Energy-based variational modeling of adiabatic shear bands structure evolution

A novel energy-based variational approach is proposed for modeling adiabatic shear band (ASB) structure evolution, including elasticity, work hardening, and heat conduction. Conservation laws are formulated as a mathematical optimization problem with respect to a limited set of scalars. Consequently, by means of canonical expressions of displacement and temperature, the bandwidth and the central temperature can be accurately computed as internal variables. Based on this thermo-mechanical coupled variational framework, we can verify the generality of the proposed analytical approach with respect to constitutive models, as illustrated through various thermal softening laws such as power laws or the popular Johnson–Cook model. In addition, accounting for work hardening and elasticity, we propose an effective (or macroscopic) thermo-elasto-viscoplastic model of the shear localization zone in transient regime. A new loading/unloading condition, stemming as a Kuhn–Tucker relation, is introduced for this variational model. The stress evolution and the capacity of the approach to handle cyclic loading are analyzed, presenting a very good correspondence with ASB simulations by finite element method.