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In this paper, a new thermo-viscoplastic constitutive relation is proposed to approximate behaviour of steels for a wide range of strain rates and for large deformations. Two analytical formulations are proposed to define a strain evolution of strain hardening rate. It allows for taking into account different strain hardening evolutions. Two models proposed are flexible enough to approximate the strain hardening rates associated with different micro-mechanisms of plastic deformation. An advantage of such analytical formulations is a reduced number of constants. In the present case, the number of material constants of the strain hardening functions is three. Using a systematic method for determining the material parameters just three different mechanical tests are necessary to calibrate both constitutive relations. Thus, the set of constants for each model is unique and independent on the user. The constitutive relations are validated using experimental data for ES steel. Satisfactory agreement has been obtained between experiments and analyticalpredictions.