Connecting rate-dependent loading and relaxation behaviors of glassy polymers by fractional models

In this paper, a fractional constitutive model is constructed to link the rate-dependent loading and relaxation stages. As for strain rate effects, an inverse relationship between relaxation time and strain rate is established with assuming fractional order following the microbial growth curve in the loading stage. The anomalous stress relaxation behaviors of glassy polymers under various strain rates are successfully characterized by establishing the relationship between model parameters and initial stress. The proposed model is validated by numerical results applied to various strain rates and initial relaxation strains. Compared with the existing model, the proposed fractional model presents higher accuracy.