Conductivity of rough contact interfaces (MULT-PHYS)

We study conductivity of complex-shaped spots in contact interfaces both isolated ones and assembled in clusters. Flower-, star- and gear-like spots are studied along with self-affine and fractal ones. Complex contact interfaces resulted from solving contact problem between rough surfaces are also studied with and without oxide films present in the interface.

Hierarchical matrices for Fast-BEM (NUM)

We use ACA+ and SVD low rank matrices to construct hierarchical matrices for fast BEM. The method is implemented in C++ and Python. The method is applied to electric and thermal stationary conductivity problems. We work on its application to contact problems within the flexibility method in Finite Element context.

Stability of frictional slip at bi-material interface under non-uniform contact pressure (MECH)

We study theoretically a nucleation and propagation of frictional slip at bi-material interfaces. In analogy to fracture mechanics, we suggest to use a friction resistance curve (FR-curve) to determine stable and unstable slip growth. The FR-curve is determined by contact pressure and friction heterogeneity in vicinity of the weakest zone, where the slip nucleates. We show the nucleation of the slip process may be either stable or unstable as well as its propagation. We give an interpretation of "slow fronts" as being stable slip propagation, whose velocity is proportional to the external loading rate. The coefficient of proportionality depends on the geometry, material properties and loading conditions. We suggest two universal adimensional parameters controlling stability of frictional growth. We give a condition on space discretization which enables to capture the slip onset. "Supercooled" slip, metastable slip: the stability is lost before slip starts, i.e. any infinitesimal small perturbation at the interface results in an unstable slip growth.

Incompressible fluid transport at contact interface between rough solids (MECH)
with Guillaume Anciaux, Jean-Fran�ois Molinari

We study transmissivity of the interface formed by two elastic solids with self-affine surfaces brought in contact. Results for incompressible laminar viscous flow for thin film (Reynolds equation for Pouiseille flow) is solved by the finite element method. Mechanical contact is solved by FFT-based boundary element method. Different transmissivity regimes are identified, a simple equation is obtained, which links the transmissivity with applied pressure (and area) through geometrical characteristics. Moreover, a a simple model for percolation on a graph is justified, topology of graph connections and the graph-node spatial density are linked with the surface power spectrum and the critical junction model.

Detachment wave and frictional drop at bi-material interface in subcritical and critical regimes (MECH)

We demonstrate by numerical simulations that two distinct mechanism of friction can be observed in the similar set-up: sliding of an elastic half-space on a rigid flat surface. At friction coefficients under the critical value f < 1, a series of Weertman pulses propagating at interface is observed in according to theoretical prediction of Adams and Bui. For friction coefficients in the potentially unstable friction f > 1 (Renardy), the slip occurs as a single Schallamach wave. Note that previously it was shown that the problem of elastodynamic frictional slip for such friction coefficients is an ill-posed mathematical problem. We however obtain reasonable results, as a perfect contact was assumed at the interface, whereas in our case a detachment, which regularizes the problem, occurs and propagates at the interface. It is interesting to note that the conversion of Weertman's wave to opening wave results in a abrupt lost of frictional resistance as opening waves do not dissipate the energy. Thus for locally higher friction, one may obtain quite a small global coefficient of friction and it can even become negative.

Comparison of asperity-based models with full scale FEM/BEM simulations (MECH)

Taken a random self-affine surface there are different ways to perform mechanical contact analysis, among them (1) a full scale numerical resolution using either boundary element model of finite element model, (2) asperity based model (with and without long range elastic interaction) which would also imply asperity detection and characterization. In this study we compare these two approaches for infinite periodic geometries and compact contact zones (hertzian contact).

Statistics of contact pressure between contacting rough surfaces (MECH)
with Guillaume Anciaux, Jean-Fran�ois Molinari

We study the evolution of the contact-pressure distribution with increasing externally applied pressure using accurate numerical methods (FFT-based boundary element method). The results are compared with predictions of Persson's contact model.

