Micromechanical Model for Deformation in Solids with Universal Predictions for Stress-Strain Curves and Slip Avalanches

Abstract

A basic micromechanical model for deformation of solids with only one tuning parameter (weakening $\ensuremath{\epsilon}$) is introduced. The model can reproduce observed stress-strain curves, acoustic emissions and related power spectra, event statistics, and geometrical properties of slip, with a continuous phase transition from brittle to ductile behavior. Exact universal predictions are extracted using mean field theory and renormalization group tools. The results agree with recent experimental observations and simulations of related models for dislocation dynamics, material damage, and earthquake statistics.