Keywords: contact mechanics, interfaces, multi bodies systems, coulomb law, multiscale problem, bi-potential theory.

The aim of this study is to identify laws of interfaces between two bodies when this interface is a microstructure composed by grains. These grains can be viewed as microscopic particles extracted from macroscopic bodies. The grains considered are rigid and interact together subject to the Coulomb law with dry friction [1]. This situation occurs for example in clutches, brakes, on rails or whenever an important friction appears. Today, this situation is very often modeled using only a Coulomb law with friction, but this interface law is not sufficient to handle all the complexity of this problem. In this paper, we propose a numerical analysis of the contact interface in order to compute the interaction of the two macroscopic bodies in this situation.

This problem has clearly two different scales that requires a specific numerical treatment. The bodies represent the macroscopic scale and the grains are the microscopic scale. In order to solve the numerical problem, the bodies are discretized with a standard finite elements method. The interface behavior is computed in two different ways.

First, we consider domain decomposition techniques, with overlapping domains [2]. The total energy of the system is the sum of the energy of each part (the interface and the continuous material), and a weighting function is considered to take into account the relative influence of each subdomain on the overlapping area. Moreover, the displacement has to be equal in the grains and in the continuous material in the overlapping area. This properties provides a constraint to be satisfied. Finally, the problems to be solved consist of minimizing the total energy under the constraint of continuity of the displacements.

The second method consist in really considering the two scales of the problems, following the ideas of Feyel [3]. Here, the interface is also discretized with finite elements, but the behavior law for each element is computed at the microscale, using a discrete element method. The forces on the boundary of these elements are coming from the computation on the macroscopic bodies. The discrete elements method permits the corresponding displacement to be obtained.

1

J. Fortin, O. Millet, G. de Saxcé, "Numerical simulation of granular materials by an improved discrete element method", Int. J. Numer. Meth. Engng, 62, 639-663, 2005. doi:10.1002/nme.1209

2

E. Frangin, "Adaptation de la méthode des éléments discrets à l'échelle de l'ouvrage en béton armé", Ph. D Thesis, Grenoble University, 2008.

3

F. Feyel, J.-L. Chaboche, "FE² multiscale approach for modelling the elastoviscoplastic behaviour of long fibre SiC/Ti composite materials", Comput. Methods Appl. Mech. Engrg., 183, 309-330, 2000. doi:10.1016/S0045-7825(99)00224-8

purchase the full-text of this paper (price £20)

go to the previous paper
go to the next paper
return to the table of contents
return to the book description
purchase this book (price £145 +P&P)