, Elastic rough contact: boundary integral methods

, Case-by-case analysis should then be conducted to determine the most appropriate numerical method. However, because the physical problems considered in this thesis lend themselves to periodicity, we shall not undertake such analysis

R. Aghababaei, T. Brink, and J. Molinari, Asperity-Level Origins of Transition from Mild to Severe Wear, Physical Review Letters, vol.120, p.186105, 2018.

. Aghababaei, D. H. Ramin, J. Warner, and . Molinari, Critical Length Scale Controls Adhesive Wear Mechanisms, Nature Communications, vol.7, p.11816, 2016.

. Aghababaei, D. H. Ramin, J. Warner, and . Molinari, On the Debris-Level Origins of Adhesive Wear, Proceedings of the National Academy of Sciences, p.28696291, 2017.

A. Akchurin, R. Bosman, and P. M. Lugt, A Stress-Criterion-Based Model for the Prediction of the Size of Wear Particles in Boundary Lubricated Contacts, Tribology Letters, vol.64, p.35, 2016.

A. Almqvist, C. Campañá, N. Prodanov, and B. N. Persson, Interfacial Separation between Elastic Solids with Randomly Rough Surfaces: Comparison between Theory and Numerical Techniques, Journal of the Mechanics and Physics of Solids, vol.59, pp.2355-2369, 2011.

A. Almqvist, F. Sahlin, R. Larsson, and S. Glavatskih, On the Dry Elasto-Plastic Contact of Nominally Flat Surfaces, Tribology International 40, vol.4, pp.574-579, 2007.

. Amba-rao and L. Chintakindi, Fourier Transform Methods in Elasticity Problems and an Application, Journal of the Franklin Institute, vol.287, issue.69, pp.90100-90108, 1969.

P. Amestoy, I. Duff, J. L'excellent, and J. Koster, A Fully Asynchronous Multifrontal Solver Using Distributed Dynamic Scheduling, SIAM Journal on Matrix Analysis and Applications, vol.23, pp.15-41, 2001.
URL : https://hal.archives-ouvertes.fr/hal-00808293

G. Amontons, De La Résistance Causée Dans Les Machines, Mémoires de l' Académie Royale, pp.206-222, 1699.

J. F. Archard, Elastic Deformation and the Laws of Friction, Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences 243.1233, vol.24, pp.190-205, 1953.

J. F. Archard and W. Hirst, The Wear of Metals under Unlubricated Conditions, Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences 236.1206, pp.397-410, 1956.

J. Armand, L. Salles, C. W. Schwingshackl, D. Süß, and K. Willner, On the Effects of Roughness on the Nonlinear Dynamics of a Bolted Joint: A Multiscale Analysis, European Journal of Mechanics -A/Solids, vol.70, pp.44-57, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01730023

U. Ayachit, The ParaView Guide: Updated for ParaView Version 4.3. Ed. by Lisa Avila, collab. with Berk Geveci. Full color version. OCLC: 944221263. Los Alamos: Kitware. 261 pp, 2015.

F. Barras, When Dynamic Cracks Meet Disorder: A Journey along the Fracture Process Zone, 2018.

F. Barras, M. Aldam, T. Roch, E. A. Brener, E. Bouchbinder et al., The Emergence of Crack-like Behavior of Frictional Rupture: Edge Singularity and Energy Balance, 2019.

. Barras, P. H. Fabian, J. Geubelle, and . Molinari, Interplay between Process Zone and Material Heterogeneities for Dynamic Cracks, Physical Review Letters, vol.119, p.144101, 2017.

E. Bayart, I. Svetlizky, and J. Fineberg, Slippery but Tough: The Rapid Fracture of Lubricated Frictional Interfaces, Physical Review Letters, vol.116, p.194301, 2016.

A. Bemporad and M. Paggi, Optimization Algorithms for the Solution of the Frictionless Normal Contact between Rough Surfaces, International Journal of Solids and Structures, pp.94-105, 2015.

T. Beyer, F. Sadeghi, T. Chaise, J. Leroux, and D. Nelias, A Coupled Damage Model and a Semi-Analytical Contact Solver to Simulate Butterfly Wing Formation around Nonmetallic Inclusions, International Journal of Fatigue, vol.127, pp.445-460, 2019.

E. G. Birgin, M. José, M. Martínez, and . Raydan, Spectral Projected Gradient Methods: Review and Perspectives, Journal of Statistical Software, vol.60, p.3, 2014.

J. Bleyer, Advances in the Simulation of Viscoplastic Fluid Flows Using Interior-Point Methods, Computer Methods in Applied Mechanics and Engineering, vol.330, pp.368-394, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01672045

S. Bocanegra, F. F. Campos, and A. R. Oliveira, Using a Hybrid Preconditioner for Solving Large-Scale Linear Systems Arising from Interior Point Methods, Computational Optimization and Applications, vol.36, issue.2, pp.149-164, 2007.

. Bonnet, ;. J. Marc, and . Wiley, A Modified Volume Integral Equation for Anisotropic Elastic or Conducting Inhomogeneities: Unconditional Solvability by Neumann Series, Journal of Integral Equations and Applications, vol.391, pp.271-295, 1995.
URL : https://hal.archives-ouvertes.fr/hal-01417944

M. Bonnet and S. Mukherjee, Implicit BEM Formulations for Usual and Sensitivity Problems in Elasto-Plasticity Using the Consistent Tangent Operator Concept, 1996.
URL : https://hal.archives-ouvertes.fr/hal-00092370

, International Journal of Solids and Structures, vol.33, issue.95, pp.279-279

F. P. Bowden and D. Tabor, The Area of Contact between Stationary and between Moving Surfaces, Proceedings of the Royal Society of London. Series A, vol.169, p.97287, 1939.

, Mechanism of Metallic Friction, Nature 150, vol.3798, pp.197-199, 1942.

