Mechanical relaxation of linear viscoelastic materials described by the modified anelastic element

The stress relaxation and creep in amorphous materials, the dielectric relaxation in conducting polymers, the spin relaxation in spin-glasses, are examples of processes described by the mathematical formalism of the theory of linear viscoelasticity. This description, given by a spectrum or distribution function, allows to express the temporal evolution of the relaxation through integral transformations. In many cases, however, this evolution is given directly using the empirical expression exp [-(t/τ) γ ], known as fractional exponential behaviour, where τ is a characteristic relaxation time and γ is a constant (0 < γ ≤ 1). It is shown that this empirical expression can be derived from the modified anelastic element (MAE) whose relaxation time depends on the time of the quasistatic test. From this dependence the spectrum for the MAE is calculated and correlated with the log normal distribution. A novel procedure to calculate the parameters of the MAE is presented and applied to stress relaxation curves.