Scale effect in elastic-plastic asperity models (MECH)
with Samuel Forest (MINES)

We formulate contact and friction constraints for Cosserat and other generalized continuum models. Next, we simulate nano-indentation tests and create a scale dependent elastic-plastic asperity based model, which permits us to simulate shallow contact between a smooth sphere and rough elastic-plastic solid.

Global vs local friction for cylindrical solids (MECH)

We consider a rigid punch sliding on hyper-elastic elastic layer. Under high pressure the frictional and normal tractions cannot be decoupled, which leads to a problem which is hardly traceable analytically. We suggest a geometrical consideration which allows us to link the contact area and the local coefficient of friction with the global coefficient of friction. Some remarks are given on the shallow ironing problem, widely used in the computational contact mechanics community.

Joint effective statistics of homologue rough surfaces (MATH)

We carry out an extended statistical analysis of real and synthetic rough surfaces. The objective of this study is to suggest a realistic model for rough surfaces, deduce the key parameters and give a reliable estimation for them. We analyse different real surfaces and compare various algorithm to synthesize roughness. As an application of this study we aim the contact mechanics of rough surfaces, accordingly, some comments are given on this topic.

Morphology of contact clusters in contact between rough surfaces (MATH)
with Guillaume Anciaux, Jean-Fran�ois Molinari

We study shape and statistical distribution of contact clusters at interface between random rough solids. Trapped area, perimeter, compactness and percolation properties are studied and a link is established with critical path model for fluid transport through the contact interface.

Crypto-billiard: application of asymmetric Lorentz gaz model to cryptography (MATH)

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Large scale distribution of non-interacting matter in the Universe (MATH)

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Critical analysis of regularized and Coulomb's friction at bimaterial interfaces (MATH)
with David S. Kammer

We study frictional slip at bi-material interface (rigid-deformable) of inertial solids. By introducing a small harmonic perturbation on the frictional interface, we show that that its evolution is always exponential with time for regularized Coulomb's friction (Prakash-Clifton friction law). Analytical analysis of poles in Laplace space and numerical simulations demonstrate that introducing the regularization always results in appearance of unstable roots even if the non-regularized regime was well-posed.

Dynamic properties of asymmetric architectured materials (MATH)

We study a new class of materials with internal contact resulting in asymmetric and discontinuous elastic behavior. We suggest different configurations for architectures of such materials both for stiff-in-compression-- soft-in-tension and soft-in-compression--stiff-in-tension. Two such asymmetric architectured cells are combined in a way that the resulting effective behavior is symmetric. Such a system is approximated by a simple mass spring model with two masses and a dynamic analysis in parametric space (stiffness ratio, damping and forcing frequency) is performed. Transition to chaos is characterized and some strange attractors are analysed in more details.

Strong coupling of solid and fluid mechanical problems for sealing applications (NUM)

Sealing is an important branch of engineering, which deals with the analysis and control of fluid exchange between regions separated by an interface. Sealing technology is crucial for many industrial applications, especially for the automotive and nuclear industry: rotary mechanical seals, gaskets and O-rings for pipeline connections and nuclear vessels. In this study we are interested in a particular class of seals: static contact seals, in which the seal body comes in mechanical contact with the substrate to prevent leakage. However, due to microscopic surface roughness and potentially high gradients of the hydrostatic fluid pressure, the quality of sealing strongly depends on mechanical pressure applied to the seal body. We study the leakage rate for incompressible viscous fluid through a contact interface between two infinite randomly rough surfaces brought in normal elastic contact. Our objective is to link roughness characteristics with the variation of the leakage rate under increasing pressure.

