Homogeneous nucleation of dislocations as bifurcations in a periodized discrete elasticity model

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: 23 November 2007

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 , the strained dislocation-free state becomes unstable via a subcritical pitchfork bifurcation. Selecting a fixed final applied strain , different simultaneously stable stationary configurations containing two or four edge dislocations may be reached by setting 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.