Implicit stress integration method of Shape Memory material model

The phenomenological SMA material model proposed by Lagoudas [1] is modified and implemented in finite element software PAK [2]. Critical thermodynamic force is derived to match implicit integration method. All variables are derived to depend on effective values of stress, strain and martensitic volume fraction. One scalar equation need to be solved in the integration point using trial stress direction for each time step. The integration in the trial deviatoric stress direction provides possibility to solve large strain problems using the algorithms developed for small strains. Two one‐dimensional and one non‐proportional large strain example verified accuracy of proposed modifications. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)