### Stability of thermally-induced martensitic transformations in bi-atomic crystals

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Ryan Elliott, University of Michigan
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Shape memory alloys (SMAs), such as equi-atomic NiTi, exhibit two remarkable properties: the shape memory effect and pseudoelasticity. The shape memory effect is the ability of the material to erase relatively large mechanically induced strains (up to 8%) by moderate increases in temperature

Previous work in this area has focused on phenomenological characterization of the continuum energy density, *W*. Physically several phases can coexist. Unfortunately constructing a phenomenological energy density is exceedingly difficult, even for the case of two coexisting phases. Thus, a new nano-scale based approach is proposed. It consists of deriving the continuum energy density function *W*(**F**,q) (where **F** is the lattice’s uniform deformation gradient and q is the temperature) from temperature-dependent atomic pair-potential functions. As a first approximation to the transformation mechanism, uniform strain equilibrium solutions and their stability are investigated, as a function of temperature, for perfect bi-atomic crystals subjected to hydro-static pressure. The model is then extended to include atomic “shuffles” (as seen in actual materials) and the resulting equilibrium solutions (and their stability) are investigated.

**Abstract Author(s): **R. S. Elliott, John A. Shaw, Nicolas Triantafyllidis