Homogeneous nucleation of dislocations as bifurcations in a periodized discrete elasticity modelI. Plans1, A. Carpio2 and L. L. Bonilla1
1 G. Millán Institute for Fluid Dynamics, Nanoscience and Industrial Mathematics, Universidad Carlos III de Madrid 28911 Leganés, Spain
2 Departamento de Matemática Aplicada, Universidad Complutense de Madrid - 28040 Madrid, Spain
received 18 October 2007; accepted in final form 23 November 2007; published February 2008
published online 14 December 2007
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 = Fc, the strained dislocation-free state becomes unstable via a subcritical pitchfork bifurcation. Selecting a fixed final applied strain Ff > Fc, different simultaneously stable stationary configurations containing two or four edge dislocations may be reached by setting F = Ff t/tr during different time intervals tr. At a characteristic time after tr, 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.
61.72.Bb - Theories and models of crystal defects.
05.45.-a - Nonlinear dynamics and chaos.
82.40.Bj - Oscillations, chaos, and bifurcations.
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