A minimal integer automaton behind crystal plasticity

Abstract

Power law fluctuations and scale free spatial patterns are known to characterize steady state plastic flow in crystalline materials. In this Letter we study the emergence of correlations in a simple Frenkel-Kontorova (FK) type model of 2D plasticity which is largely free of arbitrariness, amenable to analytical study and is capable of generating critical exponents matching experiments. Our main observation concerns the possibility to reduce continuum plasticity to an integer valued automaton revealing inherent discreteness of the plastic flow.

4 pages, 5 figures

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• On the critical nature of plastic flow: one and two dimensional models
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• The role of phase compatibility in martensite
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• Stress in ordered systems: Ginzburg-Landau type density field theory
• Inelastic rotations and pseudo-turbulent plastic avalanches in crystals
• Homogeneous nucleation of dislocations as a pattern formation phenomenon
• Dislocation avalanches from strain-controlled loading: A discrete dislocation dynamics study
• Modelling avalanches in martensites
• Plate-like precipitate effects on plasticity of Al-Cu alloys at micrometer to submicrometer scales
• Exact results for a toy model exhibiting dynamic criticality
• Quantized plastic deformation
• Slip-dominated structural transitions
• Depinning as a coagulation process
• Intermittency in crystal plasticity informed by lattice symmetry