Dissipation-based approach and robust integration algorithm for 3D phenomenological constitutive models for shape memory alloys

The paper presents an innovative dissipation-based solution algorithm for a phenomenological 3D constitutive model for shape memory alloys (SMA), set in the framework of generalized standard materials, within the formalism of thermodynamics of irreversible processes. The proposed solution scheme aims at detecting all mathematical singularities inherent to the formulation itself, and, in the discrete setting, is capable of filtering out the relevant numerical instabilities applying a check and treat paradigm. No regularization is introduced into the constitutive equations. Numerical results on single material point strain/stress - driven evolutions are reported to validate the proposed method.