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

卢斯金1310835公园1310849 通过这一合作提案，研究人员开发了数值分析和改进的表面柯西-玻恩方法，以确保其可靠性并提高其效率。 纳米材料的力学行为和性能主要受表面效应的影响，随着纳米结构尺寸的减小，表面效应变得越来越重要。 表面可以引起独特的非体机械性能，包括弹性强化（即越小越强）和相变，并且可以用作位错和孪晶等缺陷的成核点。 连续弹性有限元方法的数值分析及其与原子模型的耦合的主要扩展需要使表面柯西-玻恩方法能够准确地计算表面（缺陷）和离散表面微结构的问题，因为必须面对真实的纳米结构的复杂的多阱能量景观。 许多重要的未来纳米技术，如纳米谐振传感器，纳米机电系统（NEMS），和可拉伸纳米电子，可以通过更好地了解局部纳米表面效应如何影响其有效的机械性能和可靠性来改进。 特别是，表面柯西-玻恩方法的数值分析提高了关键原子尺度表面物理的代表性，这些物理决定了缺陷成核、弹性强化或软化以及表面主导的纳米材料的失效机制。

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.