Numerical analysis of complex systems evolution with phase transformations at different spatial scales

This paper shows the existence of a critical dimension for finite length nanowires exhibiting shape memory effects. We give a brief survey of phase transformations, their classifications, and provide the basis of mathematical models for the phenomena involving such transformations, focusing on shape memory effects at the nanoscale. Main results are given for the dynamic of square-to-rectangular transformations modelled on the basis of the modified Ginzburg-Landau theory. The results were obtained by solving a fully coupled system of partial differential equations, accounting for the thermal field, a feature typically neglected in recent publications on the subject when microstructures of nanowires were modelled with phase-field approximations. Representative examples are shown for nanowires of length 2000nm and widths ranging from 200nm to 50nm. The observed microstructure patterns are different from the bulk situation due to the fact that interfacial energy becomes comparable at the nanoscale with the bulk energy

Microstructures of constrained shape memory alloy nanowires under thermal effects

In this paper, martensitic transformations in constrained Fe-Pd nanowires are studied using a mesoscopic model analyzed in detail numerically in our earlier papers. The dynamics of squareto-rectangular transformation is modeled by using the modified Ginzburg-Landau theory. The simulations are performed accounting for the thermal effects using the coupled equations of non-linear thermoelasticity. Up to date, these effects have typically been neglected in modeling microstructures at the scales of interest considered here. Nanowires of length 2000 nm and widths ranging from 200 nm to 50 nm are simulated to study the effect of size on the microstructure evolution. There exists a critical width below which the size effect is prominent. We present a series of numerical results demonstrating this phenomenon. We also have carried out the study of variations in values of bulk, shear, and Landau constants to understand the difference in evolved microstructure in the coupled and uncoupled physics