A novel analysis was made of the homogeneous nucleation of dislocations in sheared two-dimensional crystals as described by a periodized discrete-elasticity model. When the crystal was sheared beyond a critical strain, F = Fc, the strained dislocation-free state became unstable via a sub-critical pitchfork bifurcation. Selecting a fixed final applied strain, Ff  > Fc, various simultaneously stable stationary configurations containing two or four edge dislocations could be reached by setting F = Fft/tr during various time intervals, tr. At a characteristic time after tr, one or two dipoles were nucleated and split, and the resultant two edge dislocations moved in opposite directions to the sample boundary. Numerical continuation showed how configurations with differing numbers of edge dislocation pairs emerged as bifurcations from the dislocation-free state.

Homogeneous Nucleation of Dislocations as Bifurcations in a Periodized Discrete Elasticity Model. I.Plans, A.Carpio, L.L.Bonilla: EPL, 2008, 81, 36001