Statistical dynamics of early creep stages in disordered materials

This project focused on how materials deform plastically over extended periods when they bear a load below their yield stress. This phenomenon is known as creep and is of interest since many critical civil structures hold loads for long periods, such as, e.g., bridges or damns. These conditions are also relevant in natural systems such as, e.g., the earth’s crust or the arctic ice.

I implemented a stochastic model of plastic deformation based on the Kinetic Monte Carlo method, which considers thermally-activated plastic deformation a Poisson process. Stochasticity represents our imperfect knowledge about processes occurring at tiny scales beyond the model resolution, which eventually impacts the simulation scale. For some materials, it can be understood as the effects of temperature.

I simulated materials under a range of conditions. With the simulated data, I studied how those conditions statistically affect the evolution of the material’s local strength and the spatial correlation of the plastic activity. The most exciting finding was that changes in any of those conditions or properties induce changes anywhere we look, except in a specific statistical law that remains unchanged. Even more interesting is that this law does change, but only as a function of the material’s local strength heterogeneity. This law describes how the average time between consecutive plastic events evolves in the early stages of the creep deformation process.

Why is it relevant? Because such behavior matches remarkably well Omori’s law of earthquake aftershocks. Scientists have studied seismic activity for many decades, including the changes in Omori’s law (specifically, its exponent p) across different locations and times. Such changes might have something to teach us about the occurrence of earthquakes. This simulation work suggests that changes in Omori’s law might be related primarily to variations in the earth’s crust heterogeneity. Although the initial focus was the deformation of material samples, this work might unexpectedly be another little step in the big puzzle of seismic activity. You can find a continuation of this work here.