The development of models for the macroscopic modeling shape memory alloys and other materials that under-go martensitic phase transformations has been moving towards a common generalized thermodynamic framework. Several promising models utilizing single martensitic variants and some with multiple variants have appeared recently. In this work we develop a model using some new results in quasi-convexity theory in a general multivariant framework for single crystals that is based upon lattice correspondence variants. These new results are based upon some surprisingly simple energy bounds which we are able to show are quite tight under certain common circumstances. The completion of the macroscopic model is effected by the use of canonical dissipation arguments for the generation of specialized evolution equations. The evolution equations that appear are of a unique nature in that not only are the thermodynamic forces restricted in range but so are their kinematic conjugates. This unusual situation complicates model time integration especially in a discrete time setting. We show that the trial elastic state method that is popular in metal plasticity is inadequate in the present situation and needs to be replaced by a nonlinear programming problem with a simple geometric interpretation. The developed integration methodology is robust and leads to symmetric tangent moduli. Example computations show the behaviour of the model in the pseudoelastic range. Of particular interest is the fact that the model can predict the generation of habit plane-like variants solely from the lattice correspondence variants; this is demonstrated through a comparison to the experimental work of Shield .