This problem resolution includes two distinct physics: mechanical contact and laminar viscous fluid flow. When two randomly rough surfaces are brought in mechanical contact by moderate externally applied pressure, the real contact area presents just a portion of the nominal contact area. The gap distribution in the contact interface is given by h(x,y), where x,y are Cartesian in-plane coordinates. The contact clusters are determined by h(x,y)=0 and the free space, available for fluid transfer, is given by h(x,y)>0. This free space is used to compute the viscous fluid flow through the contact interface using Reynolds planar equations for thin films for averaged Poiseuille distribution of fluid velocity. The flow rate is proportional to the product of the hydrostatic pressure gradient and the cube of the gap and inversely proportional to the fluid viscosity

If the hydrostatic pressure is small compared to contact pressure arising in the interface, the mechanical and fluid parts are only weakly and unilaterally coupled, thus they can be solved consequently. To generate isotropic Gaussian self-affine random surfaces, we use a filtering algorithm in Fourier space, which enables us to control rms height or rms gradient of the surface, its spectral content vounded between the shortest and the longest wavelengths, and also the Hurst exponent H of equivalently the fractal dimension D=3-H. We use spectral based boundary element method, based on Kalker's variational formulation, to solve mechanical contact problem between elastic half-spaces with generated roughness under externally applied mechanical pressure. Afterwards, we transmit the gap field, found in the mechanical problem, to a finite element code, which solves the stationary transport equation for viscous fluid flow. This procedure is repeated for different pressure up to the percolation. Close to the percolation limit, in addition to the fluid analysis, a percolation analysis on contact clusters is performed.

When the value of the hydrostatic pressure is comparable with developed mechanical contact pressures, a fully coupled fluid-structure resolution is needed. Precisely, the mechanical contact problem is solved with additional hydrostatic pressure applied at the entire interface, which arises from the solution of the fluid problem. The solution of the latter, in turn, depends on the gap field, being the solution of the mechanical problem. This coupled problem is resolved within a unique iterative procedure using iterative solvers.

Multi-material and multi-scale electric contact for weak currents: experiments and simulations (MULT-PHYS)
with Frederick Sorel Mballa Mballa (postdoc), Georges Cailletaud (MINES), Henry Proudhon (MINES), Sophie No�l (LGEP), Fr�d�ric Houz� (LGEP)

An experimental and numerical study of electric contact for low currents in sphere-plane set-up is presented. A three-level multi-scale model is proposed. We use the finite element analysis for macroscopic mechanical and electric simulations. It takes into account the setup geometry, elastoplastic mechanical behavior of contacting components in the finite-strain-plasticity framework and electrostatic properties. A sensitivity analysis with respect to the brass plastic behavior and to the thickness of coating layers is also performed. The finite element results are used for an asperity-based model, which includes elasto-plastic deformation of asperities and their mutual elastic interactions. This model enables us to simulate the real morphology of contact spots at the roughness scale using the experimentally measured surface topography. Finally, the Greenwood multi-spot model is used to estimate the electric contact resistance. This three-level model yields results which are in good agreement with experimental measurements carried out in this study.

Thermo-mechanical coupling in contact and friction problems involving incompressible fluids (MULT-PHYS)
with Andrei Shvarts (PhD student), Georges Cailletaud (MINES)

Multi-scale and multi-physical coupling of the contact interaction is a relatively unexplored topic in the domain of computational mechanics (physics) because of the geometrical complexity of contacting surfaces and the strong coupling involved phenomena. In this project we plan to use advanced numerical simulations within the homogenisation paradigm ``from-down-to-top''. Taking into account the essential physics and roughness of contacting solids at small scales will enable us to construct new advanced model at macroscopic scale, which will be implemented in our finite element software Z-set. This enhancement in terms of multi-functionality and polyvalency will allow us to interact with the industry on new challenging problems, which cannot be treated in the actual state of our expertise and software capabilities.

