A Model of Shape Memory Materials with Hierarchical Twinning : Statics and Dynamics

Abstract

We consider a model of shape memory material in which hierarchical twinning near the habit plane (austenite-martensite interface) is a new and crucial ingredient. The model includes (1) a triple-well potential ({phi} model) in local shear strain, (2) strain gradient terms up to second order in strain and fourth order in gradient, and (3) all symmetry allowed compositional fluctuation induced strain gradient terms. The last term favors hierarchy which enables communication between macroscopic (cm) and microscopic ({Angstrom}) regions essential for shape memory. Hierarchy also stabilizes between formation (critical pattern of twins). External stress or pressure (pattern) modulates the spacing of domain walls. Therefore the ``pattern`` is encoded in the modulated hierarchical variation of the depth and width of the twins. This hierarchy of length scales provides a hierarchy of time scales and thus the possibility of non-exponential decay. The four processes of the complete shape memory cycle -- write, record, erase and recall -- are explained within this model. Preliminary results based on 2D Langevin dynamics are shown for tweed and hierarchy formation.