J. P. Boyd, Chebyshev and Fourier Spectral Methods, vol.668, 2001.

S. P. Boyd and L. Vandenberghe, Convex Optimization, vol.716, 2004.

T. Brink and J. Molinari, Adhesive Wear Mechanisms in the Presence of Weak Interfaces: Insights from an Amorphous Model System, Physical Review Materials, vol.3, p.53604, 2019.

H. D. Bui, Some Remarks about the Formulation of Three-Dimensional Thermoelastoplastic Problems by Integral Equations, International Journal of Solids and Structures, vol.14, pp.935-939, 1978.

H. Bui and . Duong, Étude de l'évolution de la frontière du domaine élastique avec l'écrouissage et relations de comportement élasto-plastique des métaux cubiques, 1969.

J. T. Burwell and C. D. Strang, On the Empirical Law of Adhesive Wear, Journal of Applied Physics, vol.23, issue.1, pp.18-28, 1952.

J. T. Burwell, Survey of Possible Wear Mechanisms, pp.119-141, 1957.

A. W. Bush, R. D. Gibson, and G. P. Keogh, Strongly Anisotropic Rough Surfaces, Journal of Lubrication Technology, vol.101, issue.1, pp.15-20, 1979.

A. W. Bush, R. D. Gibson, and T. R. Thomas, The Elastic Contact of a Rough Surface, pp.90145-90148, 1975.

C. Campañá and M. H. Müser, Contact Mechanics of Real vs. Randomly Rough Surfaces: A Green's Function Molecular Dynamics Study, EPL (Europhysics Letters), vol.77, p.38005, 2007.

C. Campañá, Using Green's Function Molecular Dynamics to Rationalize the Success of Asperity Models When Describing the Contact between Self-Affine Surfaces, Physical Review E, vol.78, p.26110, 2008.

C. Campañá and M. H. Müser, Practical Green's Function Approach to the Simulation of Elastic Semi-Infinite Solids, Physical Review B, vol.74, p.75420, 2006.

C. Campañá, M. H. Müser, and M. O. Robbins, Elastic Contact between Self-Affine Surfaces: Comparison of Numerical Stress and Contact Correlation Functions with Analytic Predictions, Journal of Physics: Condensed Matter, vol.20, p.354013, 2008.

. Candela, E. E. Thibault, and . Brodsky, The Minimum Scale of Grooving on Faults, Geology 44, vol.8, pp.603-606, 2016.

Y. Cao, L. Wen, J. Xiao, and Y. Liu, A Fast Directional BEM for Large-Scale Acoustic Problems Based on the Burton-Miller Formulation, Engineering Analysis with Boundary Elements, vol.50, pp.47-58, 2015.

G. Carbone, M. Scaraggi, and U. Tartaglino, Adhesive Contact of Rough Surfaces: Comparison between Numerical Calculations and Analytical Theories, The European Physical Journal E, vol.30, issue.1, pp.65-74, 2009.

C. Caroli and P. Nozières, Hysteresis and Elastic Interactions of Microasperities in Dry Friction, The European Physical Journal B -Condensed Matter and Complex Systems, vol.4, pp.233-246, 1998.

S. Chaillat, M. Bonnet, and J. F. Semblat, A New Fast Multi-Domain BEM to Model Seismic Wave Propagation and Amplification in 3-D Geological Structures, Geophysical Journal International, vol.177, pp.509-531, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00338211

S. Chaillat and M. Bonnet, A New Fast Multipole Formulation for the Elastodynamic Half-Space Green's Tensor, Journal of Computational Physics, vol.258, pp.787-808, 2014.

S. Chaillat, M. Bonnet, and J. Semblat, A Multi-Level Fast Multipole BEM for 3-D Elastodynamics in the Frequency Domain, Computer Methods in Applied Mechanics and Engineering, vol.49, pp.4233-4249, 0197.
URL : https://hal.archives-ouvertes.fr/hal-00276092

S. Chaillat, L. Desiderio, and P. Ciarlet, Theory and Implementation of H-Matrix Based Iterative and Direct Solvers for Helmholtz and Elastodynamic Oscillatory Kernels, Journal of Computational Physics, vol.351, pp.165-186, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01543919

J. M. Challen, P. L. Oxley, and B. S. Hockenhull, Prediction of Archard's Wear Coefficient for Metallic Sliding Friction Assuming a Low Cycle Fatigue Wear Mechanism, pp.90188-90190, 1986.

W. Chen, S. Wayne, Q. Liu, and . Wang, Fast Fourier Transform Based Numerical Methods for Elasto-Plastic Contacts of Nominally Flat Surfaces, Journal of Applied Mechanics, vol.75, p.11022, 2008.

Z. Chen and H. Xiao, The Fast Multipole Boundary Element Methods (FMBEM) and Its Applications in Rolling Engineering Analysis, Computational Mechanics 50, vol.5, pp.513-531, 2012.

S. K. Chilamakuri and . Bhushan, Contact Analysis of Non-Gaussian Random Surfaces, Proceedings of the Institution of Mechanical Engineers, vol.212, pp.19-32, 1998.

A. Clauset, C. R. Shalizi, and M. E. Newman, Power-Law Distributions in Empirical Data, SIAM Review 51, vol.4, pp.661-703, 2009.

R. Colaço, An AFM Study of Single-Contact Abrasive Wear: The Rabinowicz Wear Equation Revisited, pp.1772-1776, 2009.

J. W. Cooley and J. W. Tukey, An Algorithm for the Machine Calculation of Complex Fourier Series, Mathematics of Computation 19, vol.90, pp.297-301, 1965.

C. Coulomb and . Augustin, Théorie des machines simples en ayant égard au frottement de leurs parties et à la roideur des cordages, Bachelier, vol.400, p.8, 1821.

