An asymptotic formula for displacement field in triangular lattice with vacancy

摘要

A harmonic triangular lattice with a vacancy under imposed volumetric strainis considered. Simple asymptotic formula for the displacement field is derived.The formula has reasonable accuracy at all lattice nodes. Strain concentrationfactor, defined as the ratio of the maximal deformation of the bonds adjacentto the vacancy to the deformations of bonds at infinity, is calculated. It isshown that the asymptotic formula predicts the strain concentration factor with4% accuracy. The results are compared with predictions of continuum elasticitytheory. Effective diameter of the vacancy is calculated.