Continuum mechanics has been extended to the nanoscale (not the atomic or molecular scale).
Continuum mechanics does well in describing macroscale phenomena, so long as we have good descriptions of material behavior, for example a good equation of state or a good description of stress-deformation behavior. The usually unspoken assumption is that, at each point in the material, these descriptions of behavior are valid out to “infinity” (perhaps 50 nm). So long as bulk behavior dominates the phenomena with which we are concerned, there is no problem. This is the case in the majority of the solid and fluid mechanics problems with which we are familiar.
However, we run into trouble in attempting to discuss phenomena that are dominated by long-range intermolecular forces from adjoining phases. In discussing single interfaces, we can correct for these effects by introducing a surface tension or a surface energy. More generally, we recommend correcting for these forces by the introduction of an appropriate body force (a mutual force).
We have successfully used this theory to predict surface tensions, supercritical adsorption, contact angles, and the critical energy release rate for the fracture of diamond and of silicon. All of these comparisons with experimental data are done with no adjustable parameters.
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