Stability of 2D triangular lattice under finite biaxial strain

Abstract

Stability of 2D triangular lattice under finite biaxial strain is investigated. In this work only diagonal strain tensor is regarded. The lattice is considered infinite and consisting of particles which interact by pair force central potential. Dynamic stability criterion is used: frequency of elastic waves is required to be real for any real wave vector. Two stability regions corresponding to horizontal and vertical orientations of the lattice are obtained. It means that a structural transition, which is equal to the change of lattice orientation, is possible. The regions’ boundaries are explained: wave equation coefficients change their signs at the border, as well as Young modulae and shear modulae. The results are proved by direct numerical simulation.