Conjectures on the crystallographic theory of martensite under load

The crystallographic theory of martensite - developed by Wechsler, Liebermann and Read in the 1950's - is generally used to calculate the rank-one deformation gradient between aystenite and a martensitic variant which are coherently connected along a habit plane. It turns out that the orientation of the habit plane and the shear and rotation of the martensite may be related to the "Bain strain", i.e. the stretch that forms part of the overall deformation. This strain must be determined from crystallographic data.
Here we attempy to extend the crystallographic theory to a loaded austenitic specimen. The Bain strain will then depend on the load, or else, the original Bain strain will be affected by the load and as a result the characteristic "wedges" formed by two martensitic variants change their angle.
The new Bain strain may be calculated from the original one by exploiting the condition that the stress vectors on the habit plane are continuous. In addition the temperature for which the deformation occurs may be related to the load by the requirement that the normal component of the Eshelby tensor is continuous at the habit plane. Thus we are able to derive the analogue to the Clausius-Clapeyron equation in a liquid-vapour phase transition. In the present case this turns out to be a monotone relation between the uniaxial stress applied to the specimen and the temperature.
All this - for purposes of simplicity - is demonstrated for the two-dimensional case.