B. Dacorogna, Introduction to the Calculus of Variations, vol.311, 2015.

W. B. Dapp, A. Lücke, N. J. Bo, M. H. Persson, and . Müser, Self-Affine Elastic Contacts: Percolation and Leakage, Physical Review Letters, vol.108, p.244301, 2012.

S. Das, K. Varalakshmi, V. Jayaram, and S. K. Biswas, Ultra Mild Wear in Lubricated Tribology of an Aluminium Alloy, Journal of Tribology, vol.129, pp.942-951, 2007.

R. Dautray and J. Lions, Mathematical Analysis and Numerical Methods for Science and Technology: Volume 2 Functional and Variational Methods, p.913437931, 2000.

C. David and P. Gosselet, Équations aux dérivées partielles: cours et exercices corrigés. OCLC: 920695853, 2015.

G. Davidesko, A. Sagy, and Y. H. Hatzor, Evolution of Slip Surface Roughness through Shear, Geophysical Research Letters, vol.16, 2014.

J. H. Dieterich, Modeling of Rock Friction: 1. Experimental Results and Constitutive Equations, Journal of Geophysical Research: Solid Earth, vol.84, pp.2161-2168, 1979.

J. H. Dieterich and B. D. Kilgore, Imaging Surface Contacts: Power Law Contact Distributions and Contact Stresses in Quartz, Calcite, Glass and Acrylic Plastic, pp.219-239, 1994.

D. C. Drucker and W. Prager, Soil Mechanics and Plastic Analysis or Limit Design, Quarterly of Applied Mathematics 10, vol.2, pp.157-165, 1952.

J. M. Firth, Discrete Transforms, vol.187, 1992.

J. R. Fleming and N. P. Suh, The Relationship between Crack Propagation Rates and Wear Rates, pp.90084-90093, 1977.

J. Fontaine, T. Le-mogne, J. L. Loubet, and M. Belin, Achieving Superlow Friction with Hydrogenated Amorphous Carbon: Some Key Requirements, Thin Solid Films. EMRS, vol.1, pp.99-108, 2004.

I. Fredholm, Sur les équations de l'équilibre d'un corps solide élastique, Acta Mathematica 23.1, pp.1-42, 1900.

L. Frérot, Supplementary Codes and Data to "Crack Nucleation in the Adhesive Wear of an Elastic-Plastic Half-Space, 2018.

L. Frérot, R. Aghababaei, and J. Molinari, A Mechanistic Understanding of the Wear Coefficient: From Single to Multiple Asperities Contact, Journal of the Mechanics and Physics of Solids, vol.114, pp.172-184, 2018.

L. Frérot, G. Anciaux, and J. Molinari, Crack Nucleation in the Adhesive Wear of an Elastic-Plastic Half-Space, 2019.

L. Frérot, G. Anciaux, V. Rey, and S. Pham-ba, Tamaas, a High-Performance Library for Periodic Rough Surface Contact, collab. with Jean-François Molinari. Zenodo, 2019.

L. Frérot, M. Bonnet, J. Molinari, and G. Anciaux, A Fourier-Accelerated Volume Integral Method for Elastoplastic Contact, Computer Methods in Applied Mechanics and Engineering, vol.351, pp.951-976, 2019.

M. Frigo and S. G. Johnson, The Design and Implementation of FFTW3, Proceedings of the IEEE 93, vol.2, pp.216-231, 2005.

L. Gallego, D. Nélias, and C. Jacq, A Comprehensive Method to Predict Wear and to Define the Optimum Geometry of Fretting Surfaces, Journal of Tribology, vol.128, pp.476-485, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00938584

X. Gao and T. G. Davies, An Effective Boundary Element Algorithm for 2D and 3D Elastoplastic Problems, International Journal of Solids and Structures, vol.37, pp.4987-5008, 2000.

N. T. Garabedian, A. Bhattacharjee, M. N. Webster, G. L. Hunter, P. W. Jacobs et al., Quantifying, Locating, and Following Asperity-Scale Wear Processes Within Multiasperity Contacts, Tribology Letters 67, vol.3, p.89, 2019.

C. Geuzaine and J. Remacle, Gmsh: A 3-D Finite Element Mesh Generator with Built-in Pre-and Post-Processing Facilities, International Journal for Numerical Methods in Engineering, vol.79, pp.1309-1331, 2009.

H. Ghaednia, X. Wang, S. Saha, Y. Xu, A. Sharma et al., A Review of Elastic-Plastic Contact Mechanics". In: Applied Mechanics Reviews, vol.69, pp.60804-060804, 2017.

D. Gintides and K. Kiriaki, Solvability of the Integrodifferential Equation of Eshelby's Equivalent Inclusion Method, The Quarterly Journal of Mechanics and Applied Mathematics, vol.68, pp.85-96, 2015.

J. Gondzio, Matrix-Free Interior Point Method, Computational Optimization and Applications 51, vol.2, pp.457-480, 2012.

J. A. Greenwood and J. B. Williamson, Contact of Nominally Flat Surfaces, Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences 295.1442, pp.300-319, 1966.

A. A. Griffith, VI. The Phenomena of Rupture and Flow in Solids, Phil. Trans. R. Soc. Lond. A, vol.221, pp.163-198, 1921.

J. -. Gu, J. R. Cheng, A. L. Rice, S. T. Ruina, and . Tse, Slip Motion and Stability of a Single Degree of Freedom Elastic System with Rate and State Dependent Friction, Journal of the Mechanics and Physics of Solids, vol.32, issue.84, pp.90007-90010, 1984.

M. Guiggiani and A. Gigante, A General Algorithm for Multidimensional Cauchy Principal Value Integrals in the Boundary Element Method, Journal of Applied Mechanics, vol.57, pp.906-915, 1990.

C. Hardy, C. N. Baronet, and G. V. Tordion, The Elasto-Plastic Indentation of a Half-Space by a Rigid Sphere, International Journal for Numerical Methods in Engineering, vol.3, pp.451-462, 1971.

