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			@book{bonnet_boundary_1995,
			title = {Boundary Integral Equation Methods for Solids and Fluids},
			author = {Bonnet, Marc},
			year = {1995},
			publisher = {{J. Wiley}},
			address = {{Chichester ; New York}},
			isbn = {978-0-471-97184-9},
			keywords = {Boundary element methods,Fluid mechanics,Mathematics,Mechanics; Applied},
			lccn = {TA347.B69 B6848 1995},
			note = {OCLC: ocm41368652}
			}

			@article{frerot_crack_2019,
			title = {Crack {{Nucleation}} in the {{Adhesive Wear}} of an {{Elastic}}-{{Plastic Half}}-{{Space}}},
			author = {Fr{\'e}rot, Lucas and Anciaux, Guillaume and Molinari, Jean-Fran{\c c}ois},
			year = {2019},
			month = oct,
			abstract = {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. The crack nucleation process in a rough elastic-plastic contact is investigated in a comparative study with a classical \$J\_2\$ plasticity approach and a saturation plasticity model. We show that plastic residual deformations in the \$J\_2\$ 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 confirmed 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.},
			archivePrefix = {arXiv},
			eprint = {1910.05163},
			eprinttype = {arxiv},
			journal = {arXiv:1910.05163 [cond-mat]},
			keywords = {Condensed Matter - Soft Condensed Matter},
			primaryClass = {cond-mat}
			}

			@article{frerot_fourieraccelerated_2019,
			title = {A {{Fourier}}-Accelerated Volume Integral Method for Elastoplastic Contact},
			author = {Fr{\'e}rot, Lucas and Bonnet, Marc and Molinari, Jean-Fran{\c c}ois and Anciaux, Guillaume},
			year = {2019},
			month = jul,
			volume = {351},
			pages = {951--976},
			issn = {0045-7825},
			doi = {10.1016/j.cma.2019.04.006},
			abstract = {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\textendash{}plastic FEM Hertz normal contact simulation and showcase its ability to simulate contact of rough surfaces with plastic flow.},
			copyright = {All rights reserved},
			journal = {Computer Methods in Applied Mechanics and Engineering},
			keywords = {Condensed Matter - Soft Condensed Matter,Contact,Fourier,Mindlin,Physics - Computational Physics,Plasticity,Rough surface,Volume integral equation}
			}

			@article{frerot_mechanistic_2018,
			title = {A Mechanistic Understanding of the Wear Coefficient: {{From}} Single to Multiple Asperities Contact},
			shorttitle = {A Mechanistic Understanding of the Wear Coefficient},
			author = {Fr{\'e}rot, Lucas and Aghababaei, Ramin and Molinari, Jean-Fran{\c c}ois},
			year = {2018},
			month = may,
			volume = {114},
			pages = {172--184},
			issn = {0022-5096},
			doi = {10.1016/j.jmps.2018.02.015},
			abstract = {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.},
			copyright = {All rights reserved},
			journal = {Journal of the Mechanics and Physics of Solids},
			keywords = {Cluster statistics,Contact,Self-affine surface,Wear coefficient}
			}

			@article{hu_simulation_1992,
			title = {Simulation of 3-{{D}} Random Rough Surface by 2-{{D}} Digital Filter and Fourier Analysis},
			author = {Hu, Y.Z. and Tonder, K.},
			year = {1992},
			month = feb,
			volume = {32},
			pages = {83--90},
			issn = {08906955},
			doi = {10.1016/0890-6955(92)90064-N},
			journal = {International Journal of Machine Tools and Manufacture},
			language = {en},
			number = {1-2}
			}

			@article{mindlin_thermoelastic_1950,
			title = {Thermoelastic {{Stress}} in the {{Semi}}-{{Infinite Solid}}},
			author = {Mindlin, Raymond D. and Cheng, David H.},
			year = {1950},
			month = sep,
			volume = {21},
			pages = {931--933},
			issn = {0021-8979},
			doi = {10.1063/1.1699786},
			journal = {Journal of Applied Physics},
			number = {9}
			}

			@article{persson_nature_2005,
			title = {On the Nature of Surface Roughness with Application to Contact Mechanics, Sealing, Rubber Friction and Adhesion},
			author = {Persson, B. N. J. and Albohr, O. and Tartaglino, U. and Volokitin, A. I. and Tosatti, E.},
			year = {2005},
			volume = {17},
			pages = {R1},
			issn = {0953-8984},
			doi = {10.1088/0953-8984/17/1/R01},
			abstract = {Surface roughness has a huge impact on many important phenomena. The most important property of rough surfaces is the surface roughness power spectrum C ( q ). We present surface roughness power spectra of many surfaces of practical importance, obtained from the surface height profile measured using optical methods and the atomic force microscope. We show how the power spectrum determines the contact area between two solids. We also present applications to sealing, rubber friction and adhesion for rough surfaces, where the power spectrum enters as an important input.},
			journal = {Journal of Physics: Condensed Matter},
			language = {en},
			number = {1}
			}

