Abstract
ABSTRACT The boundary equation establishes the relationship between the displacement and the external force on the boundary of a solid. In the short-range interaction approximation, the boundary equation of a half-infinite lattice can be formally derived in lattice statics. Based on a model of cubic lattice, the boundary matrix as the kernal of the boundary equation is studied and calculated. In particular, the boundary matrix is completely presented for quasi one-dimensional problem and the leading order correction to the results in the elastic continuum theory is explicitly determined. The boundary equation can be used to derive the dislocation equation as a generalisation of classical Peierls equation. As an application, the modification of the Peierls equation is obtained and relevant coefficients are successfully related to bulk properties of solids.
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