New paper on preventing seismic slip and controlling self-organized criticality

Please find enclosed a new work on earthquake and self-organized criticality control: https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2021JB023410

Based on the mathematical developments presented in this paper and on others to follow, we show mathematically that fluid pressure can be used to stabilize and control the unstable fast seismic slip of a mature fault. In a more general framework, we discuss also the possibility of controlling complex systems exhibiting self-organized criticality due to frictional instabilities.

New paper on Thermodynamics-based Artificial Neural Networks (TANN) for the constitutive modeling of inelastic materials with microstructure

Please find enclosed the second of a series of three works on TANN that was recently published in Computer Methods in Applied Mechanics and Engineering (doi: 10.1016/j.cma.2022.115190, https://authors.elsevier.com/c/1fGS5AQEIzV-w).

In this paper we show how thermodynamics can be explicitly inserted into neural networks to guarantee thermodynamically consistent predictions of the behavior of complex materials with inelastic microstructure. We also show how internal state variables can be automatically discovered and give access to the salient micro-mechanisms that are related to the non-linear macroscopic behavior. Finally, based on a double-scale asymptotic homogenization scheme, we perform multiscale analyses achieving speed-ups of many orders of magnitude compared to micromechanical simulations.

Any comments will be highly appreciated!

Congratulations to Dr Alexandros Stathas for his successful PhD thesis defense!

I am very happy and proud of you Alexandre! Excellent work and presentation!
For those that could not attend the defense here is the full recording:
https://youtu.be/naSJC2cMEJs

Earthquake control: impossible or adjacent possible?

Check out the talk by Ioannis Stefanou and Filippo Masi at the Data-Centric Engineering Institute of the University of Sydney

Earthquakes nucleate when large amounts of elastic energy are suddenly released due to abrupt sliding over seismic faults. Besides physical causes, this energy release can be also triggered by injecting large amounts of fluids in the earth’s crust. Indeed, recent events show that injections can reactivate existing seismogenic faults and induce/trigger important earthquakes.

However, one can see the problem of fluid injections from another perspective. The dependence of fault friction on fluid pressure can be used as an input for stabilizing it. New results based on the mathematical theory of control show that it is indeed possible to stabilize and restrict chaos in this kind of non-linear unstable frictional systems and assure slow frictional dissipation toward desirable global asymptotic equilibria of lower potential energy.

Our mathematical derivations show that earthquake robust control is possible, provided that fault friction is bounded. Friction is a complex phenomenon involving several spatio-temporal scales and complex dynamics. In spite of complexity, the finiteness of energy of any physical process influencing friction as well as existing laboratory and in-situ experiments, support the boundedness of friction. However, the quantification of these bounds is challenging as experiments are difficult to perform deep down in the earth. As a result, we have to rely also on numerical simulations and digital twins of seismic faults, which until know are computationally very demanding.

To this end, we develop a novel deep learning approach for modeling complex materials, by enforcing the laws of thermodynamics. The method is accurate, fast and scalable, and will allow, in the near future, to derive reliable quantitative estimations of the bounds of fault friction under the effect of multiphyics couplings and complex grain/particle dynamics. In parallel, it will enable to optimize our earthquake control strategies by performing large scale simulations of real fault systems in a virtual, data- and physics-driven environment, that fits on a laptop.

Presentation slides are available here

Does viscosity regularize mesh dependency and strain localization on a mathematical plane?

The answer is no! In https://authors.elsevier.com/a/1dux9AQEIviHm (https://doi.org/10.1016/j.cma.2021.114185) we prove mathematically and show numerically that viscoplasticity of Perzyna or consistency type in combination with inertia cannot prevent (a) strain localization on a mathematical plane and (b) mesh dependency in numerical calculations.

We show also the existence of emergent traveling plastic waves and we investigate some of their properties. These waves can be related to the Portevin–Le Chatelier effect and are also observed in numerical simulations of fault gouges under large shear. To be continued!

Complex 3D plot of dispersion functions derived after bifurcation analysis.