Contact unilatéral de surfaces périodiquement rugueuses : modélisation et simulation

Unilateral contact between two surfaces is a phenomenon often present in physics, mechanics and civil engineering. A nominally smooth surface on a macroscopic scale is actually rough on the microscopic scale. The presence of surficial roughness considerably modifies the stress distribution and the strain field in the vicinity of the surfaces in contact. Consideration of surficial roughness at the microscopic scale is often a key to understanding and modeling a large number of macroscopic interface/surface phenomena such as friction, adhesion, wear and thermal or electrical conduction. This work focuses on the unilateral contact of two half-spaces whose surfaces are periodically rough. In the first part of the work where the two half-spaces consist of two linearly elastic materials, a simple and efficient numerical approach is proposed and elaborated on the basis of the boundary element method and the matrix inversion method and by exploiting the periodicity of the problem in question. This numerical approach is first compared with and validated by available analytical results and then applied to several cases of practical interest. In the second and third parts of the work, the numerical approach proposed in the elastic case is extended to cases where the half-spaces are formed of materials that are first linearly thermoelastic and then linearly viscoelastic. Some existing analytical results in these two cases are used as benchmarks to test the accuracy and efficiency of the resulting approaches. Numerical examples are given to bring out some physical phenomenaLe contact unilatéral entre deux surfaces est un phénomène omniprésent en physique, en mécanique et en génie civil. Une surface nominalement lisse à l’échelle macroscopique est en réalité rugueuse à l’échelle microscopique. La présence de rugosités modifie considérablement la distribution des contraintes et le champ des déformations au voisinage des surfaces en contact. La prise en compte de rugosités surfaciques à l’échelle microscopique constitue souvent une clé pour appréhender et modéliser un grand nombre de phénomènes d’interface/surface observés à l’échelle macroscopique, tels que le frottement, l’adhésion, l’usure et la conductivité thermique ou électrique. Ce travail de thèse porte sur le contact unilatéral de deux demi-espaces dont les surfaces sont périodiquement rugueuses. Dans la première partie du travail où les deux demi-espaces sont constitués de deux matériaux linéairement élastiques, une approche numérique simple et efficace est proposée et élaborée en se basant sur la méthode des éléments de frontière et la méthode d’inversion matricielle et en exploitant la périodicité du problème en question. Cette approche numérique est d’abord comparée avec et validée par des résultats analytiques et ensuite appliquée à plusieurs cas d’intérêt pratique. Dans les deuxième et troisième parties du travail, l’approche numérique proposée dans le cas élastique est étendue aux cas où les demi-espaces sont formés de matériaux d’abord linéairement thermoélastiques et ensuite linéairement viscoélastiques. Des résultats analytiques existants dans ces deux cas sont utilisés comme benchmarks pour tester la précision et l’efficacité des approches résultantes. Des exemples numériques sont donnés pour mettre en évidence des phénomènes physique

Unilateral contact of periodically rough surfaces : modelling and simulation

Le contact unilatéral entre deux surfaces est un phénomène omniprésent en physique, en mécanique et en génie civil. Une surface nominalement lisse à l’échelle macroscopique est en réalité rugueuse à l’échelle microscopique. La présence de rugosités modifie considérablement la distribution des contraintes et le champ des déformations au voisinage des surfaces en contact. La prise en compte de rugosités surfaciques à l’échelle microscopique constitue souvent une clé pour appréhender et modéliser un grand nombre de phénomènes d’interface/surface observés à l’échelle macroscopique, tels que le frottement, l’adhésion, l’usure et la conductivité thermique ou électrique. Ce travail de thèse porte sur le contact unilatéral de deux demi-espaces dont les surfaces sont périodiquement rugueuses. Dans la première partie du travail où les deux demi-espaces sont constitués de deux matériaux linéairement élastiques, une approche numérique simple et efficace est proposée et élaborée en se basant sur la méthode des éléments de frontière et la méthode d’inversion matricielle et en exploitant la périodicité du problème en question. Cette approche numérique est d’abord comparée avec et validée par des résultats analytiques et ensuite appliquée à plusieurs cas d’intérêt pratique. Dans les deuxième et troisième parties du travail, l’approche numérique proposée dans le cas élastique est étendue aux cas où les demi-espaces sont formés de matériaux d’abord linéairement thermoélastiques et ensuite linéairement viscoélastiques. Des résultats analytiques existants dans ces deux cas sont utilisés comme benchmarks pour tester la précision et l’efficacité des approches résultantes. Des exemples numériques sont donnés pour mettre en évidence des phénomènes physiquesUnilateral contact between two surfaces is a phenomenon often present in physics, mechanics and civil engineering. A nominally smooth surface on a macroscopic scale is actually rough on the microscopic scale. The presence of surficial roughness considerably modifies the stress distribution and the strain field in the vicinity of the surfaces in contact. Consideration of surficial roughness at the microscopic scale is often a key to understanding and modeling a large number of macroscopic interface/surface phenomena such as friction, adhesion, wear and thermal or electrical conduction. This work focuses on the unilateral contact of two half-spaces whose surfaces are periodically rough. In the first part of the work where the two half-spaces consist of two linearly elastic materials, a simple and efficient numerical approach is proposed and elaborated on the basis of the boundary element method and the matrix inversion method and by exploiting the periodicity of the problem in question. This numerical approach is first compared with and validated by available analytical results and then applied to several cases of practical interest. In the second and third parts of the work, the numerical approach proposed in the elastic case is extended to cases where the half-spaces are formed of materials that are first linearly thermoelastic and then linearly viscoelastic. Some existing analytical results in these two cases are used as benchmarks to test the accuracy and efficiency of the resulting approaches. Numerical examples are given to bring out some physical phenomen

