A physically based visco-hyperelastic constitutive model for soft materials

Viscoelasticity is an essential mechanical property of soft materials. Many constitutive models have been proposed to capture this mechanical behavior, but few physically based models were developed due to the challenge to incorporate the micro-mechanisms of viscoelasticity into the formulation. In a previous paper, we proposed a constitutive model to characterize the hyperelastic response under different deformation states with only three parameters (Xiang et al., 2018). Based on the above work and the tube theory of polymer dynamics, we develop herein a physically based viscoelastic constitutive model in this paper. We start from a new microscopic picture at the molecular chain scale, and decompose the stress into a hyperelastic part which comes from the elastic ground network (crosslinked network and entanglement network), and a viscous part which is originated from free chains. Utilizing the same scheme from the previous work (Xiang et al., 2018), we are able to decompose the free chains into two parts, the untangled crosslinked network and the entanglement network. The contour length relaxation and disentanglement from the free chain's networks give the viscous behavior. We test VHB 4910 to validate our model. The model is applied to the mechanical behavior of the soft digital materials (DMs). In addition, the model can explain the Shore A index independent relaxation time of DMs and the asymmetry of viscoelasticity under loading and unloading. This viscoelastic model can be used to predict the mechanical response of soft materials.