The main objective of this study is to introduce a self expanding 'dissipationless band' to model inner hysteresis loops of shape memory alloys (SMAs). Dissipation that occurs when the material undergoes phase transformation is critical to the modeling of hysteretic behavior. Using a dissipationless virtual response of the material, a logical framework for the onset transformation under reversal of cycles is simulated. It is identified that this dissipationless band occurs due to the difference between the starting states of forward and reverse transformation. Width of dissipationless band varies for inner hysteresis with loading history.

The construction of the generalized driving force for the transformation along with the rate of dissipation function is formulated. Simulated hysteresis loops for different kinds of partial and complete loading cycles at different thermo-mechanical conditions. The constitutive model is implemented within the finite-element software ABAQUS using a user defined material subroutine (UMAT) and USERMAT using ANSYS. An implicit algorithm has been developed to analyse varies applications.