Statistical dynamics of creep: a Monte Carlo model of materials and earthquakes (||)

This post is a follow-up to a previous post. As explained in that post, materials loaded well-bellow to their maximum capacity over extended periods might eventually fracture by damage accumulation and localization. If this happens, a structure can fail catastrophically and unexpectedly, even operating within its expected safety limits, which is especially dangerous in civil structures such as bridges and damns. Moreover, this type of deformation has also been related to natural catastrophic events such as landslides, cliff collapses, and some earthquakes and volcanic eruptions.
We can extend the Monte Carlo model of the previous post to allow it to simulate the approach to fracture. To this end, we consider material damage, defined as a reduction of the material’s local strength due to plastic deformation. This kind of damage generation mechanism leads to a positive feedback loop: deformation induces damage, which fosters future deformation, leading to more damage… This is observed in an accelerated deformation rate. When damage is severe enough, the material fractures. You can find details about the model here.

Analyzing the data from the simulated material samples under different applied loads, temperatures, system sizes, and material heterogeneity, I looked at how the deformation’s statistical properties change over time as the fracture point is approached. The findings reveal a systematic evolution in the intensity and time separation between plastic events as the fracture approaches. These changes might serve as early warning signals of an imminent catastrophic event and help enhance hazard assessment techniques.

Here are some videos of a creep fracture simulation:

On the left, we see the amount of plastic deformation versus time. On the right, the spatial activity map shows how the deformation is spread through the material. Initially, the activity is quite random, but as time passes, correlations emerge, and the deformation localizes into a shear band. Eventually, the deformation rate diverges, and the material fractures.

In this other video, we can see the deformation of a sample under compressive loading, as fracture is approached:

Moreover, as discussed in the previous post, the results prove a deep connection between this model –designed to simulate plastic deformation in materials– and the phenomenology observed in earthquakes. Specifically, the model reproduces the Gutenberg-Richter law of event magnitudes. Even more, it reproduces the reduction of the law’s exponent as the fracture is approached, similar to what is sometimes observed when a big earthquake is about to occur. Also, as the fracture comes, we find the inverse Omori law, which in seismicity is the observation that, before a big earthquake, swarms of accelerating smaller earthquakes occur. Finally, we found a very good match in the distribution of plastic events and the time separation between consecutive earthquakes.
In summary, the model shows how a great deal of phenomenology is shared between regular material samples deforming under creep conditions and the occurrence of earthquakes on the earth’s crust. This similarity can allow us better understand earthquakes by performing laboratory tests on materials. On the other hand, it can enable us to better understand materials by exploring the tremendous amount of data in earthquake catalogs built over many decades.