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

TL;DR

This paper analyzes how dislocations nucleate in sheared 2D crystals using a periodized discrete elasticity model, revealing bifurcation phenomena and stable configurations with multiple dislocations.

Contribution

It introduces a novel bifurcation analysis of dislocation nucleation in a periodized discrete elasticity framework, highlighting the role of strain and bifurcation structures.

Findings

Dislocation-free state becomes unstable beyond critical strain F_c.

Multiple stable configurations with different dislocation numbers exist.

Dislocation nucleation occurs via bifurcations and dipole formation.

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 $F=F_{f}t/t_{r}$ 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.