A thermodynamically consistent formulation of the Johnson–Cook model

The model of Johnson and Cook, which includes a viscoplastic flow rule and a damage criterion, is widely used to describe the mechanical behaviour of metallic materials subjected to severe loading conditions, such as those encountered during fabrication operations or impact. This model has been built on empirical, rather than physical, grounds. The present paper therefore aims at revisiting the model of Johnson and Cook from the view point of thermodynamics with internal variables. The interest of this approach is twofold. First, it provides a guide for the construction of a complete thermomechanical constitutive model, with some constitutive relations not only for the stress tensor but also specific internal energy, specific entropy and heat flux vector. Second, it allows highlighting some possible limitations of the original model of Johnson and Cook. Such limitations can be circumvented with an alternative model, which is described in the present work. For illustration purpose, some applications of both the original and alternative models are presented in the final section