Lucas Frérot

Evolution of the contact between rough viscoelastic solids after decreasing loads: memory erasure and monotonic increase

Tue, 25 Nov 2025 00:00:00 +0000

Authors: Zichen Li, Renald Brenner, Lucas Frérot

The real area of contact governs, in part, the magnitude of the friction force, yet its time evolution in rough viscoelastic interfaces remains incompletely understood. In experiments of contact between polymethylmethacrylate blocks under decreasing normal loads, Dillavou and Rubinstein have shown that the true contact area exhibits, after unloading, a decreasing phase and long-term memory of the contact state prior to unloading. It is however unclear what modeling ingredients are necessary to reproduce these two features. Here, we investigate these effects using fractional viscoelastic rough contact models. By adapting existing contact theories and numerical simulation methods to fractional viscoelasticity, which induces a wide relaxation spectrum, we reproduce logarithmic aging under constant load, but show that memory of the contact state is erased upon unloading. Indeed, the contact area behaves as if it had always experienced the reduced load, even on short time-scales, contrasting with the response of a standard linear solid. Moreover, none of our results show a decreasing regime of the contact area after unload: we ultimately prove that this is the case for all linear viscoelastic models—despite capturing logarithmic aging—leading to the conclusion that additional local internal variables are required to explain both long-term contact memory and contact area reduction after unloading.

Cover art: made with Matplotlib, computed with Tamaas

Presentation at ICTAM 2024, Daegu, South Korea

Tue, 27 Aug 2024 00:00:00 +0000

I participated, as a presenter in the ICTAM 2024 organized in Daegu, South Korea, and gave a talk on:

Elastic shakedown and roughness evolution in repeated elastic-plastic contact

Co-authors: Lars Pastewka

ICTAM is a four-year cycle conference on all areas of mechanics, with experimental, numerical and theoretical approaches showcased. The tribology and contact mechanics symposium was organized by Ramin Aghababaei and Marco Paggi.

Presentation at ECCOMAS 2024, Lisbon, Portugal

Mon, 03 Jun 2024 10:00:44 +0200

I presented, in the European Congress on Computational Methods in Applied Sciences and Engineering, some high-performance aspects and code design of Tamaas, in the open-source softwares in mechanics symposium co-organized by Vladislav Yastrebov (Mines PSL), Lukasz Kaczmarczyk (U. Glasgow), Tzanio Kolev (Laurence Livermore National Labs), Andrei Shvarts (U. Glasgow).

Presentation at CMIS 2024, Lyon, France

Thu, 30 May 2024 17:29:04 +0200

I participated, as a presenter, in the Contact Mechanics International Symposium (CMIS) organized in Lyon by LaMCoS and LTDS, and gave a talk on:

Elastic shakedown and roughness evolution in repeated elastic-plastic contact

Co-authors: Lars Pastewka

CMIS is a symposium dedicated to bringing together scientists working in all aspects of contact mechanics, from applied mathematicians to tribologists, with a good balance of theoretical, numerical and experimental approaches.

CMIS Group Photo

Akantu: an HPC finite-element library for contact and dynamic fracture simulations

Fri, 23 Feb 2024 00:00:00 +0000

Authors: Nicolas Richart, Guillaume Anciaux, Emil Gallyamov, Lucas Frérot, David Kammer, Mohit Pundir, Marco Vocialta, Aurelia Cuba Ramos, Mauro Corrado, Philip Müller, Fabian Barras, Shenghan Zhang, Roxane Ferry, Shad Durussel, and Jean-François Molinari

Complex, nonlinear, and transient phenomena are at the heart of modern research in mechanics of materials. For example, the buildup and release of elastic energy at geological fault is what causes earthquakes, and the intricate details of the slip zone, the propagation of slip fronts and waves radiated through the various geological media are still active areas of research (Kammer et al., 2012, 2014; Roch et al., 2022). Similarly, understanding fracture in heterogeneous materials such as concrete, masonry or ceramics necessitates the modeling of interaction of crack fronts with complex materials (A. I. Cuba Ramos et al., 2018; Taheri Mousavi et al., 2015; Yilmaz et al., 2017), the representation of residual shear stresses in the contact of newly-formed crack surfaces (Pundir & Anciaux, 2021; Zhang et al., 2017), and the accurate characterization of transient dynamics (Corrado & Molinari, 2016; Vocialta et al., 2018) and material structure evolution (A. I. Cuba Ramos et al., 2018; Gallyamov et al., 2020). The finite-element method is now ubiquitous in virtually all areas of solid mechanics. With meticulous care on code architecture and performance, we show that our finite-element library Akantu can handle the requirements mentioned above for state-of-the-art research in mechanics of materials. Akantu is designed from the ground up for high-performance, highly distributed computations, while retaining the necessary flexibility to handle:

crack propagation with cohesive elements
non-local damage models
plastic and visco-plastic constitutive laws
large deformations
contact constraints (including rate and state friction)
interaction between contact and cohesive elements (residual crack shear strength)

Cover art: dynamic fragmentation of a sheared interface simulated in large deformations with Akantu and rendered with Paraview

Teaching

Sun, 11 Feb 2024 00:00:00 +0000

At Sorbonne University, I currently teach:

