Sliding without slipping under Coulomb friction: opening waves and inversion of frictional force

An elastic layer slides on a rigid flat governed by Coulomb's friction law. We demonstrate that if the coefficient of friction is high enough, the sliding localizes within stick-slip pulses, which transform into opening waves propagating at intersonic speed in the direction of sliding or, for high Poisson's ratios, at supersonic speed in the opposite direction. This sliding mode, characterized by marginal frictional dissipation, and similar to carpet fold propagation, may result in inversion of the frictional force direction; at longer time intervals the system demonstrates stick-slip behavior. The mechanism is described in detail and a parametric study is presented.Comment: 17 pages, 4 figures, 1 tabl

Electrical and Thermal Conductivity of Complex-Shaped Contact Spots

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 multi-scale 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.Comment: 40 pages, 28 figure

The role of phase interface energy in martensitic transformations: a lattice Monte-Carlo simulation

To study martensitic phase transformation we use a micromechanical model based on statistical mechanics. Employing lattice Monte-Carlo simulations and realistic material properties for shape-memory alloys (SMA), we investigate the combined influence of the external stress, temperature, and interface energy between the austenitic and martensitic phase on the transformation kinetics and the effective material compliance. The one-dimensional model predicts well many features of the martensitic transformation that are observed experimentally. Particularly, we study the influence of the interface energy on the transformation width and the effective compliance. In perspective, the obtained results might be helpful for the design of new SMAs for more sensitive smart structures and more efficient damping systems.Comment: 10 pages, 3 figures, 22 reference

Couplage de codes éléments finis et dynamique discrète de dislocations

National audienceLe calcul couplé entre la méthode des éléments finis et la dynamique discrète de dislocations est utilisé pour simuler le comportement cyclique d'un agrégat polycristallin. La convergence et la validation du couplage sont discutées

Stabilized MorteX method for mesh tying along embedded interfaces

We present a unified framework to tie overlapping meshes in solid mechanics applications. This framework is a combination of the X-FEM method and the mortar method, which uses Lagrange multipliers to fulfill the tying constraints. As known, mixed formulations are prone to mesh locking which manifests itself by the emergence of spurious oscillations in the vicinity of the tying interface. To overcome this inherent difficulty, we suggest a new coarse-grained interpolation of Lagrange multipliers. This technique consists in selective assignment of Lagrange multipliers on nodes of the mortar side and in non-local interpolation of the associated traction field. The optimal choice of the coarse-graining spacing is guided solely by the mesh-density contrast between the mesh of the mortar side and the number of blending elements of the host mesh. The method is tested on two patch tests (compression and bending) for different interpolations and element types as well as for different material and mesh contrasts. The optimal mesh convergence and removal of spurious oscillations is also demonstrated on the Eshelby inclusion problem for high contrasts of inclusion/matrix materials. Few additional examples confirm the performance of the elaborated framework

Enrichment of the contact geometry within the finite element method

Titre du résumé français joint : Traitement des problèmes de contact en calcul parallèleInternational audienceA new approach for sub-mesh enrichment of the contact geometry has been proposed in the framework of the Finite Element Method and the Node-to-Segment contact discretization. The method is very general and multipurpose : it allows, for example, to extend the limits of the contact modeling of thin-walled structures or to account for a change of the contact geometry due to loading, for example, to simulate a shallow wear

Traitement des problèmes de contact en calcul parallèle

National audienceL'implantation numérique efficace des méthodes de traitement du contact reste encore un sujet de recherche à part entière. On détaille ici la mise en oeuvre d'une méthode de type Lagrangien augmenté. Afin de gagner en performance, l'algorithme comporte une procédure particulière de reconnaissance (séquentiel et parallèle) de noeuds venant en contact sur la surface de contact, la reconstruction à bon escient de la matrice pour les éléments de contact et une formulation en calcul parallèle

The existence of a critical length scale in regularised friction

We study a regularisation of Coulomb's friction law on the propagation of local slip at an interface between a deformable and a rigid solid. This regularisation, which was proposed based on experimental observations, smooths the effect of a sudden jump in the contact pressure over a characteristic length scale. We apply it in numerical simulations in order to analyse its influence on the behaviour of local slip. We first show that mesh convergence in dynamic simulations is achieved without any numerical damping in the bulk and draw a convergence map with respect to the characteristic length of the friction regularisation. By varying this length scale on the example of a given slip event, we observe that there is a critical length below which the friction regularisation does not affect anymore the propagation of the interface rupture. A spectral analysis of the regularisation on a periodic variation of Coulomb's friction is conducted to confirm the existence of this critical length. The results indicate that if the characteristic length of the friction regularisation is smaller than the critical length, a slip event behaves as if it was governed by Coulomb's law. We therefore propose that there is a domain of influence of the friction regularisation depending on its characteristic length and on the frequency content of the local slip event. A byproduct of the analysis is related to the existence of a physical length scale characterising a given frictional interface. We establish that the experimental determination of this interface property may be achieved by experimentally monitoring slip pulses whose frequency content is rich enough.Comment: 21 pages, 7 figure