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