A comparative study of the entanglement models toward simulating hyperelastic behaviors

Accurately predicting the hyperelastic response of soft materials under complex loading conditions has been a long-standing challenge. Previous developments have shown that incorporating the entanglement effect can significantly improve the model performance. In this work, we compare the performances of different entanglement models in simulating the stress responses through either fitting uniaxial data alone or uniaxial and equibiaxial data simultaneously. Results show that the entanglement models do not exhibit satisfactory predictive ability with parameters calibrated through uniaxial data. This disadvantage can be overcome through a newly proposed Biot chain model, which inherently incorporates the entanglement effect though a new chain stretch determination that considers the contribution of all surrounding chains. As multiple pairs of experimental data are used to calibrate the model parameter, the Davidson-Goulbourne model provides the best performance. It is also demonstrated that the entanglement effect varies with the deformation mode and plays a more critical role in biaxial deformation than that in the uniaxial deformation. This study can provide a better understanding of entanglement models, including their capabilities and limitations, facilitating the development of more accurate and reliable predictive models toward various applications.