LU3ME104, Numerical Projects, (BA3, class material)
MU4MEM03, Vibration and Waves (MA1, class material)

At Polytech’ Sorbonne, I currently teach:

Mechanics of 2D elastic solids and beams (MA1 equivalent)
Vibrations (MA2 equivalent)

Below is a list of my past teaching activities (as postdoc and graduate student), in reverse chronological order:

Apr.–Sep. 2023, High Perforamance Molecular Dynamics with C++, Teaching assistant, 56 hours, Course material
Oct.–Apr. 2023, Simulation techniques, Teaching Asssistant, 56 hours, Course material
Apr.–Sep. 2022, High Perforamance Molecular Dynamics with C++, Teaching assistant, 56 hours, Course material
Sep.–Jan. 2018, Scientific programming for engineers, Teaching assistant, 56 hours,
Feb.–Jun. 2018, Mise-à-niveau, Teaching assistant, 112 hours, First year calculus,
Sep.–Jan. 2017, Scientific programming for engineers, Teaching assistant, 56 hours,
Feb.–Jun. 2017, Numerical modeling of solids and structures, Teaching assistant, 56 hours,
Sep.–Jan. 2016, Scientific programming for engineers, Teaching assistant, 56 hours,
Feb.–Jun. 2016, Numerical modeling of solids and structures, Teaching assistant, 56 hours,
Sep.–Jan. 2015, Continuum mechanics, Teaching assistant, 12 hours,
Feb.–Jun. 2015, Statics I, Teaching assistant, 56 hours, Videos: Showing that a structure is isostatic, Show that a truss is isostatic
Feb.–Jun. 2014, Statics I, Teaching assistant, 56 hours.

Below is a list of students projects I have supervised, in reverse chronological order:

Feb. 2023–Aug. 2023, Project supervision, Multi-level sommation techniques for half-space contact in C++ (BA),
Dec. 2022–Aug. 2023, Project supervision, Material point method for solids (MA),
Feb.–Jun. 2018, Project supervision, 56 hours, Introduction to contact mechanics: Elastoplastic normal contact between solids (MA); Non-Linear Dynamic Deformations Model Applied to Earthquake Engineering (BA),
Sep.–Jan. 2017, Master project supervision, 112 hours, Modélisation et optimisation des structures en coque par éléments finis,
Feb.–Jun. 2017, Project supervision, , 28 hours, Dynamique en éléments finis (BA),
Sep.–Jan. 2016, Project supervision, 56 hours, Plasticité avec la méthode des éléments finis~: analyse unidimensionelle (BA); Coupling of finite element with Green’s functions analytic expressions (MA),
Feb.–Jun. 2016, Project supervision, 28 hours, Implementation of a Constitutive Law for Concrete (MA).

matscipy: materials science at the atomic scale with Python

Tue, 30 Jan 2024 10:32:57 +0100

Authors: Petr Grigorev, Lucas Frérot, Fraser Birks, Adrien Gola, Jacek Golebiowski, Jan Grießer, Johannes L. Hörmann, Andreas Klemenz, Gianpietro Moras, Wolfram G. Nöhring, Jonas A. Oldenstaedt, Punit Patel, Thomas Reichenbach, Thomas Rocke, Lakshmi Shenoy, Michael Walter, Simon Wengert, Lei Zhang, James R. Kermode, Lars Pastewka

Behaviour of materials is governed by physical phenomena that occur at an extreme range of length and time scales. Computational modelling requires multiscale approaches. Simulation techniques operating on the atomic scale serve as a foundation for such approaches, providing necessary parameters for upper-scale models. The physical models employed for atomic simulations can vary from electronic structure calculations to empirical force fields. However, construction, manipulation and analysis of atomic systems are independent of the given physical model but dependent on the specific application. matscipy implements such tools for applications in materials science, including fracture, plasticity, tribology and electrochemistry.

Cover art: made with Blender, BCC edge dislocation junction data provided by Petr Grigorev.

Elastic Shakedown and Roughness Evolution in Repeated Elastic-Plastic contact

Wed, 17 Jan 2024 00:00:00 +0000

Authors: Lucas Frérot, Lars Pastewka

Surface roughness emerges naturally during mechanical removal of material, fracture, chemical deposition, plastic deformation, indentation, and other processes. Here, we use continuum simulations to show how roughness which is neither Gaussian nor self-affine emerges from repeated elastic-plastic contact of a rough and rigid surface on a flat elastic-plastic substrate. Roughness profiles change with each contact cycle, but appear to approach a steady-state long before true elastic shakedown of the substrate. We propose a simple dynamic collapse for the emerging power-spectral density, which shows that the multi-scale nature of the roughness is encoded in the first few indentations. In contrast to macroscopic roughness parameters, roughness at small scales and the skewness of the height distribution of the resulting roughness do not show a steady-state, with the latter vanishing asymptotically.

Cover art: made with Blender, computed with Tamaas, HDRI from Polyhaven.

