Abstract
With a view toward helping to bridge the gap, from the continuum side, between discrete and continuum models of crystalline, elastic solids, explicit results are presented for nonlocal stress tensors that describe exactly some lattice dynamical models that have been widely used in the literature for cubic lattices. The surface Green function matching (SGFM) method, which has been used successfully for a variety of surface problems, is then extended, within a continuum approach, to a nonlocal continuum that models a three-dimensional discrete lattice. The practical use of the method is demonstrated by performing a fairly complete analytical study of the vibrational surface modes of the SCC semi-infinite medium. Some results are presented for the [100] direction of the (001) surface of the SCC lattice.
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