Atomistic and Continuum Models of Solids

固体的原子模型和连续体模型

• 批准号: 0407866
• 负责人: Weinan E
• 金额: $ 33.32万
• 依托单位: Princeton University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-09-01 至 2007-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0407866&HistoricalAwards=false
• 关键词: Atomistic; Continuum; Models; Solids

The PI proposes to develope theoretical models of crystalline solidsthat are based on the positions of the atoms that make up the crystal. As a first step, the PI proposes to study (large) elastic deformation of perfect crystals. This will help us to understand the critical strain thatthe material can sustain before defects form. The PI then proposes tostudy the formation, structure, energetics and dynamics of defects in crystals.Understanding defects in crystals is crucial since defects control the response and failure of the material, as in, e.g. nano-devicesand semi-conductor thin films. By understanding the interplay between loading and failure mechanisms as well as their microscopic origin, the PI hopes to give guidelines fordesigning materials that avoid certain modes of failure.To obtain simplified models that can be readily linked with traditional theories of continuum mechanics, the PI also proposes to develop continuum models in the form of nonlinear elasticity theory that are derived directly from the atomistic models. Such a theory gives a much simplified description for the material properties and are therefore easier to use. As applications, the PI proposes to study the mechanical properties ofcarbon nano-tubes. Nano-tubes are very good examples for this projectsince they can sustain very large elastic deformation before failure. In fact they are the strongest fiber known to us. The PI proposes to study large (therefore nonlinear) deformations of nano-tubes, their modes of failure, as well as properties of nano-tube-reinforced materials.

PI建议开发基于组成晶体的原子位置的晶体固体的理论模型。作为第一步，PI建议研究完美晶体的（大）弹性变形。这将帮助我们理解材料在缺陷形成之前所能承受的临界应变。因此，PI建议研究晶体中缺陷的形成、结构、能量学和动力学。理解晶体中的缺陷是至关重要的，因为缺陷控制着材料的响应和失效，例如纳米器件和半导体薄膜。 通过理解加载和失效机制之间的相互作用以及它们的微观起源，PI希望为设计避免某些失效模式的材料提供指导。为了获得可以容易地与传统连续介质力学理论联系起来的简化模型，PI还建议以直接从原子模型导出的非线性弹性理论的形式发展连续介质模型。这种理论对材料性质的描述非常简化，因此更易于使用。 作为应用，PI提出了研究碳纳米管的力学性能。纳米管是这个项目的一个很好的例子，因为它们在失效前可以承受很大的弹性变形。事实上，它们是我们所知的最强的纤维。PI建议研究纳米管的大变形（因此是非线性的）、失效模式以及纳米管增强材料的性能。