Tamaas update, press mentions and future work

Tue, 28 Nov 2023 10:30:55 +0100

Tamaas’ footprint in the tribology community

Tamaas, the open-source, high-performance rough contact simulation library, is slowly seeing adoption in the academic and industrial tribology communities. Since its first public release in 2019, after 4 years of git-recorded history, and longer prior apocryphal development, Tamaas has been used outside of its research “birthplace” to study contact of non-Gaussian surfaces, benchmark a spherical cap harmonic analysis method for non-flat rough surfaces, validate finite-element rough contact solutions, investigate conductivity of rough contacts, gain insights in elastic-plastic rock contacts and ice friction, probably among other uses that I am not aware of.

The December 2023 cover story of Tribology & Lubrication Technology, the magazine of the Society of Tribologists and Lubrication Engineers, mentions Tamaas as a positive example of open-source code in the tribology community, which is still very closed when it comes to modeling efforts.

This is the perfect occasion for me to talk about the evolution of Tamaas: what new features were added since the first public release, what is the state of Tamaas’ support (human and financial), and what developments are planned for its future.

Retrospective

PhD work — Development at LSMS on volumetric elastic-plastic contact

When Guillaume Anciaux shared his code with the Computational Solid Mechanics Laboratory, and Ramin Aghababaei chose the name Tamaas, at the start of my PhD thesis in 2016, the library was only capable of solving normal elastic contact of rough surfaces. The first year of development saw the addition of adhesive and saturated contact solvers by Valentine Rey and associated friction solvers by myself (later reimplemented in the new core by Son Pham-Ba). In the middle of 2017 I started reimplementing the core of the library in anticipation of the 3D developments necessary for elastic-plastic contact. After the derivation of the Fourier-space Mindlin solution in December 2017, 2018 saw the implementation of the Fourier-accelerated volume integral method, which was presented at ECCOMAS 2018 in Glasgow.

The last year of my PhD was dedicated to polishing the code (e.g. with a symbolic, compile-time integration library, expolit, now part of Tamaas’ source tree), creating the documentation, preparing a Python package installable with pip. In fall of 2019, a Zenodo release, coinciding with the submission of my thesis manuscript and the preprint submission of my article on crack nucleation in rough contacts, marked the first public release of Tamaas.

Post-PhD work — Improving usability and performance

This first release, version 2.0.0, marks a soft feature freeze in terms of modeling abilities, but the start of significant improvements to quality of life and performance features.

Since version 2.0.0, feature improvements are documented in the CHANGELOG. The year 2020 marks the publication of the JOSS article, the transition to Gitlab, the improvement of ease of use of the build-system, and most importantly a working MPI implementation. In 2021, the Python interface of core objects was reworked to be more Pythonic, and input-output routines were improved. In 2022, a good number of utility functions were added, the scipy.sparse.linalg.LinearOperator interface was implemented for a number of Tamaas’ integral operators, allowing seamless integration with Scipy’s linear solvers. Finally, new modeling features and performance improvements were added in 2023: among them the ability to simulate non-periodic contact, as well the possibility of modeling contact with heterogeneous materials. An Anderson-mixing iteration was implemented, drastically improving the reliability and performance of elastic-plastic contact simulations, and more of Tamaas’ internals were exposed on the user-facing Python API, giving more flexibility in prototyping new simulation procedures.

Buildup of roughness from elastic-plastic indentation, computed with Tamaas on 30 CPUs with MPI, made possible with Anderson acceleration

Perspective

Having found a permanent academic position in an institution supportive of high-performance mechanics simulation codes (Basilisk and the PARIS Simulator Code, among many others, are supported by ∂‘Alembert), the future of Tamaas as an, open, active tribology research project is secure!

I cannot discuss new modeling efforts in store for Tamaas yet (research proposals in the pipeline), but several major technical improvements are planned for the near future:

Integration with the PETSc matrix-free API and solvers (linear, non-linear and constrainted) is in the works. Tamaas’ solvers are good but rather limited, and Scipy’s solvers are not parallel. PETSc implements robust solvers that can be used in an MPI context, and is used by much larger projects than Tamaas (e.g. Akantu, FEniCS and MoFEM).
MFront is a tool that generates optimized code for constitutive laws written in a domain-specific language. It boasts a large number of tested constitutive laws, and has been successfully integrated in codes like FEniCS. With the recent rework of materials classes in Tamaas, an MFront integration could drastically improve the modeling capabilities of Tamaas.
The MPI implementation has been very robust thus far (I have pushed elastic simulations upwards of 1 billion DOFs and elastic-plastic simulations larger than 150 million DOFs) and should soon make it out of experimental.
In the long-term, consolidation efforts are planned with other open-source packages for contact simulations, like SurfaceTopography and ContactEngineering. The latter is an open-platform cojointly developed by the groups of Lars Pastewka and Tevis Jacobs for the multi-scale analysis of rough surface measurements. A recent plugin system should allow the integration of Tamaas among the analysis methods available!

More than ever, contributions are welcome! Modeling research in tribology is becoming more and more diverse, and Tamaas aims to be a base platform to support this complex endeavor. I wholeheartedly encourage researchers using Tamaas to share their code with the community, or even better, contribute their code back to Tamaas.

Assistant Professor / Maître de Conférences at Institut ∂'Alembert

Fri, 01 Sep 2023 00:00:00 +0000

I joined on September 1st the Solids & Structures (MISES) team of the ∂‘Alembert Institute, at the Sorbonne Université in Paris. I’ll be working on multi-scale modeling of friction between rough surfaces. I’m looking forward to exploring this topic with future colleagues, and to bring my rough surface and contact expertise to their research projects, while contributing to free and open-source software for scientific computing, and promoting open-data and open-access science!