C. Hatchett, Being the Substance of a Report Made to the Right Honourable the Lords of the Committee of Privy Council, Appointed to Take into Consideration the State of the Coins of This Kingdom, and the Present Establishment and Constitution of His Majesty's Mint, Philosophical Transactions of the Royal Society of London, vol.93, p.107069, 1803.

M. Hodapp, G. Anciaux, and W. A. Curtin, Lattice Green Function Methods for Atomistic/Continuum Coupling: Theory and Data-Sparse Implementation, Computer Methods in Applied Mechanics and Engineering, vol.348, pp.1039-1075, 2019.

K. Hokkirigawa, Wear Mode Map of Ceramics, Wear 151, vol.2, pp.219-228, 1991.

R. Holm, Electric Contacts: Theory and Applications, vol.482, 2000.

S. M. Hsu and M. Shen, Wear Prediction of Ceramics, Wear. Special Issue on Wear Modelling, vol.256, pp.867-878, 2004.

Y. Z. Hu and K. Tonder, Simulation of 3-D Random Rough Surface by 2-D Digital Filter and Fourier Analysis, International Journal of Machine Tools and Manufacture, vol.32, issue.1-2, pp.83-90, 1992.

I. M. Hutchings, Leonardo Da Vinci's Studies of Friction, pp.51-66, 2016.

S. Hyun, L. Pei, J. Molinari, and M. O. Robbins, Finite-Element Analysis of Contact between Elastic Self-Affine Surfaces, Physical Review E, vol.70, p.26117, 2004.

M. O. Hyun and . Robbins, Elastic Contact between Rough Surfaces: Effect of Roughness at Large and Small Wavelengths, Tribology International. Tribology at the Interface: Proceedings of the 33rd Leeds-Lyon Symposium on Tribology, vol.40, pp.1413-1422, 2006.

C. Jacq, D. Nélias, G. Lormand, and D. Girodin, Development of a Three-Dimensional Semi-Analytical Elastic-Plastic Contact Code, Journal of Tribology, vol.124, p.653, 2002.
URL : https://hal.archives-ouvertes.fr/hal-00454903

H. Jin, K. Runesson, and K. Mattiasson, Boundary Element Formulation in Finite Deformation Plasticity Using Implicit Integration, Computers & Structures. Special Issue: Finite Element Methods in Engineering, vol.31, issue.1, pp.90164-90172, 1989.

K. L. Johnson, An Experimental Determination of the Contact Stresses between Plastically Deformed Cylinders and Sphere, International Conference on the Applications of Plastic Theory in Engineering Design, pp.341-461, 1968.

K. L. Johnson, J. A. Greenwood, and J. G. Higginson, The Contact of Elastic Regular Wavy Surfaces, International Journal of Mechanical Sciences, vol.27, issue.6, pp.90029-90032, 1985.

E. Jones, T. Oliphant, and P. Peterson, SciPy: Open Source Scientific Tools for Python, 2001.

J. J. Kalker, Variational Principles of Contact Elastostatics, IMA Journal of Applied Mathematics, vol.20, pp.199-219, 1977.

D. S. Kammer, M. Radiguet, J. Ampuero, and J. Molinari, Linear Elastic Fracture Mechanics Predicts the Propagation Distance of Frictional Slip, Tribology Letters, vol.57, p.23, 2015.

K. Kato, Wear in Relation to Friction -a Review, Wear 241, vol.2, pp.151-157, 2000.

K. Kato and K. Adachi, Wear Mechanisms, Modern Tribology Handbook. Bharat Bhushan, pp.273-299, 2001.

D. A. Knoll and D. E. Keyes, Jacobian-Free Newton-Krylov Methods: A Survey of Approaches and Applications, Journal of Computational Physics, vol.193, pp.357-397, 2004.

H. Kong and M. F. Ashby, Wear Mechanisms in Brittle Solids, Acta Metallurgica et Materialia 40.11, p.90455, 1992.

K. Krabbenhoft, A. V. Lyamin, S. W. Sloan, and P. Wriggers, An Interior-Point Algorithm for Elastoplasticity, International Journal for Numerical Methods in Engineering, vol.69, pp.592-626, 2007.

. Krithivasan, R. L. Vijaykumar, and . Jackson, An Analysis of Three-Dimensional Elasto-Plastic Sinusoidal Contact, Tribology Letters 27.1, pp.31-43, 2007.

L. Cruz, J. William, M. Martínez, and . Raydan, Spectral Residual Method without Gradient Information for Solving Large-Scale Nonlinear Systems of Equations, Mathematics of Computation 75, vol.255, pp.1429-1448, 2006.

P. Ladevèze, N. Moës, and B. Douchin, Constitutive Relation Error Estimators for (Visco)Plastic Finite Element Analysis with Softening, Computer Methods in Applied Mechanics and Engineering, vol.176, issue.1, pp.340-345, 1999.

J. Li and E. J. Berger, A Semi-Analytical Approach to Three-Dimensional Normal Contact Problems with Friction, Computational Mechanics, vol.30, pp.310-322, 2003.

. Li, T. E. Qunyang, D. Tullis, R. W. Goldsby, and . Carpick, Frictional Ageing from Interfacial Bonding and the Origins of Rate and State Friction, Nature 480, vol.7376, pp.233-236, 2011.

T. Li, J. Shi, S. Wang, E. Zio, and Z. Ma, Mesoscale Numerical Modeling for Predicting Wear Debris Generation, Tribology Letters 67, vol.2, p.38, 2019.
URL : https://hal.archives-ouvertes.fr/hal-02428546

X. Liang, B. Lin, X. Han, and S. Chen, Fractal Analysis of Engineering Ceramics Ground Surface, Applied Surface Science, vol.258, pp.6406-6415, 2012.

