Avalanches, loading, and finite-size effects in 2D amorphous plasticity

Plastic deformation at the mesoscale is commonly simulated based on stochastic processes and a set of simplifying assumptions. On the other hand, the Finite Element Method is commonly used in engineering settings for describing the mechanics of solid bodies under realistic conditions.

I implemented a model in C++ which combined both techniques, which allowed us to perform stochastic simulations under conditions closer to reality than stochastic models usually can. Specifically, the model allowed to simulate the plastic deformation of materials bounded by surfaces, a situation much closer to reality than the periodic boundaries typically used by stochastic models. From the data produced by the model, I estimated the probability distributions for different properties and computed spatial maps of plastic activity. The results showed that surfaces lead to changes in the spatial activity maps due to the changes they induce in the elastic interactions. Despite those changes, the main statistical laws behind plastic activity remain unchanged. You can find a continuation of this work here.

Here is a video of a simulation run. On the left, we see the stress externally applied on the material’s surfaces versus the total deformation (strain). On the right, the spatial activity map shows how the deformation is spread through the material. Initially, the activity is quite random, but correlations become very important as the stress approaches a critical value, known as the macroscale yield stress. This leads to spatial patterns and avalanches of plastic deformation.