			@article{polonsky_numerical_1999,
			title = {A Numerical Method for Solving Rough Contact Problems Based on the Multi-Level Multi-Summation and Conjugate Gradient Techniques},
			author = {Polonsky, I. A. and Keer, L. M.},
			year = {1999},
			month = jul,
			volume = {231},
			pages = {206--219},
			issn = {0043-1648},
			doi = {10.1016/S0043-1648(99)00113-1},
			abstract = {An alternative numerical method for solving contact problems for real rough surfaces is proposed. The real area of contact and the contact pressure distribution are determined using a single-loop iteration scheme based on the conjugate gradient method, which converges for arbitrary rough surfaces. The surface deflections and subsurface stresses are computed using an alternative two-dimensional multi-level multi-summation algorithm, which allows the summation error to be kept under the discretization error for any number of contact points. The proposed method is fast: rough contact problems for surface samples with 105\textendash{}106 data points are solved on a personal computer in a few hours. The numerical algorithms are described in full detail so that an interested reader can implement the new contact solver in a computer code. Numerical examples demonstrating the method advantages are presented. The method is compared with other fast contact solvers that have emerged in the last few years.},
			journal = {Wear},
			keywords = {Conjugate gradient techniques,Multi-level multi-summation,Rough contact problems},
			number = {2}
			}

			@article{renard_constant_2013,
			title = {Constant Dimensionality of Fault Roughness from the Scale of Micro-Fractures to the Scale of Continents},
			author = {Renard, Fran{\c c}ois and Candela, Thibault and Bouchaud, Elisabeth},
			year = {2013},
			volume = {40},
			pages = {83--87},
			issn = {1944-8007},
			doi = {10.1029/2012GL054143},
			abstract = {Many faults and fractures in various natural and man-made materials share a remarkable common fractal property in their morphology. We report on the roughness of faults in rocks by analyzing the out-of-plane fluctuations of slip surfaces. They display a statistical power-law relationship with a nearly constant fractal exponent from millimeter scale micro-fractures in fault zones to coastlines measuring thousands of kilometers that have recorded continental breakup. A possible origin of this striking fractal relationship over 11 orders of magnitude of length scales is that all faulting processes in rocks share common characteristics that play a crucial role in the shaping of fault surfaces, such as the effects of elastic long-range stress interactions and stress screening by mechanical heterogeneities during quasi-static fracture growth.},
			copyright = {\textcopyright{}2012. American Geophysical Union. All Rights Reserved.},
			journal = {Geophysical Research Letters},
			language = {en},
			number = {1}
			}

			@article{rey_normal_2017,
			title = {Normal Adhesive Contact on Rough Surfaces: Efficient Algorithm for {{FFT}}-Based {{BEM}} Resolution},
			shorttitle = {Normal Adhesive Contact on Rough Surfaces},
			author = {Rey, Valentine and Anciaux, Guillaume and Molinari, Jean-Fran{\c c}ois},
			year = {2017},
			month = mar,
			pages = {1--13},
			issn = {0178-7675, 1432-0924},
			doi = {10.1007/s00466-017-1392-5},
			abstract = {We introduce a numerical methodology to compute the solution of an adhesive normal contact problem on rough surfaces with the Boundary Element Method. Based on the Fast Fourier Transform and the Westergaard's fundamental solution, the proposed algorithm enables to solve efficiently the constrained minimization problem: the numerical solution strictly verifies contact orthogonality and the algorithm takes advantage of the constraints to speed up the minimization. Comparisons with the analytical solution of the Hertz case prove the quality of the numerical computation. The method is also used to compute normal adhesive contact between rough surfaces made of multiple asperities.},
			journal = {Computational Mechanics},
			language = {en}
			}

			@article{rey_quantifying_2019,
			title = {Quantifying Uncertainties in Contact Mechanics of Rough Surfaces Using the Multilevel {{Monte Carlo}} Method},
			author = {Rey, V. and Krumscheid, S. and Nobile, F.},
			year = {2019},
			month = may,
			volume = {138},
			pages = {50--64},
			issn = {0020-7225},
			doi = {10.1016/j.ijengsci.2019.02.003},
			abstract = {We quantify the effect of uncertainties on quantities of interest related to contact mechanics of rough surfaces. Specifically, we consider the problem of frictionless non adhesive normal contact between two semi infinite linear elastic solids subject to uncertainties. These uncertainties may for example originate from an incomplete surface description. To account for surface uncertainties, we model a rough surface as a suitable Gaussian random field whose covariance function encodes the surface's roughness, which is experimentally measurable. Then, we introduce the multilevel Monte Carlo method which is a computationally efficient sampling method for the computation of the expectation and higher statistical moments of uncertain system output's, such as those derived from contact simulations. In particular, we consider two different quantities of interest, namely the contact area and the number of contact clusters, and show via numerical experiments that the multilevel Monte Carlo method offers significant computational gains compared to an approximation via a classic Monte Carlo sampling.},
			journal = {International Journal of Engineering Science},
			keywords = {Contact clusters,Frictionless contact,Multilevel Monte Carlo,Random surface generator,Rough surfaces}
			}