R. Lipton, D. Rose, and R. Tarjan, Generalized Nested Dissection, SIAM Journal on Numerical Analysis, vol.16, issue.2, pp.346-358, 1979.

J. Liu, J. K. Notbohm, R. W. Carpick, and K. T. Turner, Method for Characterizing Nanoscale Wear of Atomic Force Microscope Tips, ACS Nano 4.7, pp.3763-3772, 2010.

S. Liu, Q. Wang, and G. Liu, A Versatile Method of Discrete Convolution and FFT (DC-FFT) for Contact Analyses, pp.101-111, 2000.

Y. J. Liu and N. Nishimura, The Fast Multipole Boundary Element Method for Potential Problems: A Tutorial, vol.5, pp.371-381, 2006.

Y. Liu and I. Szlufarska, Chemical Origins of Frictional Aging, Physical Review Letters, vol.109, p.186102, 2012.

M. Longuet-higgins, G. Selwyn, and . Deacon, Statistical Properties of an Isotropic Random Surface, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, vol.250, pp.157-174, 1957.

A. E. Love, A Treatise on the, Mathematical Theory of Elasticity, vol.1, pp.0-5, 1892.
URL : https://hal.archives-ouvertes.fr/hal-01307751

A. Majumdar and B. Bhushan, Role of Fractal Geometry in Roughness Characterization and Contact Mechanics of Surfaces, Journal of Tribology, vol.112, pp.205-216, 1990.

, Fractal Model of Elastic-Plastic Contact Between Rough Surfaces, Journal of Tribology, vol.113, pp.1-11, 1991.

K. W. Man, M. Aliabadi, and D. Rooke, Bem Frictional Contact Analysis: Load Incremental Technique, Computers & Structures, vol.47, issue.93, p.90294, 1993.

. Mandelbrot and B. Benoit, Stochastic Models for the Earth's Relief, the Shape and the Fractal Dimension of the Coastlines, and the Number-Area Rule for Islands, Proceedings of the National Academy of Sciences 72.10, p.16578734, 1975.

. Mandelbrot, B. Benoit, E. Dann, A. J. Passoja, and . Paullay, Fractal Character of Fracture Surfaces of Metals, pp.721-722, 1984.

J. Mason, Methods of Functional Analysis for Application in Solid Mechanics. Studies in Applied Mechanics 9, vol.392, p.pp, 1985.

C. Mayeur, P. Sainsot, and L. Flamand, A Numerical Elastoplastic Model for Rough Contact, Journal of Tribology, vol.117, pp.422-429, 1995.

P. Meakin, Fractals, Scaling, and Growth Far from Equilibrium, Cambridge Nonlinear Science Series, vol.5, 1998.

S. Mehrotra, On the Implementation of a Primal-Dual Interior Point Method, SIAM Journal on Optimization, vol.2, issue.4, pp.575-601, 1992.

H. C. Meng and K. C. Ludema, Wear Models and Predictive Equations: Their Form and Content, Wear. 10th International Conference on Wear of Materials, vol.181, pp.443-457, 1995.

N. Menga and G. Carbone, The Surface Displacements of an Elastic Half-Space Subjected to Uniform Tangential Tractions Applied on a Circular Area, European Journal of Mechanics -A/Solids, vol.73, pp.137-143, 2019.

E. Milanese, T. Brink, R. Aghababaei, and J. Molinari, Emergence of Self-Affine Surfaces during Adhesive Wear, Nature Communications, vol.10, p.1116, 2019.

R. D. Mindlin, Force at a Point in the Interior of a Semi-Infinite Solid, Journal of Applied Physics, issue.5, pp.195-202, 1936.

R. D. Mindlin, H. David, and . Cheng, Thermoelastic Stress in the Semi-Infinite Solid, Journal of Applied Physics, vol.21, pp.931-933, 1950.

S. Mischler and A. I. Muñoz, Wear of CoCrMo Alloys Used in Metal-on-Metal Hip Joints: A Tribocorrosion Appraisal, pp.1081-1094, 2013.

H. Moulinec and P. Suquet, A Numerical Method for Computing the Overall Response of Nonlinear Composites with Complex Microstructure, Computer Methods in Applied Mechanics and Engineering, vol.157, issue.1, pp.218-219, 1998.
URL : https://hal.archives-ouvertes.fr/hal-01282728

M. H. Müser, Internal, Elastic Stresses below Randomly Rough Contacts, Journal of the Mechanics and Physics of Solids, vol.119, pp.73-82, 2018.

M. H. Müser, B. Wolf, R. Dapp, P. Bugnicourt, N. Sainsot et al., András Vernes, Soheil Solhjoo, Antonis I, Tribology Letters, vol.65, p.118, 2017.

M. Müser and A. Wang, Contact-Patch-Size Distribution and Limits of Self-Affinity in Contacts between Randomly Rough Surfaces, p.85, 2018.

P. Nayak and . Ranganath, Random Process Model of Rough Surfaces, Journal of Lubrication Technology, vol.93, pp.398-407, 1971.

Y. Nesterov and M. Todd, Primal-Dual Interior-Point Methods for Self-Scaled Cones, SIAM Journal on Optimization, issue.2, pp.324-364, 1998.

L. Pastewka and M. O. Robbins, Contact between Rough Surfaces and a Criterion for Macroscopic Adhesion, Proceedings of the National Academy of Sciences 111.9, p.24550489, 2014.

L. Pastewka, T. A. Sharp, and M. O. Robbins, Seamless Elastic Boundaries for Atomistic Calculations, Physical Review B, vol.86, p.75459, 2012.

L. Pei, S. Hyun, J. Molinari, and M. O. Robbins, Finite Element Modeling of Elasto-Plastic Contact between Rough Surfaces, Journal of the Mechanics and Physics of Solids, vol.53, pp.2385-2409, 2005.

