## Background/Motivation

The second order frictional behavior of materials is important to understanding of engineering problems, industrial production processes, and to modeling the behavior of earthquakes. Laboratory experiments are often performed to measure the frictional constitutive parameters of various materials. Analyzing these data requires a forward model of the rate-and-state frictional framework and an inversion method.  The system of equations is very stiff, making the solution very sensitive to the integrator settings. Experimentalists often like to try modifications to the constitutive equations by using different state evolution relations and are in need of a proven and easy to use modeling framework.

Currently, most scientists use numerical methods that are generally not well tested and there is little unit testing and code vetting. Our goal is to develop a framework for both experimentalists and modelers to use in a testable and reliable way.

## Methods

We have developed a simple forward modeling tool that allows open experimentation and can be used for data fitting. This tool nicely compliments other data analysis routines we have developed in Python specifically for rock and sediment mechanics data analysis.

The tool is used to model data collected during laboratory scale fault friction experiments conducted on a large, servo-controlled hydraulic press. This allows us to obtain the velocity behavior of the experimental fault and predict how such materials would behave in a natural setting.

Using Python enables us to employ very well tested integrators and completely decouple the model problem from the numerical method. This allows rooms for numerical experimentation and provides an interface that is much easier to use than current systems.

## Results

Our tool, rsfmodel, produces results comparable to tools currently in use by the community, but in a way that is much easier to interface with. Experimental data can be well represented by the model. Development is underway to implement data inversion with the covariance matrix adaptation evolutionary strategy  (CMA-ES). Without the versatility of Python, such a tool would require many more SLOC and be more difficult for users to interface with.

## Conclusions

We present a working model that can represent the complex transient frictional behavior of real materials with applications to problems ranging from earthquakes to railroad transportation and granular material handling.


## Short
We have developed a tool to model transitional frictional behavior, important to industrial problems of granular material handling and natural problems such as earthquake physics. Without Python and its well tested numerical packages, we would be unable to implement such a clean and easy to interface with solution. This is much more desirable than each scientist writing their own model with differing amounts of unit testing and error checking. The interface also encourages trials of different solving methods and numerical formulations of the problem.