Collaborative Research: Novel Multiscale Computational Mathematics for Surface-Dominated Nanomaterials

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Luskin1310835Park1310849 Through this collaborative proposal, the investigators develop numerical analysis and improved surface Cauchy-Born methods to ensure their reliability and improve their efficiency. The mechanical behavior and properties of nanomaterials is dominated by the effects of surfaces, whose effects become increasingly important with decreasing nanostructure size. Surfaces can cause unique, non-bulk mechanical properties, including elastic strengthening (i.e. smaller is stronger) and phase transformations, and can serve as the nucleation point for defects such as dislocations and twins. Major extensions of the numerical analysis of finite element methods for continuum elasticity and its coupling to atomistic models is required to enable the surface Cauchy-Born methods to accurately compute problems with surfaces (defects) and discrete surface microstructure, because the complex multi-well energy landscape of real nanostructures must be confronted. Many important future nanotechnologies, such as nanoscale resonant sensors, nanoelectromechanical systems (NEMS), and stretchable nanoelectronics, can be improved by a better understanding of how localized nanoscale surface effects impact their effective mechanical properties and reliability. In particular, the numerical analysis of surface Cauchy-Born methods improves the representation of the key atomic-scale surface physics that govern defect nucleation, elastic strengthening or softening, and the failure mechanisms of surface-dominated nanomaterials.