Interconversions between linear viscoelastic functions with a time-dependent bulk modulus

The interconversion relations for viscoelastic functions are derived with the consideration of the time-dependent bulk modulus, K( t), for both traditional and fractional Prony series representations of viscoelasticity. The application of these relations is to replace the fitting parameters of Young’s relaxation modulus, E( t), by the unknown parameters of K( t) and the known parameters of the shear relaxation modulus, G( t), and to fit the E( t) to the experimental data for obtaining the parameters of K( t). The fitting results show that only two experiments for measuring the viscoelastic functions of an isotropic material are not enough to determine the other viscoelastic functions. However, if we consider the relaxation rates of K( t) and G( t), we may conclude that the constant bulk modulus is a more reasonable assumption, and the corresponding Poisson’s ratio, ν( t), is a monotonic-increasing function.