The fact that shape memory and superelastic alloys admit morphological
(phase) transformations under mechanical/electrical/thermal loadings gives
them their very unique properties and makes them attractive for designing novel engineering systems.
One impediment, however, to effective design with
such materials is the lack of a general purpose (constitutive) model
suitable for use in solving boundary value problems using analysis software
such as FEA programs. Recently, however, there has been a concerted effort
in the development of such models for macro-scale modeling. Most approaches
have been moving toward a common generalized thermodynamic framework employing
varying degrees of internal variables. Several promising models utilizing
internal variables to describe single martensitic variants and some with
multiple variants have appeared. In this work we present a model using
results in quasi-convexity theory in a general multivariant framework for
single crystals that is based upon lattice correspondence variants. These
results are based upon some surprisingly simple energy bounds which we are
able to show are quite tight under certain common circumstances.
An overview of the theory will be presented along applications of the
theory to a selection of examples to highlight practical possibilities.
Included in the examples are comparisons to multi-axial deformation experiments.