A variable order fractional constitutive model of the viscoelastic behavior of polymers

The multiple timescale evolution of polymers' microstructure due to an applied load is a well-known challenge in building models that accurately predict its mechanical behavior during deformation. Here, a constitutive model involving a variable order fractional derivative with piecewise definition is presented to describe the viscoelasticity of polymers under the condition of uniaxial loading at constant strain rates. It is shown that our model requires three parameters for small strains while five parameters are defined for large deformations. By comparing the predictions made by the proposed model with published experimental data and an existing model for polymers, we demonstrate that our model has higher accuracy while it benefits from its simple form of linearly decreasing order function to predict large deformations. An illustration based on the mechanism of molecular chain resistance indicates that the hardening process and the rate dependence of polymers are captured by the variation of fractional order. We conclude that the evolution of microstructure and mechanical properties of polymers during deformation is well represented by the variable order fractional constitutive model.