses in multi-axial deformation modes for soft materials with an absence of strain stiffening effect, which is beyond the capability of the widely used neo-Hookean model. A new two-parameter hyperelastic model is further developed by combining the new micro-macro transition and non-Gaussian Langevin chain distribution. Compared with other two-parameter hyperelastic models based on Langevin statistics, such as the eight-chain model, affine full network model, and equilibrated microsphere model, our new model exhibits greatly improved predictive ability for complex loading types. The new model is also implemented for finite element analysis, which shows the ability to capture the responses of soft materials with heterogeneous strain distribution. In all cases, the parameters in our models can be determined through the data of uniaxial loading tests, along with the behaviors in other loading modes being well forecast, which is a challenge for various other existing hyperelastic models. This novel micro-macro transition is shown to properly capture the inherent correlations between different deformation modes, which may advance fundamentally modeling hyperelasticity and other constitutive behaviors for soft materials.