Electrical and Thermal Conductivity of Complex-Shaped Contact Spots

Paul Beguin; Vladislav A. Yastrebov

doi:10.5802/crmeca.266

Article de recherche

Electrical and Thermal Conductivity of Complex-Shaped Contact Spots
[Conductivité électrique et thermique des tâches de contact de forme complexe]

Paul Beguin ¹ ; Vladislav A. Yastrebov ¹

¹ MINES Paris, PSL University, Centre des Matériaux, CNRS UMR 7633, Evry, France

Comptes Rendus. Mécanique, Volume 353 (2025), pp. 195-234.

Résumé
Abstract

Cet article étudie la conductivité électrique et thermique de points de contact complexes à la surface d’un demi-espace. Diverses géométries complexes ont été étudiées à l’aide d’une mise en œuvre interne de la méthode des éléments de frontière rapides. Notre étude commence par des points de contact annulaires afin d’évaluer l’impact de la connexité. Nous étudions ensuite les effets de forme sur des points « multi-pétales » présentant une symétrie dièdre et ressemblant à des fleurs, des étoiles et des engrenages. L’analyse culmine avec les formes auto-affines, qui représentent une généralisation multi-échelle des formes multi-pétales. Dans chaque cas, nous introduisons des normalisations appropriées et développons des modèles phénoménologiques. Pour les formes multi-pétales, notre modèle repose sur un seul paramètre géométrique : le nombre normalisé de « pétales ». Cette approche a inspiré la forme du modèle phénoménologique pour les taches auto-affines, qui maintient la cohérence physique et repose sur quatre caractéristiques géométriques : l’écart type, le deuxième moment spectral, le paramètre de Nayak et l’exposant de Hurst. Ces modèles nous ont permis de proposer des estimations de flux pour un nombre infini de pétales et la limite fractale. Cette étude représente une première étape dans la compréhension de la conductivité des interfaces de contact complexes, qui se produisent couramment dans le contact des surfaces rugueuses.

This paper explores the electrical and thermal conductivity of complex contact spots on the surface of a half-space. Employing an in-house Fast Boundary Element Method implementation, various complex geometries were studied. Our investigation begins with annulus contact spots to assess the impact of connectedness. We then study shape effects on “multi-petal” spots exhibiting dihedral symmetry, resembling flowers, stars, and gears. The analysis culminates with self-affine shapes, representing a multiscale generalization of the multi-petal forms. In each case, we introduce appropriate normalizations and develop phenomenological models. For multi-petal shapes, our model relies on a single geometric parameter: the normalized number of “petals”. This approach inspired the form of the phenomenological model for self-affine spots, which maintains physical consistency and relies on four geometric characteristics: standard deviation, second spectral moment, Nayak parameter, and Hurst exponent. As a by product, these models enabled us to suggest flux estimations for an infinite number of petals and the fractal limit. This study represents an initial step into understanding the conductivity of complex contact interfaces, which commonly occur in the contact of rough surfaces.

Reçu le : 2023-11-24
Révisé le : 2024-08-26
Accepté le : 2024-09-03
Publié le : 2025-01-13

DOI : 10.5802/crmeca.266

Keywords: conductivity, flower-shaped spots, self-affine spots, boundary element method, fractal limit
Mots-clés : conductivité, tâches en forme de fleur, tâches auto-affines, méthode des éléments de frontière, limite fractale

Affiliations des auteurs :

Paul Beguin ¹ ; Vladislav A. Yastrebov ¹

¹ MINES Paris, PSL University, Centre des Matériaux, CNRS UMR 7633, Evry, France

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     author = {Paul Beguin and Vladislav A. Yastrebov},
     title = {Electrical and {Thermal} {Conductivity} of {Complex-Shaped} {Contact} {Spots}},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {195--234},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {353},
     year = {2025},
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     language = {en},
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Paul Beguin; Vladislav A. Yastrebov. Electrical and Thermal Conductivity of Complex-Shaped Contact Spots. Comptes Rendus. Mécanique, Volume 353 (2025), pp. 195-234. doi : 10.5802/crmeca.266. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.266/

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