Abstract. A novel analysis of homogeneous nucleation of dislocations in sheared two-dimensional crystals described by periodized-discrete-elasticity models is presented. When the crystal is sheared beyond a critical strain F=F_c, the strained dislocation-free state becomes unstable via a subcritical pitchfork bifurcation. Selecting a fixed final applied strain F_f >F_c, different simultaneously stable stationary configurations containing two or four edge dislocations may be reached by setting F=F_ft/t_r during different time intervals t_r. At a characteristic time after t_r, one or two dipoles are nucleated, split, and the resulting two edge dislocations move in opposite directions to the sample boundary. Numerical continuation shows how configurations with different numbers of edge dislocation pairs emerge as bifurcations from the dislocation-free state.

PACS numbers: 61.72.Bb, 05.45.-a, 82.40.Bj

Print publication: Issue 3 (February 2008)
Received 18 October 2007, accepted for publication 23 November 2007
Published 14 December 2007