An equivalence between generalized Maxwell model and fractional Zener model

• We present a comparison of the performance of the generalized Maxwell model and fractional Zener model to describe viscoelasticity.
• The discrete cumulative relaxation spectrum of the generalized Maxwell model forms a staircase approximation of that of the fractional Zener model.
• The results show that the two models are quantitatively equivalent under various loading conditions.

Both classic rheological models and fractional derivative models have been widely adopted to model the viscoelastic behaviors of materials. In this work, we present a detailed comparison of the performance of the generalized Maxwell model and fractional Zener model. We first describe a method to determine the parameters of the generalized Maxwell model from the fractional Zener model based on the equivalence of complex modulus in the frequency domain of the two models. The two models are then applied to investigating the stress response under constant strain rate, stress relaxation, cyclic and random loading conditions. The simulation results of the two models show excellent quantitatively equivalence. This finding can provide insight into choosing the more suitable model for specific conditions.