Stress drop and contact stiffness measured from stick-slip experiments on PMMA-PMMA friction

We present results from an extensive stick-slip study on PMMA-PMMA dry friction, where we studied the influence of a wide range of normal stresses, loading velocities and roughnesses of the sliding surfaces. In this paper we focus (a) on the analysis of a residual coefficient of friction, i.e., shear stress measured at the end of the slip phase divided by the corresponding normal stress, and (b) on the contact stiffness measured by plotting the relative displacement between sample against the shear stress during the stick phase. It is shown that the residual coefficient of friction (i) decreases as normal stress increases, (ii) shows a slight increase when the roughness of the sliding surfaces increases and (iii) does not vary according to the loading velocity. The contact stiffness proved independent of loading conditions and of the roughness of the sliding surfaces. These results are interpreted in terms of asperity interlocking. This revised version was published online in July 2006 with corrections to the Cover Date.     

Acceleration of the abstract fixpoint computation in numerical program analysis

Static analysis by abstract interpretation aims at automatically proving properties of computer programs, by computing invariants that over-approximate the program behaviors. These invariants are defined as the least fixpoint of a system of semantic equations and are most often computed using the Kleene iteration. This computation may not terminate so specific solutions were proposed to deal with this issue. Most of the proposed methods sacrifice the precision of the solution to guarantee the termination of the computation in a finite number of iterations. In this article, we define a new method which allows to obtain a precise fixpoint in a short time. The main idea is to use numerical methods designed for accelerating the convergence of numerical sequences. These methods were primarily designed to transform a convergent, real valued sequence into another sequence that converges faster to the same limit. In this article, we show how they can be integrated into the Kleene iteration in order to improve the fixpoint computation in the abstract interpretation framework. An interesting feature of our method is that it remains very close to the Kleene iteration and thus can be easily implemented in existing static analyzers. We describe a general framework and its application to two numerical abstract domains: the interval domain and the octagon domain. Experimental results show that the number of iterations and the time needed to compute the fixpoint undergo a significant reduction compared to the Kleene iteration, while its precision is preserved.