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In this paper a physical-based constitutive relation for defining the thermo-viscoplastic behaviour of FCC metals with dependence on strain on thermal activation processes is presented. The model, based on previous considerations reported by Rusinek and Klepaczko [Rusinek A, Klepaczko JR. Shear testing of sheet steel at wide range of strain rates and a constitutive relation with strain-rate and temperature dependence of the flow stress. Int J Plasticity 2001;17:87-115], is founded on physical aspects of the material behaviour. The proposed constitutive relation is applied to define the behaviour of oxygen-free high conductivity (OFHC) copper using the experimental data reported in Nemat-Nasser and Li [Nemat-Nasser S, Li Y. Flow stress of FCC polycrystals with application to OFHC copper. Acta Mater 1998;46:565-77]. The description of the material behaviour provided by the model gets satisfactory agreement with the experiments. The analytical predictions of this constitutive description are compared with those obtained from the models due to Voyiadjis and Almasri [Voyiadjis GZ, Almasri AH. A physically based constitutive model for fcc metals with applications to dynamic hardness. Mech Mater 2008;40:549-63], and Nemat-Nasser and Li. This comparison reveals that the original formulation proposed in this paper is a suitable alternative to other physically based relations for modeling OFHC copper.