I will also be teaching in the Bachelor and Master mechanical engineering curriculum at la Sorbonne, and the mechanical engineering major of the engineering school Polytech’ Sorbonne.

Presentation at ECCOMAS YIC 2023, Porto, Portugal

Wed, 21 Jun 2023 00:00:00 +0000

I participated, as a presenter, in the ECCOMAS 7th Young Investigators Conference in Porto, and gave a talk on:

Non-linear elasticity and contact of Zinc-Phosphate tribofilms

Co-authors: Lars Pastewka

ECCOMAS YIC is a europe-wide conference “with the main purpose of bringing together, within a relaxed environment, students and young researchers developing their work on all areas related with computational science and engineering.”

Analytic elastic coefficients in molecular calculations: Finite strain, non-affine displacements, and many-body interatomic potentials

Mon, 05 Jun 2023 00:00:00 +0000

Authors: Jan Grießer, Lucas Frérot, Jonas A. Oldenstaedt, Martin H. Müser, Lars Pastewka

Elastic moduli are among the most fundamental and important properties of solid materials, which is why they are routinely characterized in both experiments and simulations. While conceptually simple, the treatment of elastic is complicated by two factors not yet having been concurrently discussed: finite-strain and non-affine, internal displacements. Here, we revisit the theory behind zero-temperature, finite-strain elastic constants and extend it to explicitly consider non-affine displacements. We further present analytical expressions for second-order derivatives of the potential energy for two-body and generic many-body interatomic potentials, such as cluster and empirical bond-order potentials. Specifically, we revisit the elastic constants of silicon, silicon carbide and silicon dioxide under hydrostatic compression and dilatation. Based on existing and new results, we outline the effect of multiaxial stress states as opposed to volumetric deformation on the limits of stability of their crystalline lattices.

Publisher’s version (Physical Review Materials, CC-BY): doi:10.1103/PhysRevMaterials.7.073603
Preprint (arXiv, Open Access): doi:10.48550/arXiv.2302.08754

Cover art: made with Blender with the Atomic Blender addon, amorphous silicon configuration from Matscipy, and assets from ambientCG

From molecular to multi-asperity contacts: how roughness bridges the friction scale gap

Tue, 24 Jan 2023 00:00:00 +0000

Authors: Lucas Frérot, Alexia Crespo, Jaafar A. El-Awady, Mark O. Robbins, Juliette Cayer-Barrioz, Denis Mazuyer

The tangential force required to observe slip across a whole frictional interface can increase over time under constant load, due to any combination of creep, chemical or structural changes of the interface. In macroscopic rate-and-state models, these frictional aging processes are lumped into an ad-hoc state variable. Here, we explain, for a frictional system exclusively undergoing structural aging, how the macroscopic friction response emerges from the interplay between the surface roughness and the molecular motion within adsorbed monolayers. The existence of contact junctions and their friction dynamics are studied through coupled experimental and computational approaches. The former provides detailed measurements of how the friction force decays, post-stiction-peak, to a steady-state value over a few nanometers of sliding distance, while the latter demonstrates how this memory distance is related to the evolution of the number of cross-surface attractive physical links, within contact junctions, between the molecules adsorbed on the rough surfaces. We also show that roughness is a sufficient condition for the appearance of structural aging. Using a unified model for friction between rough adsorbed monolayers, we show how contact junctions are a key component in structural aging, and how the infrajunction molecular motion can control the macroscopic response.

Publisher’s version (ACS Nano, Open Access): doi:10.1021/acsnano.2c08435
Preprint (arXiv, Open Access): doi:10.48550/arXiv.2111.13588
École Centrale de Lyon press release (FR)
Johns Hopkins Press release
Johns Hopkins MechE press release
Phys.org
Azonano report
RCF Interview of Juliette Cayer-Barrioz and Denis Mazuyer (FR)
News CNRS INSIS (FR)
News Nach Welt (GE)
SDSC Story
HPC Wire

Cover art: made with Blender with the Atomic Blender addon, roughness generated with Tamaas from the LTDS AFM measurements (data available), assets from ambientCG, atomic trajectories computed with LAMMPS

Presentation at MMM 2022, Baltimore, USA

Mon, 03 Oct 2022 00:00:00 +0000

I participated, as a presenter, in the Multiscale Materials Modeling conference in Blatimore, and gave a talk on:

From molecular to multi-asperity contacts: the role of roughness in the transient friction response

Co-authors: Alexia Crespo, Jaafar El-Awady, Mark Robbins, Juliette Cayer-Barrioz, Denis Mazuyer

MMM is a world-wide multi-scale material science meeting, with a strong focus on modeling and simulations.

Presentation at WTC 2022, Lyon, France

Mon, 11 Jul 2022 00:00:00 +0000

I participated, as a presenter, in the World Tribology Congress in Lyon, and gave two talks on:

From molecular to multi-asperity contacts: the role of roughness in the transient friction response

Co-authors: Alexia *Crespo, Jaafar El-Awady, Mark Robbins, Juliette Cayer-Barrioz, Denis Mazuyer

Crack nucleation in the adhesive wear of an elastic-plastic half-space

Co-authors: Guillaume Anciaux, Jean-François Molinari

WTC is a world-wide tribology meeting with experimentalists and theoreticians alike.

