Abstract
The advance in nanotechnology has lead to necessity to determine strength properties of crystal structures. Stability of a structure under finite deformations is closely connected with its strength. In this work stability of plane triangular (single atomic layer of FCC and HCP) and FCC lattices under finite strain is investigated. Analysis and modeling based on discrete atomistic methods is proposed. The medium is represented by a set of particles which interact by a pair force central potential, e.g. Lennard-Jones and Morse. Direct tensor calculus is used. Dynamic stability criterion is established: frequency of elastic waves is required to be real for any real wave vector. The considered approach allows to describe structural transitions in solids on the base of stability investigation of pre-strained crystal lattices. The results of direct MD simulation do not contradict the results of the calculations.
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