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

V. Magnenet , R. Rahouadj , J.-F. Ganghoffer , C. Cunat

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.

Mots clés: Thermodynamics of relaxations; Lie groups; DNLR approach; Williams Landel Ferry relation

V. Magnenet, R. Rahouadj, J.-F. Ganghoffer, C. Cunat. Continuous symmetry analysis of a dissipative constitutive law: Application to the time-temperature superposition. European Journal of Mechanics - A/Solids, 2010, 28 (4), pp.744. ⟨10.1016/j.euromechsol.2009.02.002⟩. ⟨hal-00617071⟩