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提议开发晶体固体的理论模型基于构成晶体的原子的位置。作为第一步，PI提议研究（大）完美晶体的弹性变形。这将有助于我们了解材料在缺陷形式之前可以承受的关键压力。然后，PI提出了晶体中缺陷的形成，结构，能量和动力学。理解晶体中的缺陷是至关重要的，因为缺陷控制了材料的响应和失败，例如纳米驱动器和半导体薄膜。 通过了解负载和故障机制之间的相互作用及其显微镜起源，PI希望提供指南避免避免某些失败模式的材料。要获得可以轻松地与连续机械理论相关的简化模型，PI也提议以非线性弹性理论的形式开发连续模型，这些模型直接源自派生的模型。这样的理论给出了对材料属性的简化描述，因此更易于使用。 作为应用，PI建议研究碳纳米管的机械性能。纳米管是该项目的很好的例子，它们可以在失败前维持非常大的弹性变形。实际上，它们是我们已知的最强纤维。 PI提议研究纳米管的大型（因此非线性）变形，其失效模式以及纳米管增强材料的特性。