ECCM 2010 IV European Conference on Computational Mechanics Palais des Congrès, Paris, France, May 16-21, 2010 Numerical Analysis of Phase Transformations in Finite Size Nanostructures with Mesoscopic Models R.V.N. Melnik 1 , L. Wang 2 , R. Dhote 3 , J. Zu 3 1 M 2 Net Lab, Wilfrid Laurier University, Waterloo, Canada, rmelnik@wlu.ca 2 Faculty of Mechanical Engineering, Hangzhou Dianzi University, Xiasha, Hangzhou, 310018, P.R. China 3 Department of Mechanical & Industrial Engineering, University of Toronto, Canada In a series of recent papers we developed several efficient methodologies to solve 2D models describ- ing square-to-rectangle phase transformations in materials with memory, in particular the finite volume methodology [9] and a numerical reduction procedure based on the Proper Orthogonal Decomposition (POD) [8]. In this contribution we discuss the application of the models and numerical methodologies develoepd there to modelling finite nanostructures, in particular nanowires and nanoplates. Our motivation for this study came from the fact that in gold (Au) nanowires, the energy as a function of lattice spacing exhibits two distinct minima that correspond to fcc and bct phases. These nanowires exhibit shape memory effects which has been confirmed computationally with such methodologies as tight-binding and density functional theory (e.g., [1]). A similar situation holds for ZnO nanowires and many other types of nanowires that show substantial potential for many applications in nano- and bio-nanotechnologies, including Cu, Ni, Al, Ag (e.g., [2] and references therein). Our major interests here include iron-based (FePd) and zinc-based oxide(ZnO) nanowires nanowires. The simulated re- sults include nanowires in the length range of 30-200 nm for different diameter-length ratios as well as nanoplates. Typical test results obtained in the Comsol finite element package are given in Fig. 1 where we present microstructures of a nanowire and a nanoplate that are not observable in the corresponding bulk materials. Figure 1: Evolution of microstructures in nanostructures (nanowire (left) and square nanoplate (right)). We develop a relatively simple and computationally inexpensive model to study phase transforma- tions in finite nanostructures. We build on the models describing shape memory effects at the mesoscopic level, in particular those described in [5, 3, 4]. We study the cubic-to-tetragonal transformations in which case the 2D analogue of the model describes the square-to-rectangle phase transformations. In particular, our considerations are based on a modification of the following coupled system of PDEs for the evolution