The traditional viscoelastic constitutive models encounter the problems of massive parameters and ambiguous physical meanings. A new concept of variable-order viscoelastic constitutive (called VOVC) model is put forward based on the constant fractional-order constitutive model and the viscoelastic theory. The determination methods of the two parameters in the VOVC model, including the material coefficient and the viscoelastic coefficient, are discussed both in the tensile and the resilient processes. The comparisons are made between the VOVC model and the traditional constitutive models i.e. the constant fractional-order Kelvin-Voigt (CFKV) model, the Zhu-wang-tang nonlinear thermo-viscoelastic constitutive (ZWT) model and the Ogden nonlinear hyper-elastic (Ogden) model. The results show that the VOVC model with the constant material coefficient and the variable viscoelastic coefficient predicts the whole evolution of the constitutive behavior of the viscoelastic material under the constant strain rate more precisely. The constant material coefficient in the VOVC model means the stiffness of the viscoelastic material. The variable viscoelastic coefficient in the model means the distribution of the elasticity and viscosity. The VOVC model contains a simpler structure, fewer parameters, clearer physical meanings and higher precision.