Presentation at ECCOMAS 2022, Oslo, Norway

Tue, 07 Jun 2022 00:00:00 +0000

I participated, as a presenter, in the ECCOMAS conference in Oslo, for which I gave a talk on:

From molecular to multi-asperity contacts: the role of roughness in the transient friction response

Co-authors: Alexia Crespo, Jaafar El-Awady, Mark Robbins, Juliette Cayer-Barrioz, Denis Mazuyer

ECCOMAS is the largest european conference in the field of computational mechanics, with a strong orientation towards engineering.

Started post-doc at Freiburg University

Mon, 01 Nov 2021 00:00:00 +0000

Today I am starting a postdoctoral fellowship at Freiburg University. I’ll be working with prof. Lars Pastewka on mechanical properties of phosphate glasses and ZDDP tribofilms.

Member of Tribology Letters' Early Career Editorial Board

Wed, 13 Oct 2021 00:00:00 +0000

As per the official announcement, I was appointed to Tribology Letters’ Early Career Editorial Board. Tribology Letters is the leading journal in Tribology and publishes impactful fundamental results from both experimental and computational tribology. As an ECEB member I’ll be doing reviews in my expertise areas and promoting publication of early career tribologists.

Cover art: illustration from unDraw by Katerina Limpitsouni

Winner of the SWICCOMAS Award 2021!

Tue, 23 Feb 2021 00:00:00 +0000

For my PhD work, I was awarded the SWICCOMAS Prize 2021 (archive link).

Cover art: illustration from unDraw by Katerina Limpitsouni

Codes

Fri, 01 Jan 2021 00:00:00 +0000

Programming simulations is a large part of my research work, and I believe developing and maintaining codes for high performance computations and long-term reproducibility is incredibly important, both for environmental reasons and for the sustainability of the research. Software should be treated as any other kind of scientific output. To ensure reproducibility and adoption, I think the only way to distribute scientific software is under an open-source, preferably copy-left, code license.

Below are open-source codes for which I am the lead developer or an active developer.

Tamaas

Tamaas is an open-source library for contact mechanics of rough surfaces. It implements several high-performance contact routines in C++ and makes them available in Python, with a tight integration to Numpy arrays.

UVW

UVW (Universal VTK Writer) is a small open-source Python package I developed in my free time to help with writing VTK formatted files without requiring VTK as a dependency.

Akantu

Akantu is a C++ finite-elements high-performance open source library developed by the LSMS laboratory at EPFL.

Matscipy

Matscipy is a Python framework for material science, atomistic calculations, developped in part by Prof. Pastewka’s group at the University of Freiburg, that is built on top of the Atomic Simulation Environment.

Minor contributions

I’ve also made minor contributions (mostly bugfixes and minor updates) to various codes:

ASE (!2660)
BlackDynamite (!1, !2)
Spack (#10823, #17719, #30292, #30296, #30297, #30449, #31501, #32351)
LAMMPS (#2565)
github/gitignore (#3001)
pytest-mpi (#5)
snakemake (#1951, #1986, #3389)

Publications

Fri, 01 Jan 2021 00:00:00 +0000

Below is a list of my publications (peer-reviewed and preprints), in reverse chronological order, with links to the open-access PDF:

Research

Fri, 01 Jan 2021 00:00:00 +0000

My research revolves around tribology, the science of surfaces. I am particularly interested in the modeling of rough contact interfaces and how understanding these interfaces can help modeling friction and wear of solids.

For a complete list of publications, see my publications list.

Rough contact interfaces

Virtually all real surfaces (from geological fault faces to hard drives, from roads to cartilage) are rough if one looks closely enough. This means that contact between two solids is never perfect, or even smooth: the solids only touch in sparse areas with complex geometries. The “true contact area” is typically only a few percent of the apparent area of contact (the macroscopic dimensions of the solids), and it is from the surface interactions at this “true contact area” that properties like friction and wear emerge (see nanoscale tribology below).

Many natural surfaces exhibit a fractal-like behavior: as one “zooms-in” on roughness, one discovers more roughness at smaller scales.

A "fractal" rough surface, rendered with Blender

The fact that surface roughness does not have a characteristic scale makes contact interfaces challenging to model, because all roughness scales can be relevant and should be accounted for. Things become even more complex when non-linear material behavior comes into play.

During my doctoral work, I have developed an efficient numerical method to model contact of rough surfaces with elastic-plastic materials (such as metals). Below is a picture of such a simulation, where we can see the plastic zones that develop due to the heterogeneous contact pressure.

Distribution of plastic zones below asperties in contact, computed with Tamaas, rendered with Paraview

Such simulations are possible thanks to the use of Fourier-domain Green’s functions that I derived (cf. The Mindlin Fundamental Solution - A Fourier Approach). I have implemented this Fourier-based numerical method for elastic-plastic contact in an open-source code called Tamaas, which is a hybrid C++/Python library for simulating all sorts of contact situations. Feel free to check out the tutorials.