			@article{rey_stability_2018,
			title = {Stability Analysis of Rough Surfaces in Adhesive Normal Contact},
			author = {Rey, Valentine and Bleyer, Jeremy},
			year = {2018},
			month = mar,
			pages = {1--13},
			issn = {0178-7675, 1432-0924},
			doi = {10.1007/s00466-018-1556-y},
			abstract = {This paper deals with adhesive frictionless normal contact between one elastic flat solid and one stiff solid with rough surface. After computation of the equilibrium solution of the energy minimization principle and respecting the contact constraints, we aim at studying the stability of this equilibrium solution. This study of stability implies solving an eigenvalue problem with inequality constraints. To achieve this goal, we propose a proximal algorithm which enables qualifying the solution as stable or unstable and that gives the instability modes. This method has a low computational cost since no linear system inversion is required and is also suitable for parallel implementation. Illustrations are given for the Hertzian contact and for rough contact.},
			journal = {Computational Mechanics},
			language = {en}
			}

			@article{richart_implementation_2015,
			title = {Implementation of a Parallel Finite-Element Library: {{Test}} Case on a Non-Local Continuum Damage Model},
			shorttitle = {Implementation of a Parallel Finite-Element Library},
			author = {Richart, N. and Molinari, J. F.},
			year = {2015},
			month = aug,
			volume = {100},
			pages = {41--46},
			issn = {0168-874X},
			doi = {10.1016/j.finel.2015.02.003},
			abstract = {This paper presents an efficient method to implement a damage law within an explicit time-integration scheme, in an open-source object-oriented finite-element framework. The hybrid object/vector design of the framework and implementation choices are detailed in the special case of non-local continuum damage constitutive laws. The computationally demanding aspect of such constitutive laws requires efficient algorithms, capable of using High Performance Computing (HPC) clusters. The performance of our approach is demonstrated on a numerically and physically challenging 3D dynamic brittle-fragmentation test case. An almost perfect scalability is achieved on parallel computations. The global dynamics and energy terms are in good agreement with classical cohesive models' predictions.},
			journal = {Finite Elements in Analysis and Design},
			keywords = {Continuum damage,Finite element method,Non-local approach,Parallel computing}
			}

			@article{stanley_fftbased_1997,
			title = {An {{FFT}}-{{Based Method}} for {{Rough Surface Contact}}},
			author = {Stanley, H. M. and Kato, T.},
			year = {1997},
			month = jul,
			volume = {119},
			pages = {481--485},
			issn = {0742-4787},
			doi = {10.1115/1.2833523},
			abstract = {Elastic contact between a rigid plane and a halfspace whose surface height is described by a bandwidth-limited Fourier series is considered. The surface normal displacements and contact pressures are found by a numerical technique that exploits the structure of the Fast Fourier Transform (FFT) and an exact result in linear elasticity. The multiscale nature of rough surface contact is implicit to the method, and features such as contact agglomeration and asperity interaction\textemdash{}a source of difficulty for asperity-based models\textemdash{}evolve naturally. Both two-dimensional (2-D) and three-dimensional (3-D) contact are handled with equal ease. Finally, the implementation is simple, compact, and fast.},
			journal = {Journal of Tribology},
			number = {3}
			}

			@article{telles_application_1979,
			title = {On the Application of the Boundary Element Method to Plasticity},
			author = {Telles, J. C. F. and Brebbia, C. A.},
			year = {1979},
			month = dec,
			volume = {3},
			pages = {466--470},
			issn = {0307-904X},
			doi = {10.1016/S0307-904X(79)80030-X},
			journal = {Applied Mathematical Modelling},
			number = {6}
			}