B. N. Persson, Elastoplastic Contact between Randomly Rough Surfaces, The Journal of Chemical Physics, vol.87, pp.201-227, 2001.

B. N. Persson, O. Albohr, U. Tartaglino, A. I. Volokitin, and E. Tosatti, On the Nature of Surface Roughness with Application to Contact Mechanics, Sealing, Rubber Friction and Adhesion, In: Journal of Physics: Condensed Matter, vol.17, p.1, 2005.

. Pham-ba, T. Son, J. Brink, and . Molinari, Adhesive Wear and Interaction of Tangentially Loaded Micro-Contacts, International Journal of Solids and Structures, 2019.

A. A. Pitenis, W. Duncan-dowson, and . Sawyer, Leonardo Da Vinci's Friction Experiments: An Old Story Acknowledged and Repeated, Tribology Letters, vol.56, pp.509-515, 2014.

R. Pohrt and Q. Li, Complete Boundary Element Formulation for Normal and Tangential Contact Problems, Physical Mesomechanics 17, vol.4, pp.334-340, 2014.

I. A. Polonsky and L. M. Keer, A Numerical Method for Solving Rough Contact Problems Based on the Multi-Level Multi-Summation and Conjugate Gradient Techniques, Journal of Tribology, vol.122, pp.206-219, 1999.

V. L. Popov, . Gervé, I. Y. Kehrwald, and . Smolin, Simulation of Wear in Combustion Engines, Computational Materials Science, vol.19, issue.1, pp.285-291, 2000.

V. L. Popov and R. Pohrt, Adhesive Wear and Particle Emission: Numerical Approach Based on Asperity-Free Formulation of Rabinowicz Criterion, Friction, 2018.

W. L. Power, E. Terry, J. D. Tullis, and . Weeks, Roughness and Wear during Brittle Faulting, Journal of Geophysical Research: Solid Earth, vol.10, pp.15268-15278, 1988.

C. Putignano, L. Afferrante, G. Carbone, G. Demelio-;-riccardo, F. Sacco et al., A New Efficient Numerical Method for Contact Mechanics of Rough Surfaces, Méthodes Numériques: Algorithmes, analyse et applications. Ed. by Alfio Quarteroni, vol.49, pp.115-162, 2007.

E. Rabinowicz and D. Tabor, Metallic Transfer between Sliding Metals: An Autoradiographic Study, Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences 208.1095, pp.455-475, 1951.

E. Rabinowicz, The Effect of Size on the Looseness of Wear Fragments, vol.2, pp.4-8, 1958.

I. Ramière and T. Helfer, Iterative Residual-Based Vector Methods to Accelerate Fixed Point Iterations, Computers & Mathematics with Applications, vol.70, pp.2210-2226, 2015.

S. B. Ramisetti, C. Campañá, G. Anciaux, J. Molinari, M. H. Müser et al., The Autocorrelation Function for Island Areas on Self-Affine Surfaces, Journal of Physics: Condensed Matter, vol.23, p.215004, 2011.

B. D. Reddy and J. B. Martin, Internal Variable Formulations of Problems in Elastoplasticity: Constitutive and Algorithmic Aspects, Applied Mechanics Reviews, vol.47, pp.429-456, 1994.

F. Renard, T. Candela, and E. Bouchaud, Constant Dimensionality of Fault Roughness from the Scale of Micro-Fractures to the Scale of Continents, Geophysical Research Letters, vol.40, issue.1, pp.83-87, 2013.

V. Rey, S. Krumscheid, and F. Nobile, Quantifying Uncertainties in Contact Mechanics of Rough Surfaces Using the Multilevel Monte Carlo Method, International Journal of Engineering Science, vol.138, pp.50-64, 2019.
URL : https://hal.archives-ouvertes.fr/hal-02059926

V. Rey, G. Anciaux, and J. Molinari, Normal Adhesive Contact on Rough Surfaces: Efficient Algorithm for FFT-Based BEM Resolution, Computational Mechanics, pp.1-13, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01755724

A. R. Riahi and A. T. Alpas, Wear Map for Grey Cast Iron, Wear. 14th International Conference on Wear of Materials, vol.255, pp.100-105, 2003.

N. Richart and J. F. Molinari, Implementation of a Parallel Finite-Element Library: Test Case on a Non-Local Continuum Damage Model, Finite Elements in Analysis and Design, vol.100, pp.41-46, 2015.

A. Ruina, Slip Instability and State Variable Friction Laws, In: Journal of Geophysical Research: Solid Earth, vol.88, pp.10359-10370, 1983.

R. Sahli, G. Pallares, C. Ducottet, I. E. Ben-ali, S. Akhrass et al., Evolution of Real Contact Area under Shear and the Value of Static Friction of Soft Materials, Proceedings of the National Academy of Sciences 115.3, vol.16, p.29295925, 2018.
URL : https://hal.archives-ouvertes.fr/ujm-01789539

F. Sahlin, . Larsson, P. Almqvist, P. Lugt, and . Marklund, A Mixed Lubrication Model Incorporating Measured Surface Topography. Part 1: Theory of Flow Factors, Proceedings of the Institution of Mechanical Engineers, vol.224, pp.335-351, 2010.

P. Sainsot, C. Jacq, and D. Nélias, A Numerical Model for Elastoplastic Rough Contact, CMES: Computer Modeling in Engineering & Sciences 3.4, pp.497-506, 2002.
URL : https://hal.archives-ouvertes.fr/hal-00454931

M. Scherge, J. M. Martin, and K. Pöhlmann, Characterization of Wear Debris of Systems Operated under Low Wear-Rate Conditions, pp.458-461, 2006.

A. G. Shvarts and V. A. Yastrebov, Trapped Fluid in Contact Interface, Journal of the Mechanics and Physics of Solids, vol.119, pp.140-162, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01853388

J. C. Simo, J. R. Thomas, and . Hughes, Computational Inelasticity. Interdisciplinary Applied Mathematics v, vol.392, 1998.

