Continuous symmetry analysis of a dissipative constitutive law: application to the time-temperature superposition

The isothermal inelastic behaviour of the dry polyamid 66 (PA66) is considered. It is shown that the so called time-temperature equivalence principle can be recovered by a symmetry analysis of the differential equations governing the material rheology, which are written within a thermodynamical framework of relaxation. The symmetry analysis leads to the expression of a translation shift factor from a reference curve to another curve at a different temperature. This shift factor is compared to that given by the well-known Williams–Landel–Ferry empiric relation.