It is clear that if we overload a structure, it will collapse immediately. For this reason, having well-established safe operation limits is necessary. Nonetheless, materials loaded well-bellow their maximum capacity over extended periods can still deform plastically, in a phenomenon known as creep deformation. Moreover, a material might eventually fracture under creep conditions by damage accumulation and localization. If this happens, a structure can fail catastrophically and unexpectedly, even operating within its expected safety limits. This is especially dangerous in civil structures such as bridges and damns and has also been related to natural catastrophic events such as landslides, cliff collapses, and some earthquakes and volcanic eruptions. In this post, we will focus on the creep deformation process, and in a follow-up post, we will discuss the fracture.

To better understand how creep deformation occurs under these conditions, I implemented a stochastic model of plastic deformation based on the Kinetic Monte Carlo method, which considers thermally-activated plastic deformation a Poisson process. This method introduces stochastic behavior in the deformation process, representing our imperfect knowledge about processes occurring at tiny scales beyond the model resolution. You can find more details about this model here.

I simulated materials under various conditions, specifically applied load, temperature, system size, and material heterogeneity. With the simulated data, I studied how those conditions statistically affect the evolution of the material’s properties and the spatial correlation of the plastic activity. We can distinguish three main regimes, typically known as transient, stationary, and accelerating creep. Transient creep corresponds to small deformations that structures undergo once built. This is very well known and accounted for by architects and engineers. Transient creep corresponds to most of the life of a structure, where minimal deformation (if any) occurs. Finally, if a material sample or structure enters the accelerating creep regime, its deformation rate starts to grow quickly, resulting in fracture.

There are plenty of things to discuss during the transient and stationary creep regimes. The model shows that changes in the applied load, temperature, or system size result in changes in any material response we examine. However, the most exciting finding is the existence of a specific statistical law that remains unchanged. 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 Omori’s law of earthquake aftershocks remarkably well, which describes the evolution of earthquake swarms after big earthquakes.

Even more interesting is that the found Omori’s law does change, but only as a function of the material heterogeneity. Scientists have studied seismic activity for many decades, including the changes in Omori’s law (specifically, its exponent p) across different locations and times. The reason is that such changes might have something to teach us about the activation of earthquakes.

The results of this model suggest that changes in Omori’s law might be related primarily (or solely?) to variations in the earth’s crust heterogeneity. Although the initial focus was the deformation of material samples, this model might unexpectedly be another little step in understanding the big puzzle of seismic activity. As we will see in a follow-up post describing the accelerated creep regime, this model captures a great deal of earthquake phenomenology, showing us that the earth’s crust behaves, after all, like a big piece of material.