Y. Sinai, . Bar, A. Efim, E. Brener, and . Bouchbinder, Slow Rupture of Frictional Interfaces, Geophysical Research Letters, vol.39, 2012.

Z. Song and K. Komvopoulos, Elastic-Plastic Spherical Indentation: Deformation Regimes, Evolution of Plasticity, and Hardening Effect, Mechanics of Materials, vol.61, pp.91-100, 2013.

H. M. Stanley and T. Kato, An FFT-Based Method for Rough Surface Contact, Journal of Tribology, vol.119, pp.481-485, 1997.

I. Svetlizky and J. Fineberg, Classical Shear Cracks Drive the Onset of Dry Frictional Motion, Nature 509, vol.7499, pp.205-208, 2014.

D. Tabor, The Hardness of Metals. Monographs on the Physics and Chemistry of Materials, 1951.

J. C. Telles and C. A. Brebbia, On the Application of the Boundary Element Method to Plasticity, Applied Mathematical Modelling, vol.3, issue.6, p.80030, 1979.

J. C. Telles and J. A. Carrer, Implicit Procedures for the Solution of Elastoplastic Problems by the Boundary Element Method, Mathematical and Computer Modelling, vol.15, pp.303-311, 1991.

I. Tzanakis, M. Hadfield, B. Thomas, S. M. Noya, I. Henshaw et al., Future Perspectives on Sustainable Tribology". In: Renewable and Sustainable Energy Reviews, vol.16, issue.6, pp.4126-4140, 2012.

A. I. Vakis, V. A. Yastrebov, J. Scheibert, L. Nicola, D. Dini et al., Modeling and Simulation in Tribology across Scales: An Overview, Tribology International, vol.125, pp.169-199, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01802145

P. Vergne, B. Villechaise, and D. Berthe, Elastic Behavior of Multiple Contacts: Asperity Interaction, Journal of Tribology, vol.107, pp.224-228, 1985.

F. Wang and L. M. Keer, Numerical Simulation for Three Dimensional Elastic-Plastic Contact with Hardening Behavior, Journal of Tribology, vol.127, pp.494-502, 2005.

F. Wang, L. M. Keer, and Q. Wang, Numerical Simulation and Analysis for 3D Elastic-Plastic Rough Contacts, Proceedings of IMECE, pp.125-134, 2006.

Y. Wang, Y. Liu, G. Zhang, and Y. Wang, A Simulation Method for Non-Gaussian Rough Surfaces Using Fast Fourier Transform and Translation Process Theory, Journal of Tribology, vol.140, pp.21403-021403, 2017.

Y. Wang and S. M. Hsu, Wear and Wear Transition Modeling of Ceramics, pp.35-46, 1996.

Y. Wang, X. Zhang, H. Shen, J. Liu, B. Zhang et al., Three-Dimensional Contact Analysis with Couple Stress Elasticity, International Journal of Mechanical Sciences, pp.369-379, 2019.

Z. Wang, X. Jin, S. Liu, L. M. Keer, J. Cao et al., A New Fast Method for Solving Contact Plasticity and Its Application in Analyzing Elasto-Plastic Partial Slip, Mechanics of Materials, vol.60, pp.18-35, 2013.

B. Weber, T. Suhina, T. Junge, L. Pastewka, A. M. Brouwer et al., Molecular Probes Reveal Deviations from Amontons' Law in Multi-Asperity Frictional Contacts, Nature Communications, vol.9, p.888, 2018.

H. Westergaard, Bearing Pressures and Cracks, Journal of Applied Mechanics, 1939.

P. Wriggers, Computational Contact Mechanics, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00466790

J. Wu, Simulation of Rough Surfaces with FFT, Tribology International 33.1, pp.47-58, 2000.

, Simulation of Non-Gaussian Surfaces with FFT, Tribology International 37, vol.4, pp.339-346, 2004.

V. A. Yastrebov, G. Anciaux, and J. Molinari, On the Accurate Computation of the True Contact-Area in Mechanical Contact of Random Rough Surfaces, Tribology International, vol.86, pp.469-493, 2012.
URL : https://hal.archives-ouvertes.fr/hal-01518514

V. A. Yastrebov, J. Durand, H. Proudhon, and G. Cailletaud, Rough Surface Contact Analysis by Means of the Finite Element Method and of a New Reduced Model, Comptes Rendus Mécanique. Surface Mechanics : Facts and Numerical Models, vol.339, pp.473-490, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00624090

K. Yonekura and Y. Kanno, Second-Order Cone Programming with Warm Start for Elastoplastic Analysis with von Mises Yield Criterion, Optimization and Engineering 13, vol.2, pp.181-218, 2012.

K. Yu, A. Hwa, H. Halim-kadarman, and . Djojodihardjo, Development and Implementation of Some BEM Variants-A Critical Review, pp.884-899, 2010.

J. Zechner and G. Beer, A Fast Elasto-Plastic Formulation with Hierarchical Matrices and the Boundary Element Method, Computational Mechanics 51, vol.4, pp.443-453, 2013.

J. Zeman, T. W. De-geus, J. Vond?ejc, R. H. Peerlings, and M. G. Geers, A Finite Element Perspective on Nonlinear FFT-based Micromechanical Simulations, International Journal for Numerical Methods in Engineering, vol.111, pp.903-926, 2017.

F. Zhang, J. Liu, X. Ding, and R. Wang, Experimental and Finite Element Analyses of Contact Behaviors between Non-Transparent Rough Surfaces, Journal of the Mechanics and Physics of Solids, vol.126, pp.87-100, 2019.

J. Zhang and A. T. Alpas, Transition between Mild and Severe Wear in Aluminium Alloys, Acta Materialia, vol.45, pp.191-198, 1997.