A simple numerical approach for solving the frictionless contact problem of elastic wavy surfaces

International audienceThe contact between rough surfaces plays an important role in numerous situations of theoretical and practical interest. The present work deals with the problem of frictionless contact between the periodically wavy surfaces of two elastic half-spaces. To solve this problem, a numerical approach, which is reminiscent of the boundary element method, is proposed on the basis of the matrix inversion method and by exploiting the periodicity of the problem. Compared with the finite element method, the proposed numerical approach turns out to be very simple and efficient for computing the actual contact areas and the contact pressure distribution. It is first tested and validated in the cases where periodical roughness is sinusoidal for the one- and two-dimensional situations. It is then applied to other cases where periodical roughness is paraboloidal, conical or pyramidal

Influence of the in-plan distribution of asperities on the normal contact of periodically rough surfaces

International audienceThe present work aims to analyze the influence of the in-plan distribution of asperities on the contact between periodically rough surfaces. Square pattern and hexagonal pattern rigid surfaces are considered. Their contact with an elastic half-space is analyzed by numerical simulations. Three surfaces are generated with identical asperities periodically distributed in a plan according to different patterns. It follows from numerical results that when the load and the real contact area are small, the asperities act almost independently. However, the interaction between close asperities increases with the load becomes intensified and has a significant effect on the contact area when the situation is close to full contact

Numerical simulations of the frictionless contact between the rough surfaces of two elastic or viscoelastic bodies

EUROMECH 575 - CONTACT MECHANICS AND COUPLED PROBLEMS IN SURFACE PHENOMENA, LUCQUES, ITALIE, 30-/03/2015 - 02/04/2015International audienceNumerical simulations of the contact between two rough surfaces are of great importance for understanding many mechanical and physical phenomena in solids. Such simulations are still a challenging task even in frictionless cases because the reel contact area is unknown in general and the accurate determination of this area requires very fine mesh [1]. When a great number of asperities are involved, the numerical simulation becomes excessively time consuming if the finite element method is used. This work presents the development of efficient approaches for simulating the contact between the frictionless rough surfaces of two elastic and viscoelastic solids by using a boundary element method. Periodically and randomly rough surfaces are considered. In the case of periodically rough surfaces, the contact problem can be solved for a unit cell by using the periodical conditions [2]. With respect to finite element method, the number of elements is then drastically reduced and the calculation is accurate and fast. The method has been validated by comparing the numerical results with the available analytic solutions for one dimensional sinusoidal surfaces under both full and partial contact situations. For two dimensional wavy surfaces, the validation has been made firstly in the full contact situation where the analytic solutions are available. In the case of partial contact, comparisons have been made with some incomplete analytic solutions and other numerical solutions. Fig. 1 shows an example of the distribution of contact pressure. For the contact between randomly rough surfaces, a multi asperity approach has been developed and successfully applied to the contact between a tire and a road surface [3, 4]. The method solves the contact problem in two steps. At the first step, the contact force at the summit of each asperity is calculated. The distribution of the contact pressure is calculated at the second step and the accuracy is improved by using an iterative method. Fig. 2 shows an example of distribution of the contact pressure. The method can be extended to the viscoelastic situation if the whole contact history is known. At each instant, the contribution of the anterior force to the current situation is represented by a time integral and the viscoelastic contact problem is then transformed into an elastic-like one. The method can also be extended to situations when adhesion forces or fluids are present between rough surfaces