On non-monotonicity of linear viscoelastic functions

The monotonicity of the linear viscoelastic functions, namely, the shear creep compliance, the Young's relaxation modulus, the stretch creep compliance, the P-wave relaxation modulus, the Lamé's first function, and the time-dependent Poisson's ratio, were examined analytically and numerically. It was shown that both the Lamé's first function and time-dependent Poisson's ratio can be non-monotonic. Furthermore, in contrast to the reports by other researchers, the values of the time-dependent Poisson's ratio were found to be bounded by the limits between -1 and 0.5 after the physical constraints of the bulk and shear relaxation moduli are taken into account.