Currently, I am working with my student Zichen Li and colleague Renald Brenner on homogenization techniques for rough contacts with heterogeneous materials.

Illustration of heterogeneous rough contact, rough surface generated with Tamaas, rendered with Blender

Nanoscale tribology

Friction is a phenomenon that takes root in the many, both in kind and in number, molecular interactions that occur when two surfaces are close enough. However, these interactions are greatly influenced by the inevitably present roughness of these surfaces, and by the long distance dialog between micro-contact junctions that takes place through the medium of bulk interactions. This distortion of the molecular picture explains in part why macroscopic friction models, like Amontons–Coulomb friction or the more general “rate-and-state” friction, remain empirical. With energy efficiency being a foremost societal focus in the face of climate change, predictive friction models could provide a boon to design surfaces that greatly reduce friction losses.

My research at molecular scale aims to lift the veil on the mechanisms that occur at the nano-scale, interact with the roughness and greatly influence the macroscopic friction and wear response. For this, I use molecular dynamics to describe the objects in contact and the interactions between surfaces that are rough at the nanoscale. During my two postdocs, I have studied the friction behavior of fatty acid monolayers adsorbed on rough surfaces and how molecular interaction within contact jonctions can explain the transient friction behavior observed in experiments, and contact properties of heterogeneous zinc-polyphosphate tribofilms.

Fatty acid monolayer adsorbed on a nanometrically rough surface, rendered with Blender

Zinc-phosphate tribofilm, rendered with Blender

Scientific Communication

I believe proper scientific communication, targeted at peers but also at the greater public, is an important part of a researcher’s work. To create figures that appeal to the people outside the scientific field, I use cutting edge (open-source) tools like Blender. I recently made a render from roughness measured on a nanoscrystalline diamond surface by Luke A. Thimons and co-workers (doi:10.57703/ce-4r74d), which was used in a press release for the Contact.Engineering open platform, whose goal it is to standardize rough surface analysis, facilitize that analysis and the open sharing of data, in the spirit of reproducibility.

Nanocrystalline diamond surface, rendered with Blender

I also believe visuals are the opportunity for science to meet art, and artistically appealing visuals can be the start of a scientific conversation.

Elastic contact pressures, in the style of Andy Warhol, computed with Tamaas, rendered with Matplotlib

Search

Fri, 01 Jan 2021 00:00:00 +0000

Students & Collaborators

Fri, 01 Jan 2021 00:00:00 +0000

PhD students

Zichen Li (started Nov. 2024): Rough heterogeneous contacts : from micro to macro (in collaboration with Renald Brenner)

Visiting students

Flavio Lorez (Mar. – Jun. 2025): Contact simulation methods in a Eulerian frame (from ETH Zurich, supervised by David Kammer)

Winner of the EDCE Distinction 2020 (EPFL)!

Mon, 21 Dec 2020 00:00:00 +0000

For my PhD work, I was awarded the EPFL Outstanding Ph.D Thesis Distinction in Civil and Environmental Engineering” 2020 (archive link).

Cover art: illustration from unDraw by Katerina Limpitsouni

A parameter-free mechanistic model of the adhesive wear process of rough surfaces in sliding contact

Fri, 20 Nov 2020 00:00:00 +0000

Authors: Tobias Brink, Lucas Frérot, Jean-François Molinari

In order to develop predictive wear laws, relevant material parameters and their influence on the wear rate need to be identified. Despite decades of research, there is no agreement on the mathematical form of wear equations and even the simplest models, such as Archard’s, contain unpredictable fit parameters. Here, we propose a simple model for adhesive wear in dry sliding conditions that contains no fit parameters and is only based on material properties and surface parameters. The model connects elastoplastic contact solutions with the insight that volume detachment from sliding surfaces occurs in the form of wear particles, the minimum size of which can be estimated. A novelty of the model is the explicit tracking of the sliding process, which allows us to meaningfully connect particle emission rates and sizes to the macroscopic wear rate. The results are qualitatively promising, but we identify the necessity for more controlled wear experiments and the parameters needed from such work in order to fully verify and improve our model.

Publisher’s version (JMPS, Open Access): doi:10.1016/j.jmps.2020.104238

Cover art: Tobias Brink, CC-BY

Crack nucleation in the adhesive wear of an elastic-plastic half-space

Tue, 18 Aug 2020 00:00:00 +0000

Authors: Lucas Frérot, Guillaume Anciaux, Jean-François Molinari

The detachment of material in an adhesive wear process is driven by a fracture mechanism which is controlled by a critical length-scale. Previous efforts in multi-asperity wear modeling have applied this microscopic process to rough elastic contact. However, experimental data shows that the assumption of purely elastic deformation at rough contact interfaces is unrealistic, and that asperities in contact must deform plastically to accommodate the large contact stresses. We therefore investigate the consequences of plastic deformation on the macro-scale wear response using novel elastoplastic contact simulations. The crack nucleation process at a rough contact interface is analyzed in a comparative study with a classical J2 plasticity approach and a saturation plasticity model. We show that plastic residual deformations in the J2 model heighten the surface tensile stresses, leading to a higher crack nucleation likelihood for contacts. This effect is shown to be stronger when the material is more ductile. We also show that elastic interactions between contacts can increase the likelihood of individual contacts nucleating cracks, irrespective of the contact constitutive model. This is supported by a statistical approach we develop based on a Greenwood–Williamson model modified to take into account the elastic interactions between contacts and the shear strength of the contact junction.

