Energy-based variational modeling of fully formed adiabatic shear bands

An energy-based variational modeling approach of adiabatic shear bands (ASB) for thermo-viscoplastic materials is proposed. In the process of derivation of this thermo-mechanical coupled problem, the variational methodology is first applied to classical problems, such as Couette flow, thermal conduction in a fluid layer and thermal Couette flow. The solutions are compared to the corresponding analytical solutions. In a second part, a slab under stationary simple shear is analyzed by a Ritz–Galerkin method combined with an energy-based variational approach of thermo-mechanical problems. The velocity and temperature profiles within an ASB are parameterized by two quantities: the shear band width and central temperature. It is shown that this variational formulation works for various material constitutive models, as illustrated by adopting two popular constitutive models (power law and Johnson–Cook law) and the results are checked by using a variational Finite Element Method. In a last part, mixed heat exchange boundary conditions are introduced to limit the effect of slab width on the solution. The profiles of velocity and temperature in the slab, as well as the influence of material properties on the formation of shear band are evaluated and in good agreement with results from the literature. [Display omitted] •We present a variational approach to adiabatic shear bands (ASB) in steady-state.•This method efficiently computes ASB width, velocity and temperature profiles.•The proposed approach is valid for general thermo-visco-plasticity models.•The influence of thermal boundary conditions is studied in details.