Meeting the Contact-Mechanics Challenge

Abstract

This paper summarizes the submissions to a recently announced contact-mechanics modeling challenge. The task was to solve a typical, albeit mathematically fully defined problem on the adhesion between nominally flat surfaces. The surface topography of the rough, rigid substrate, the elastic properties of the indenter, as well as the short-range adhesion between indenter and substrate, were specified so that diverse quantities of interest, e.g., the distribution of interfacial stresses at a given load or the mean gap as a function of load, could be computed and compared to a reference solution. Many different solution strategies were pursued, ranging from traditional asperity-based models via Persson theory and brute-force computational approaches, to real-laboratory experiments and all-atom molecular dynamics simulations of a model, in which the original assignment was scaled down to the atomistic scale. While each submission contained satisfying answers for at least a subset of the posed questions, efficiency, versatility, and accuracy differed between methods, the more precise methods being, in general, computationally more complex. The aim of this paper is to provide both theorists and experimentalists with benchmarks to decide which method is the most appropriate for a particular application and to gauge the errors associated with each one

The role of adhesion in contact mechanics

“…Solutions are typically obtained over a rectangular grid with initial nodal heights chosen to approximate a surface with the PSD of equation (10). However, computational considerations place limits on the practical mesh refinement, so that even the most sophisticated codes such as those of Pastewka and Robbins [48] and that used in Müser's recent 'Contact Challenge' [51] can only describe surfaces with PSDs spanning about three decades -e.g. nanometer to micrometer scales.…”

Application of the finite element submodeling technique in a single point contact and wear problem

“…Laboratory tests can be useful to achieve information about the damaging process but rarely reproduce the effective working conditions. Numerical wear predictions are thus gaining increasing interest though, in most cases, they are also prohibitively time consuming . Such drawbacks are due to the iterative combination of two modeling issues: a nonlinear contact analysis, which usually requires extremely fine meshes, and an update of the geometry and mesh after material removal .…”

“…Numerical wear predictions are thus gaining increasing interest though, in most cases, they are also prohibitively time consuming. 19 Such drawbacks are due to the iterative combination of two modeling issues: a nonlinear contact analysis, which usually requires extremely fine meshes, and an update of the geometry and mesh after material removal. 20 This process becomes particularly heavy when wear is simulated over a long period of time and/or in case of complex three-dimensional (3D) geometries.…”

A Fourier-accelerated volume integral method for elastoplastic contact

“…Because of the previously mentioned property of displacements obtained by our volume integral approach, Γ can be readily approximated using the span space of the interpolation functions underlying the discrete Fourier transform. The minimization of the functional defined in problem (36) has been the subject of extensive literature, and the reader is referred to (Campañá and Müser, 2006;Müser et al, 2017;Polonsky and Keer, 1999a,b;Rey et al, 2017;Stanley and Kato, 1997) for various examples in the realm of normal friction-less contact. Note that although we consider neither adhesion nor friction in the elastic contact problem, they can without difficulty be included in the global formulation (see e.g.…”

“…We now showcase the applicability of the method to rough surface contact. Self-affine surfaces are commonly used in this context (Müser et al, 2017;Yastrebov et al, 2012) Figure 7: Relative computation times for VIM and FEM. We compare the application of the operator N to an elastostatic FEM solve step (Cholesky factorization).…”