Microbiology-inspired nonlinear variable-order fractional model for amorphous glassy polymer

In this paper, a variable-order fractional model is proposed to characterize the complex nonlinear temperature-dependent mechanical behaviors of amorphous glassy polymers, which play a crucial role in the wide applications. At a specific temperature, the variable order is defined to follow the microbial growth curve, which is consisted of a logarithmic growth stage and decay stage. The two stages are naturally connected on the conception that the growth rate is approaching to 0. The variable order is further physically interpreted based on microscopic mechanism. Furthermore, the relationships between elastic modulus, relaxation time and temperature are incorporated into the established model to demonstrate the temperature dependence. Various experimental results are observed to be well characterized by the proposed model, which validates the rationality and reliability. The predictive ability of the proposed model is also explored to verify its effectiveness.