---
title: 'Tamaas: a library for elastic-plastic contact of rough surfaces'
tags:
  - C++
  - Python
  - contact
  - rough surface
  - plasticity
authors:
  - name: Lucas Frérot
    orcid: 0000-0002-4138-1052
    affiliation: 1
  - name: Guillaume Anciaux
	orcid: 0000-0002-9624-5621
    affiliation: 1
  - name: Jean-François Molinari
	orcid: 0000-0002-1728-1844
    affiliation: 1
affiliations:
 - name: Civil Engineering Institute, École Polytechnique Fédérale de Lausanne, Switzerland
   index: 1
date: 13 December 2019
bibliography: paper.bib

---

# Summary

Physical phenomena that happen at solid contact interfaces, such as
friction and wear, are largely entwined with the roughness of the
surfaces in contact. For example, the fact that the friction force
between two solids in contact is independent of their apparent contact
area is due to roughness, as the solids are only in contact over a
smaller "true contact area" which only depends on the normal force.
Roughness occurs on most man-made and natural surfaces alike
[@persson_nature_2005] and can span many orders of magnitude, from the
nanometer scale to the kilometer scale [@renard_constant_2013]. This
poses a serious challenge to conventional solid mechanics numerical
approaches such as the finite-element method.

``Tamaas`` is a C++ library with a Python interface, developed in the
[Solid Mechanics Simulation Lab](https://www.epfl.ch/labs/lsms) at
EPFL, that implements a unique Fourier-accelerated volume integral
formulation of equilibrium [@frerot_fourieraccelerated_2019] for the
solution of elastic-plastic rough contact problems. The use of C++
allows for a particular focus on performance: most loops are
paralelized using ``Thrust/OpenMP`` and the fast-Fourier transforms are
computed with ``FFTW3/OpenMP``.

# Use and examples

``Tamaas`` provides access in its Python API to random rough surface
generation procedures (e.g. @hu_simulation_1992), statistical tools
(e.g. autocorrelation and power spectrum computations) and a variety
of contact algorithms:

- Normal and adhesive contact schemes based on the conjugate gradient
  [@polonsky_numerical_1999], [@rey_normal_2017];
- Frictional contact;
- Elastic-plastic contact [@frerot_fourieraccelerated_2019].

``Tamaas`` also exposes in its Python API the accelerated linear
operators it uses to compute equilibrium solutions, making prototyping
new algorithms convenient.

The following publications have been made possible with ``Tamaas``:

- @yastrebov_contact_2012
- @yastrebov_contact_2014
- @yastrebov_infinitesimal_2015
- @yastrebov_accurate_2017
- @yastrebov_role_2017
- @rey_normal_2017
- @rey_stability_2018
- @rey_quantifying_2019
- @frerot_mechanistic_2018
- @frerot_fourieraccelerated_2019
- @frerot_crack_2019

# Acknowledgements

We acknowledge the financial support of the Swiss National Science Foundation (grant #162569 "Contact mechanics of rough surfaces").

# References