Linking fractional model to power-law constitutive model with applications to nonlinear polymeric stress-strain responses

In this study, a modified constitutive model with a power-law strain-dependent modulus is developed to characterize various mechanical deformations of polymers, which is especially suitable for large nonlinear stress-strain evolutions. It is formally equivalent to the well-known generalized fractional Kelvin models with constant strain rates. Various experimental results, such as strain hardening, stress strengthening, yielding stress, and strain softening, are subsequently employed to validate the effectiveness and correctness of the proposed model. The fitting results reveal that variable modulus can be physically interpreted by the evolution of resistance to deform during the whole deformation process. It can be concluded that the proposed constitutive model is an effective tool to illustrate mechanical behaviors of polymers due to its high accuracy and simple mathematical form with a strain-dependent variable modulus.