Surface roughness at small scales determines the macroscopic properties of the contact interaction such as energy transfer across the contact interface or fluid transport along it. Moreover, this roughness play a crucial role in frictional, adhesion and wear mechanisms. However, the solution of a mechanical problem (even with explicitly modeled roughness) is not sufficient to understand and analyse coupled multi-physical problems, which are often encountered in industrial applications and natural phenomena. The fluid flow, for example, is described by the Navier-Stokes equation, whereas the heat production and diffusion is described by the non-stationary heat equation. At the same time, the emerging boundary value problems for these phenomena (geometry and boundary conditions) strongly depend on the the mechanical problem, whose solution in turn is influenced by the hydrostatic and hydrodynamic pressures of the fluid flow as well as by the thermal fields.

First, it is planned to implement in Z-set software the thermomechanical coupling for contact problems, which would enable us to simulate the heat production due to the frictional dissipation at the interface as well as the heat exchange (direct and convective) between contacting parts. This coupling will be done at the roughness scale as well as at the macroscopic scale (Hertzian contact for smooth surfaces) with constitutive equation for the interface heat transfer emerging from the microscopic simulations. The former coupling will serve to refine our understanding of the physical phenomenon and to critically analyse (and if needed adapt) existing constitutive laws of the heat transfer. The latter coupling will be of importance for industrial applications; aircraft and vehicle engines, brake systems, friction within geological faults are among the most critical applications. Moreover, since the stationary heat equation in absence of the convective term describes the electrostatics (Poisson's equation), this framework can and will be used to simulation of electric contact (possible collaboration with parallel PhD topics).

The second coupling, mechanics and fluid flow, will enable us to threat the problems of sealing and mixed lubrication. The former, essential for aeronautic and nuclear industries, requires the solution of the flow problem and its coupling to the mechanical contact at the roughness scale as well as it subsequent generalization for macroscopic scales of industrial devices. The latter problem is crucial for all industrial applications in which contacting components of a system are in relative motion, hence often the presence of liquid lubricant. The coupling shall be implemented for two-dimensional Reynolds equation (Couette and Hagen-Poiseuille flow).

Both couplings will be implemented within a general architecture enabling to integrate the complete ultimate thermomechanical coupling with the fluid flow with marginal efforts. Moreover, the architecture of the novel contact scheme (dual mortar method), which will be used in this study and implemented in parallel by another PhD candidate, will be adapted for efficient realisation of the current project. The primary objective of this project is to refine our understanding of multi-physical and multi-scale aspects in frictional contact problems. The secondary objective is to ensure the readiness of our finite element software to new industrial challenges in the domain of computational mechanics.

Mechanical behavior and wear of hardmetals in hard rock drilling (MECH)
with Dmitry Tkalich (PhD student), Georges Cailletaud (MINES), Pascal-Alexandre Kane (Sintef, Norway), Charlie C. Li (NTNU, Norway)

Mechanical behavior of drilling tools made of cemented tungsten carbides is investigated in impact interaction with a hard rock. In the first step, macroscopic finite-element (FE) impact simulations with varying incident angles are carried out in order to obtain stress states evolution at critical locations within the cemented tungsten carbide impactor. Material of the impactor is modeled using a uniform field (UF) two-phase model, which is based on the Eshelby's solution of the inclusion problem, extended to elasto-plasticity by means of a b-model for plastic accommodation. Isotropic von Mises plasticity model is used for the binder phase and a non-associated Drucker-Prager model for the tungsten carbide, both models use a non-linear isotropic hardening. The validity of the UF model for cemented tungsten carbide material with its specific microstructure and material behaviors was confirmed by comparison with the FE models constructed by accurately reproducing scanning electron microscope images. In the second step, the selected stress paths are used as boundary conditions applied on three-dimensional FE models with an explicit microstructure represented by a new model based on Poisson cutting of Voronoi grains. Dispersion of stresses were studied to identify the most dangerous locations within the microstructure, which are responsible for the onset of wear and fracture of the cemented tungsten carbides.

