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In this work the influence of the constitutive description in numerical simulations of the radial expansion of annealed OFHC copper rings has been studied. For that task, three physical-based constitutive models are implemented into the FE code ABAQUS/Explicit and applied to de?ne the thermo-viscoplastic behaviour of the material in the simulations. These are those due to Rusinek et al. [A. Rusinek, J.A. Rodr´ iguez?Mart´ inez, A. Arias, A thermo-viscoplastic constitutive model for FCC metals with application to OFHC copper, Int. J. Mech. Sci., 52, 120?135, 2010], Nemat?Nasser and Li [S. Nemat?Nasser, Y. Li, Flow stress of FCC polycrystals with application to OFHC Copper, Acta Mater., 46, 565?577, 1998] and Voyiadjis and Almasri [G. Z. Voyiadjis, A.H. Almasri, A physically based constitutive model for fcc metals with applications to dynamic hardness, Mech. Mater., 40, 549?563, 2008]. The attention is primarily focussed on analyzing the in?uence of the material description on the strain localization process. Notable differences are observed in the response of the specimen under loading depending on the constitutive relation used. The numerical study indicated that the constitutive model controls the low localization, defines the strain of instability and determines the number of necks formed. The causes which reside behind such decisive role played by the constitutive relation are investigated. It has been found that the rate sensitivity definition governs the models? predictions for the strain localization process.