Publisher’s version: doi:10.1016/j.jmps.2020.104100
ArXiv: 1910.05163

Cover art: made with matplotlib, computed with Tamaas

Tamaas: a library for elastic-plastic contact of periodic rough surfaces

Tue, 28 Jul 2020 00:00:00 +0000

Authors: Lucas Frérot, Guillaume Anciaux, Valentine Rey, Son Pham-Ba, Jean-François Molinari

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 (Archard, 1957). Roughness occurs on most man-made and natural surfaces (Persson, Albohr, Tartaglino, Volokitin, & Tosatti, 2005) and can span many orders of magnitude, from the nanometer scale to the kilometer scale (Renard, Candela, & Bouchaud, 2013). This poses a serious challenge to conventional numerical approaches in solid mechanics such as the finite-element method (FEM).

Boundary integral methods (Bonnet, 1995) are commonly employed in place of the FEM for rough elastic contact because of an inherent dimensionality reduction: the computational effort is focused on the contact interface whereas the FEM requires discretization of the volume of the solids in contact. In addition, the use of a half-space geometry provides a translational invariance: the computation of periodic equilibrium solutions can then be accelerated with the fast-Fourier Transform (Stanley & Kato, 1997).

However, because of the roughness, the total contact load is distributed over a small area and local contact pressures are expected to cause non-linear material behavior, such as plasticity. In this case, volume integral methods can be employed to account for plastic deformation (Telles & Brebbia, 1979). These enjoy properties analogous to boundary integral methods and can also be accelerated with a Fourier approach (Frérot et al., 2019b). Taking plasticity into account is necessary in the accurate description of contact interfaces for the understanding of friction and wear. Moreover, high performance implementations are needed to model realistic rough surfaces with roughness spanning many orders of magnitude in scale.

Tamaas is a C++ library with a Python interface (Jakob, Rhinelander, & Moldovan, 2017), developed in the Computational Solid Mechanics Laboratory at EPFL, that implements a unique Fourier-accelerated volume integral formulation of equilibrium (Frérot et al., 2019b) for the solution of elastic-plastic rough contact problems. The use of C++ allows for a particular focus on performance: most loops are parallelized using Thrust/OpenMP and the fast-Fourier transforms are computed with FFTW3/OpenMP. Thanks to this, it can handle simulations with upwards of 100 million degrees of freedom on a single compute node (Frérot et al., 2019b). Tamaas is aimed at researchers and practitioners wishing to compute realistic contact solutions for the study of interface phenomena.

Publisher’s version (JOSS, Open Access): doi:10.21105/joss.02121

Cover art: made with matplotlib, computed with Tamaas

Started post-doc at Johns Hopkins University

Thu, 13 Feb 2020 00:00:00 +0000

Today I am starting my postdoctoral fellowship at Johns Hopkins University, funded by SNSF. I’ll be working with prof. Mark Robbins on nanoscale wear of polymers and friction mechanisms of fatty acid monolayers.

Successfully defended PhD thesis!

Mon, 13 Jan 2020 00:00:00 +0000

I successfully obtained my PhD diploma by defending my thesis titled:

Bridging scales in wear modeling with volume integral methods for elastic-plastic contact

I am proud of the work I have accomplished during these four years with Jean-François Molinari, Guillaume Anciaux and the whole of LSMS!

Manuscript: doi:10.5075/epfl-thesis-7640

A Fourier-accelerated volume integral method for elastoplastic contact

Thu, 11 Apr 2019 00:00:00 +0000

Authors: Lucas Frérot, Marc Bonnet, Jean-François Molinari, Guillaume Anciaux

The contact of solids with rough surfaces plays a fundamental role in physical phenomena such as friction, wear, sealing, and thermal transfer. However, its simulation is a challenging problem due to surface asperities covering a wide range of length-scales. In addition, non-linear local processes, such as plasticity, are expected to occur even at the lightest loads. In this context, robust and efficient computational approaches are required. We therefore present a novel numerical method, based on integral equations, capable of handling the large discretization requirements of real rough surfaces as well as the non-linear plastic flow occurring below and at the contacting asperities. This method is based on a new derivation of the Mindlin fundamental solution in Fourier space, which leverages the computational efficiency of the fast Fourier transform. The use of this Mindlin solution allows a dramatic reduction of the memory imprint (as the Fourier coefficients are computed on-the-fly), a reduction of the discretization error, and the exploitation of the structure of the functions to speed up computation of the integral operators. We validate our method against an elastic–plastic FEM Hertz normal contact simulation and showcase its ability to simulate contact of rough surfaces with plastic flow.