Q. Zhou, X. Jin, Z. Wang, J. Wang, L. M. Keer et al., Numerical EIM with 3D FFT for the Contact with a Smooth or Rough Surface Involving Complicated and Distributed Inhomogeneities, Tribology International 93, pp.91-103, 2016.

Q. Zhou, X. Jin, Z. Wang, Y. Yang, J. Wang et al., A Mesh Differential Refinement Scheme for Solving Elastic Fields of Half-Space Inclusion Problems, Tribology International 93, pp.124-136, 2016.

Y. Zhou, M. Moseler, and M. H. Müser, Solution of Boundary-Element Problems Using the Fast-Inertial-Relaxation-Engine Method, Physical Review B 99, vol.14, p.144103, 2019.

Z. Gahr and K. , Sliding Wear of Ceramic-Ceramic, Ceramic-Steel and Steel-Steel Pairs in Lubricated and Unlubricated Contact, vol.89, p.90109, 1989.

, Modeling complex contact situations with multi-scale rough surfaces Exploring the physics of contact interfaces Uncovering the underlying principles of friction and wear Computational methods Developing state-of-the-art finite-element, boundary or volume integral methods to tackle challenging problems Enabling large-scale simulations with high-performance codes Studying the mathematical properties of numerical methods Education Dec. 2015-Ongoing PhD

, Bridging Scales in Wear Modeling with Volume Integral Methods for Elastic-Plastic Contact

, Master of Science, Civil Engineering, EPFL, Lausanne. Specialization in structures and numerical simulation, 2013.

, Scientific Baccalauréat, engineering elective, Lycée Jean Monnet, 2008.

. Dec, 2015-Ongoing Doctoral assistant, EPFL, Lausanne, Supervisors: Prof. Jean-François Molinari and Dr

F. , Teaching assistant, EPFL, Lausanne, Intern, Ingeni SA, 2014.

F. , Project supervision, 56 hours, Introduction to contact mechanics: Elastoplastic normal contact between solids (MA), 2018.

. Non-linear, Dynamic Deformations Model Applied to Earthquake Engineering (BA)

. Sep, Master project supervision, 112 hours, Modélisation et optimisation des structures en coque par éléments finis. Student: Michaël Lozano, 2017.

S. , 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), 2016.

F. , Project supervision, 28 hours, Implementation of a Constitutive Law for Concrete (MA). Student: Isaac Thury Teaching activities, 2016.

S. , Scientific programming for engineers, Teaching assistant, 56 hours, 2017.

F. , Numerical modeling of solids and structures, Teaching assistant, vol.56, 2017.

S. , Scientific programming for engineers, Teaching assistant, vol.56, 2016.

F. , Numerical modeling of solids and structures, Teaching assistant, vol.56, 2016.

S. , Continuum mechanics, Teaching assistant, 12 hours, vol.56, 2014.

, Applied Mathematics Boundary and volume integral methods, Fourier analysis, Finite elements, Calculus of variations, Convex optimization

. Python, C. Bash, -. Objective, and J. , Wear, Classical fundamental solutions, Friction, Fracture, Adhesion Practical Programming C++, Scala High performance computing C++, Thrust, OpenMP, Cuda, MPI Software Tamaas, SCons, FFTW, Akantu, pybind11, ParaView, GMSH, Spack Publication in peer-reviewed journals

;. L. Fourier, M. Frérot, J. Bonnet, G. Molinari, and . Anciaux, Computer Methods in Applied Mechanics and Engineering, vol.351, pp.951-976

J. Molinari, R. Aghababaei, T. Brink, L. Frérot, and E. Milanese, Adhesive wear mechanisms uncovered by atomistic simulations, vol.6, pp.245-259

L. Frérot, R. Aghababaei, and J. Molinari, A mechanistic understanding of the wear coefficient: From single to multiple asperities contact, Journal of the Mechanics and Physics of Solids, vol.114, pp.172-184

L. Frérot, G. Anciaux, J. Molinari, ;. Frérot, M. Bonnet et al., CSMA 14ème Colloque National en Calcul des Structures, Giens, France. csma2019:240105 Contribution to international conferences 2019 Contact élastoplastique : équations intégrales accélérées par une approche Fourier, Crack Nucleation in the Adhesive Wear of an Elastic-Plastic Half-Space

L. Frérot, M. Bonnet, J. Molinari, and G. Anciaux, CECAM Workshop "Modeling tribology across scales

L. Frérot and E. Milanese, Continuum versus discrete approach in modeling of wear processes, 6th European Conference on Computational Mechanics

L. Frérot, M. Bonnet, G. Anciaux, and J. Molinari, An FFT-based Numerical Method for Elasto-Plastic Contact, 6th European Conference on Computational Mechanics

W. , L. Frérot, R. Aghababaei, J. Molinari, ;. L. Young et al., Politecnico di Milano, Italy, Presentation. Outreach activities 2017 Contact of rough surfaces, Video submission to the EPFL ACCES contest for scientific visualization. Other artifacts with documented use Open-source projects as lead developer Software Library Tamaas ( ??? ??? ??? ??? ), a high-performance library for periodic rough surface contact, 2017.

, Software Library Expolit, a compile-time symbolic integration/differentiation library

L. Frérot, . Python, and . License, Software Library UVW (Universal VTK Writer), a library to write NumPy arrays to VTK files

, Notebook The Mindlin Fundamental Solution -A Fourier Approach, L. Frérot, Python Jupyter notebook, Creative Commons Attribution-ShareAlike License

, Other open-source contributions

;. N. Sofware-library-akantu, G. Richart, J. Anciaux, A. M. Molinari, A. Aragón et al.,

G. Anciaux, N. Richart, T. Junge, M. Vocialta, L. Frérot et al.,

T. Gamblin, Software Spack, a multi-platform package manager for HPC environments