Atomistic and Continuum Models of Solids

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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.