Nanomechanics of Defects in Solids
This chapter examines different aspects of nanomechanics of defects in solids. The methods by which the classical boundary-value problems of continuum mechanics can be imbued with atomistic content are reviewed. Microscopic modeling is founded on the fundamental assertion that beneath the details of observed macroscopic phenomenology, there is a set of microscopic processes which, when understood, rationalize the observed macroscopic behavior to the extent of enabling quantitative predictions. The microscopic simulation of materials is based on the evolution of degrees of freedom that are governed by the Schrodinger equation. It is found that either phenomenologically, or through explicit calculational strategies, the electronic degrees of freedom is implicitly subsumed in the effective pair potential. Once the pair potential has been identified, it is a straightforward matter to evaluate radial derivatives and the corresponding force fields. The energy associated with each distortion may be computed explicitly by recourse to direct atomistics. The contribution due to slip may be extracted by subtracting off the bulk elastic energy. As a result, the exact misfit energy is determined from atomistics. The cohesive-zone theories applied to fracture are also elaborated.
© 1999 Academic Press. It is our special pleasure to acknowledge fruitful collaborations with Ron Miller, David Rodney, Vijay Shenoy, and Ellad Tadmor. Tadmor's Ph.D. thesis laid the groundwork for all subsequent efforts on the quasicontinuum method and included the first applications to the problem of nanoindentation. Shenoy developed the version of the quasicontinuum method in which multiple grains could be accounted for simultaneously, whereas Rodney created the first three-dimensional version of the code. We are also grateful to the AFOSR which funded much of this work through Grant F49620-95-I-0264 and the NSF which supported much of this work under Grants CMS-9414648 and DMR-9632524.