A new and consistent approach for deriving Brinson's 1-D constitutive equation for shape memory alloys

One of the first 1-D constitutive equations for shape memory alloys was presented by Brinson L.C in 1993 that became the base of later works typically. In Brinson’s equation, several proposed functions are considered in order to simplify the model and obtain the constitutive equation for SMA. In a recent paper V. R. Buravalla and A. Khandelwal (2007) have shown certain anomalies in Brinson’s model and have tried to present a modified model which unlike Brinson’s model satisfies the compatibility condition. However, their formulation, besides being lengthy, lacks clarity and in particular does not address proper expressions for transformation tensors Ωs and ΩT. In the present work, Brinson’s constitutive equation is derived from fundamental relations using a simple, clear-cut and straightforward approach. Without any extra and unnecessary assumption the consistency of the model is confirmed.