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Deformation Patterns and Surface Morphology in a Minimal Model of Amorphous Plasticity

We investigate a minimal model of the plastic deformation of amorphous materials. The material elements are assumed to exhibit ideally plastic behavior (J2 plasticity). Structural disorder is considered in terms of random variations of the local yield stresses. Using a finite element implementation of this simple model, we simulate the plane-strain deformation of long thin rods loaded in tension. The resulting strain patterns are statistically characterized in terms of their spatial correlation functions. Studies of the corresponding surface morphology reveal a non-trivial Hurst exponent of approx. 0.8, indicating the presence of long range correlations in the deformation patterns. The simulated deformation patterns and surface morphology exhibit persistent features which emerge already at the very onset of plastic deformation, while subsequent evolution is characterized by growth in amplitude without major morphology changes. The findings are compared to experimental observations.