			@article{yastrebov_accurate_2017,
			title = {On the Accurate Computation of the True Contact-Area in Mechanical Contact of Random Rough Surfaces},
			author = {Yastrebov, Vladislav A. and Anciaux, Guillaume and Molinari, Jean-Fran{\c c}ois},
			year = {2017},
			issn = {0301-679X},
			doi = {10.1016/j.triboint.2017.04.023},
			abstract = {We introduce a corrective function to compensate errors in contact area computations coming from mesh discretization. The correction is based on geometrical arguments, and apart from the contact area itself requires only one additional quantity to be computed: the length of contact/non-contact interfaces. The new technique enables to evaluate accurately the true contact area using a very coarse mesh, for which the shortest wavelength in the surface spectrum reaches the grid size. The validity of the approach is demonstrated for surfaces with different fractal dimensions and different spectral content using a properly designed mesh convergence test. In addition, we use a topology preserving smoothing technique to adjust the morphology of contact clusters obtained with a coarse grid.},
			journal = {Tribology International},
			keywords = {Boundary element Method,Contact area,Contact area correction,Simulations,surface roughness}
			}

			@article{yastrebov_contact_2012,
			title = {Contact between Representative Rough Surfaces},
			author = {Yastrebov, Vladislav A. and Anciaux, Guillaume and Molinari, Jean-Fran{\c c}ois},
			year = {2012},
			month = sep,
			volume = {86},
			issn = {1539-3755, 1550-2376},
			doi = {10.1103/PhysRevE.86.035601}
			journal = {Physical Review E},
			language = {en},
			number = {3}
			}

			@article{yastrebov_contact_2014,
			title = {The {{Contact}} of {{Elastic Regular Wavy Surfaces Revisited}}},
			author = {Yastrebov, Vladislav A. and Anciaux, Guillaume and Molinari, Jean-Fran{\c c}ois},
			year = {2014},
			month = oct,
			volume = {56},
			pages = {171--183},
			issn = {1023-8883, 1573-2711},
			doi = {10.1007/s11249-014-0395-z},
			abstract = {We revisit the classic problem of an elastic solid with a two-dimensional wavy surface squeezed against an elastic flat half-space from infinitesimal to full contact. Through extensive numerical calculations and analytic derivations, we discover previously overlooked transition regimes. These are seen in particular in the evolution with applied load of the contact area and perimeter, the mean pressure and the probability density of contact pressure. These transitions are correlated with the contact area shape, which is affected by long range elastic interactions. Our analysis has implications for general random rough surfaces, as similar local transitions occur continuously at detached areas or coalescing contact zones. We show that the probability density of null contact pressures is nonzero at full contact. This might suggest revisiting the conditions necessary for applying Persson's model at partial contacts and guide the comparisons with numerical simulations. We also address the evaluation of the contact perimeter for discrete geometries and the applicability of Westergaard's solution for three-dimensional geometries.},
			journal = {Tribology Letters},
			language = {en},
			number = {1}
			}

			@article{yastrebov_infinitesimal_2015,
			title = {From Infinitesimal to Full Contact between Rough Surfaces: {{Evolution}} of the Contact Area},
			shorttitle = {From Infinitesimal to Full Contact between Rough Surfaces},
			author = {Yastrebov, Vladislav A. and Anciaux, Guillaume and Molinari, Jean-Fran{\c c}ois},
			year = {2015},
			month = jan,
			volume = {52},
			pages = {83--102},
			issn = {00207683},
			doi = {10.1016/j.ijsolstr.2014.09.019},
			journal = {International Journal of Solids and Structures},
			language = {en}
			}

			@article{yastrebov_role_2017,
			title = {The Role of the Roughness Spectral Breadth in Elastic Contact of Rough Surfaces},
			author = {Yastrebov, Vladislav A. and Anciaux, Guillaume and Molinari, Jean-Fran{\c c}ois},
			year = {2017},
			month = oct,
			volume = {107},
			pages = {469--493},
			issn = {0022-5096},
			doi = {10.1016/j.jmps.2017.07.016},
			abstract = {We study frictionless and non-adhesive contact between elastic half-spaces with self-affine surfaces. Using a recently suggested corrective technique, we ensure an unprecedented accuracy in computation of the true contact area evolution under increasing pressure. This accuracy enables us to draw conclusions on the role of the surface's spectrum breadth (Nayak parameter) in the contact area evolution. We show that for a given normalized pressure, the contact area decreases logarithmically with the Nayak parameter. By linking the Nayak parameter with the Hurst exponent (or fractal dimension), we show the effect of the latter on the true contact area. This effect, undetectable for surfaces with poor spectral content, is quite strong for surfaces with rich spectra. Numerical results are compared with analytical models and other available numerical results. A phenomenological equation for the contact area growth is suggested with coefficients depending on the Nayak parameter. Using this equation, the pressure-dependent friction coefficient is deduced based on the adhesive theory of friction. Some observations on Persson's model of rough contact, whose prediction does not depend on Nayak parameter, are reported. Overall, the paper provides a unifying picture of rough elastic contact and clarifies discrepancies between preceding results.},
			journal = {Journal of the Mechanics and Physics of Solids},
			keywords = {Contact area,Hurst exponent,Nayak parameter,Pressure-dependent friction,Roughness,Spectrum breadth}
			}

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