A MODEL OF SHAPE-MEMORY MATERIALS WITH HIERARCHICAL TWINNING - STATICS AND DYNAMICS

We consider a model of shape memory materials in which hierarchical tw inning near the habit plane (austenite-martensite interface) is a new and crucial ingredient. The model includes (1) a triple-well potential (phi(6) model) in local shear strain, (2) strain gradient terms up to second order in strain and fourth order in gradient, and (3) all symm etry allowed compositional fluctuation-induced strain gradient terms. The last term favors hierarchy which enables communication between mac roscopic (cm) and microscopic (A) regions essential for shape memory. Hierarchy also stabilizes tweed formation (cries-cross patterns of twi ns). External stress or pressure modulates (''patterns'') the spacing of domain walls. Therefore the ''pattern'' is encoded in the modulated hierarchical variation of the depth and width of the twins. This hier archy of length scales provides a related 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 ex plained within this model. Preliminary results based on 2D molecular d ynamics are shown for tweed and hierarchy formation.