Signatures of iceberg calving in seismological data (GEO+NUM)
with Amandine Sergeant-Boy (PhD student), Anne Mangeney (IPGP), Olivier Castelnau (ENSAM), Jean-Pierre Montagner (IPGP), Eleonore Stutzmann (IPGP)

Glacial earthquakes is a class of seismic events of magnitude up to 5, occurring primarily in Greenland, in the margins of large marine-terminated glaciers with near-grounded termini. They are caused by calving of cubic-kilometer scale unstable icebergs which penetrate the full-glacier thickness and, driven by the buoyancy forces, capsize against the calving front. These phenomena produce seismic energy including surface waves with dominant energy between 10-150 s of period whose seismogenic source is compatible with the contact force exerted on the terminus by the iceberg while it capsizes. A reverse motion and posterior rebound of the terminus have also been measured and associated with the fluctuation of this contact force. Using a finite element model of iceberg and glacier terminus coupled with simplified fluid-structure interaction model, we simulate calving and capsize of icebergs. Contact and frictional forces are measured on the terminus and compared with laboratory experiments. We also study the influence of geometric factors on the force history, amplitude and duration at the laboratory and field scales. We show first insights into the force and the generated seismic waves exploring different scenarios for iceberg capsizing.

Development of advanced numerical methods in contact mechanics for aerospace applications (NUM)
with Basava Raju Akula (PhD student), Georges Cailletaud (MINES)

Recent developments in the finite element software Zset allows to solve efficiently most problems involving friction and contact. However, the implemented methods make use of specific contact discretizations that lack of accuracy in load transfer between contacting surfaces. In consequence (i) the contact patch test for non-conforming meshes cannot be passed, (ii) locally the contact pressures experience spurious oscillations, and (iii) elements with higher order interpolations require specific treatment. These problems are associated with under-interpolation of contact forces and non-satisfaction of LBB1 condition. To overcome these difficulties a new class of "surface-to-surface" contact discretizations will be implemented. Because of the weak fulfillment of contact constraints, this class of methods allows to avoid the aforementioned drawbacks and to treat contact problems with higher accuracy and improved robustness. The objective of this project is to improve numerical algorithms and resolution techniques to treat frictional contact problems in the framework of (1) parallel computing, (2) large deformation/large sliding friction contact and (3) highly non-linear materials. All developments will be carried out in the finite element software Zset and employed to solve problems from aeronautic industry including millions degrees of freedom. The ultimate aim is to deliver a robust, multipurpose and accurate contact algorithm capable to treat efficiently contact problems.

Reliability of AgSnO2 contactor systems operating in strong currents (electric arcs) (ENG)
with Fadoua Majid (master student), Georges Cailletaud (MINES), Vladimir Esin (MINES), Fr�d�ric Houz� (LGEP), Philippe Test� (LGEP), Alexandre Bonhomme (Schneider)

In this project we study microstructural evolution of the AgSnO2 contactors in operation under multiple opening/closure actions resulting in emergence of electric arcs causing damage/welding/failure of contactors. This study includes mutliple numerical experiments, microscopical observations of the microstructure evolution and coupled thermomechanical finite element simulations on effective thermo-mechanical behavior of the composite.

Simulation of inverse fracture in Drop Weight Tear Test (DWTT)(ENG)
with Takahiro Sakimoto (PhD student), Jacques Besson (MINES), Yazid Madi (MINES)

In high toughness line-pipe material, inverse fracture is sometimes observed on fracture surface of Drop Weight Tear Test (DWTT) specimen. Inverse fracture is defied as the cleavage fracture that is observed after slant ductile fracture. The initiation point of inverse fracture is mostly located in the front of delamination on slant ductile fracture surface. However, the initation mechanism of inverse fracture has not yet been clarified in details. This study aims at the simulation of slant ductile fracture in DWTT in a X65 line pipe steel. The proposed simulation includes a detailed description of the anisotropic plastic behavior and material hardening behavior under high speed deformation. The slant ductile fracture behavior is modeled using the computational cell technique. Damage in each cell is represented using the GTN model for ductile fracture which is fitted using results of the notched tensile bars. These calculations are post-processed to access both delamination and cleavage leading to inverse fracture. The computational results show good agreement with the measured experimental load-displacement curve for both tensile bars and DWTT specimens. The computational results are then used to derive macroscopic failure criteria for both delamination and cleavage over a wide temperature range. Using these results, the initiation mechanism of inverse fracture is discussed from the view point of the ductile to brittle transition initiated at delamination cracks.