Publisher’s version (CMAME, paywalled): doi:10.1016/j.cma.2019.04.006
ArXiv: 1811.11558

Cover art: made with Paraview, computed with Tamaas

Adhesive wear mechanisms uncovered by atomistic simulations

Thu, 06 Sep 2018 00:00:00 +0000

Authors: Jean-François Molinari, Ramin Aghababaei, Tobias Brink, Lucas Frérot, Enrico Milanese

In this review, we discuss our recent advances in modeling adhesive wear mechanisms using coarse-grained atomistic simulations. In particular, we present how a model pair potential reveals the transition from ductile shearing of an asperity to the formation of a debris particle. This transition occurs at a critical junction size, which determines the particle size at its birth. Atomistic simulations also reveal that for nearby asperities, crack shielding mechanisms result in a wear volume proportional to an effective area larger than the real contact area. As the density of microcontacts increases with load, we propose this crack shielding mechanism as a key to understand the transition from mild to severe wear. We conclude with open questions and a road map to incorporate these findings in mesoscale continuum models. Because these mesoscale models allow an accurate statistical representation of rough surfaces, they provide a simple means to interpret classical phenomenological wear models and wear coefficients from physics-based principles.

Publisher’s version (Friction, Open Access): doi:10.1007/s40544-018-0234-6

Cover art: made with Blender with the Atomic Blender addon

A mechanistic understanding of the wear coefficient: From single to multiple asperities contact

Wed, 28 Feb 2018 00:00:00 +0000

Authors: Lucas Frérot, Ramin Aghababaei, Jean-Fraçois Molinari

Sliding contact between solids leads to material detaching from their surfaces in the form of debris particles, a process known as wear. According to the well-known Archard wear model, the wear volume (i.e. the volume of detached particles) is proportional to the load and the sliding distance, while being inversely proportional to the hardness. The influence of other parameters are empirically merged into a factor, referred to as wear coefficient, which does not stem from any theoretical development, thus limiting the predictive capacity of the model. Based on a recent understanding of a critical length-scale controlling wear particle formation, we present two novel derivations of the wear coefficient: one based on Archard’s interpretation of the wear coefficient as the probability of wear particle detachment and one that follows naturally from the up-scaling of asperity-level physics into a generic multi-asperity wear model. As a result, the variation of wear rate and wear coefficient are discussed in terms of the properties of the interface, surface roughness parameters and applied load for various rough contact situations. Both new wear interpretations are evaluated analytically and numerically, and recover some key features of wear observed in experiments. This work shines new light on the understanding of wear, potentially opening a pathway for calculating the wear coefficient from first principles.

Publisher’s version (JMPS, paywalled): doi:10.1016/j.jmps.2018.02.015
Manuscript (CC-BY-NC-ND): PDF

Cover art: made with Paraview, computed with Tamaas

About

Mon, 01 Jan 0001 00:00:00 +0000

My name is Lucas Frérot. I’m a french researcher working on solid mechanics and in particular contact mechanics (see my research topics).

I studied civil engineering at École Polytechnique Fédérale de Lausanne, where I obtained my master’s degree (2015) with a speciality in structural engineering. I also studied for a year at Carnegie Mellon University during an exchange in my third year of bachelor studies.

After my master’s, I joined the Laboratoire de Simulation en Mécanique des Solides where I started a PhD under the supervision of Prof. Jean-François Molinari and Dr. Guillaume Anciaux. During four years, I worked on rough surface contact mechanics and how adhesive wear works in rough contact interfaces. This work was awarded with the “EPFL Outstanding PhD Thesis Distinction in Civil and Environmental Engineering” (2020) and the “SWICCOMAS Prize” (2021).

Before I graduated in January 2020, I was awarded a postdoctoral fellowship from the Swiss National Science Foundation to work at the Johns Hopkins University starting February 2020. There, I joined Prof. Mark Robbins to work on nano-scale wear of polymers and friction of fatty acid monolayers (in collaboration with Juliette Cayer-Barrioz). After Prof. Robbins’ tragic passing, I joined Prof. Jaafar El-Awady’s group and worked with Prof. Vicky Nguyen to advance on the projects I had with Prof. Robbins.

In November 2021, I started work as a postdoc in the Laboratory for Simulation - IMTEK at Freiburg University, Germany, with Prof. Lars Pastewka. There I worked on elastic properties of zinc-phosphate tribofilms with various degrees of polymerization, developing many-body algorithms for the evaluation of elastic constants. I also worked on the emergence of roughness in rough elastic-plastic indentation.

In September 2023, I started work as a Maître de Conférences at Sorbonne University, in Paris. The lab I joined is the Jean le Rond ∂‘Alembert Institute, which conducts research in all areas of mechanics (solids, fluids, acoustics, etc.). I also have teaching duties in the mechanics curriculum of the University (bachelor and master), as well as the engineering school Polytech’ Sorbonne.

Contact:

Open positions

Mon, 01 Jan 0001 00:00:00 +0000

Postdoctoral positions

January 2026 — 12 to 18 months

Fourier-accelerated rough contact simulations with large deformations. In collaboration with Vladislav Yastrebov (Mines Paris). Job offer (PDF).

PhD positions

⏳ Coming soon :)

Stages de fin d’étude / Master’s theses

Spring 2026 — 6 months

Augmentation du frottement au cours du temps : simulations de contact frottant avec matériaux viscoélastiques (co-encadrant Rénald Brenner)
Increase of the friction force over time : simulating frictional contact between viscoelastic materials

Cover art: illustration from unDraw by Katerina Limpitsouni