# rate-state dependent friction in ANSYS

Dear collegues

a quick question:- I am playing with continuum models of Contact (Hertz, Westergaard and so on) and friction laws. However, I prefer for my students to use ANSYS FEM code. In Ansys there is standard Coulomb, rate-dependence but not rate-state (unless one codes some user subroutines). See

https://www.sharcnet.ca/Software/Fluent14/help/ans_ctec/Hlp_ctec_realkey...

Dieterich (1979) and Ruina (1983), see also Dieterich (2007), suggested a rate- and state-dependent friction law to explain a large amount of laboratory data on rock friction. Other regularized friction laws exist, in particular a simplified version of a Prakash and Clifton (1993) friction law obtained experimentally was used by Cochard and Rice (2000) which confirmed in the unstable range numerical solutions do not converge through grid size reduction. Finally, Ben-Zion and Huang (2002) found that the self-sharpening and divergent behaviour exists also with a regularized law, for large enough propagation distance and that "the parameters of regularized friction have to be fine tuned to produce apparent stability for a given propagation distance".

Do you know who can have implemented these user subroutines for the classical rate-state laws?

Mike

References

Dieterich, J.H., (1979). Modeling of rock friction 1. Experimental results and constitutive equations. J. Geophys. Res. 84, 2161-2168
Dieterich J.H. (2007) Applications of Rate- and State-Dependent Friction to Models of Fault Slip and Earthquake Occurrence, Treatise on Geophysics, 2007, Chapter 4.04, Pages 107-129
Prakash V., Clifton R.J., (1993) "Time-Resolved Dynamic Friction Measurements in Pressure- Shear, Experimental Techniques in the Dynamics of Deformable Solids", Applied Mechanics Div., vol. 165, 33-48.
Cochard A., Rice J.R., (2000) "Fault rupture between dissimilar materials: Ill-posedess, regularization and slip-pulse response", Journal of Geophysical Research, 105, 25 891.

### I did find a very interesting Cattaneo Mindlin problem in ANSYS

https://www.sharcnet.ca/Software/Fluent14/help/ans_vm/Hlp_V_VM272.html

but still I was hoping to see Rate-State dependent friction to add to this.

I am not aware of anyone who has created subroutines for Ansys. There is an open-source FEM code, Pylith, which I think has rate and state friction implemented. It can be found here:
https://geodynamics.org/cig/software/pylith/#release

http://esag.harvard.edu/rice/164_Rice_SpatTempComplex_JGR93.pdf

and

http://esag.harvard.edu/rice/192_Lap_Ri_BZ_Zh_JGR_00.pdf

for formulations "in the spirit of BIE methods". I think Nadia and her students/coworkers have made many updates in the 15 years since then.

Best wishes, Jim

### Rate and state, Any Benchmark ?

I just implemented rate and state friction law uwing the FRIC subroutine in Abaqus. I would like to know if there is any benchmark to test if the implementation is fine.

Regards,

Saber

### Rate and State friction

Hello Mike, if you are still interested in modeling rate and state friction I will be more than happy to discuss. This is a very interesting topic to me personally and I believe that while R&S friction is "widely" considered in geophysics, it still has not made its way to the mechanics community as it should.

Saber: The Southern California Earthquake center holds a code validation exercise and there is a set of benchmark problems to compare to which you can find here: http://scecdata.usc.edu/cvws/

Best Wishes,

Ahmed