Numerical methods in contact mechanics (NUM)
2007-2011, with Fr�d�ric Feyel (ex Onera), Georges Cailletaud (MINES)

Computational contact mechanics is a broad topic which brings together algorithmic, geometrical, optimization and numerical aspects for a robust, fast and accurate treatment of contact problems. This book covers all the basic ingredients of contact and computational contact mechanics: from efficient contact detection algorithms and classical optimization methods to new developments in contact kinematics and resolution schemes for both sequential and parallel computer architectures. The book is self-contained and intended for people working on the implementation and improvement of contact algorithms in a finite element software. Using a new tensor algebra, the author introduces some original notions in contact kinematics and extend the classical formulation of contact elements. Some classical and new resolution methods for contact problems and associated ready-to-implement expressions are provided.

Coupling Discrete Dislocation Dynamics with Finite Element Method (MECH)
2012-2013, with Laurent Dupuy (CEA), Marc Bletry (UPEC), Marc Fivel (SIMaP), Fr�d�ric Feyel (ex Onera), Georges Cailletaud (MINES), PJ Guruprasad (IIT-Bombay, India)

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Martensitic transformations: statistical mechanics approach using Monte-Carlo simulations (MECH)
2009-2011, with Michael Fischlshweiger (Engel, Austria), Thomas Antretter (MUL, Austria), Georges Cailletaud (MINES)

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Molecular dynamics simulation of martensitic transformations using Kastner potential (MECH)
2011

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The existence of a critical length scale in regularised friction (MECH)
2011-2013, with David S. Kammer (PhD student, EPFL), Guillaume Anciaux (EPFL), Jean-Fran�ois Molinari (EPFL) ABSTRACT

Representativity of rough surfaces in normal contact application (MECH)
2011-2015, with Guillaume Anciaux (EPFL), Jean-Fran�ois Molinari (EPFL) ABSTRACT

The contact of elastic regular wavy surfaces revisited (MECH)
2011-2015, with Guillaume Anciaux (EPFL), Jean-Fran�ois Molinari (EPFL) ABSTRACT

On the Propagation of Slip Fronts at Frictional Interfaces (MECH)
2011-2013, with David S. Kammer (PhD student, EPFL), Peter Spijker (postdoc, EPFL), Jean-Fran�ois Molinari (EPFL) ABSTRACT

Crystal plasticity analysis of cylindrical indentation on a Ni-base single crystal superalloy (MECH)
2011-2013, with Prajwal A. Sabnis (PhD student, MINES), Samuel Forest (MINES), Nagaraj K. Arakere (University of Florida, USA) ABSTRACT

Nanoindentation of a gold film at roughness scale (MECH)
2011-2012, with Brice Arrazat (PhD student, MINES Saint-Etienne), Henry Proudhon (MINES), Karim Inal (CEA Leti) ABSTRACT

Impact and penetration at atomic scale (MECH)
2010-2012 ABSTRACT

Generator of bi-phase composites: circular, elliptic, polygonal particles (MECH)
2010-2012 ABSTRACT

Optimization of global search and local detection in contact problems (NUM)
2011

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Publications: [1] NLCM, [2] IJNME

Continuum damage mechanics for quasi-brittle solids (MECH)
2004-2007, with Artem S. Semenov (SPBSPU, Russia), Boris E. Melnikov (SPBSPU, Russia)

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Squeezing elastic-plastic rough surface (MECH)
2009-2011, with Julian Durand (PhD student, MINES), Henry Proudhon (MINES), Georges Cailletaud (MINES)

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