A multi-scale FEM-BEM formulation for contact mechanics between rough surfaces

Abstract

A novel multi-scale finite element formulation for contact mechanics between nominally smooth but microscopically rough surfaces is herein proposed. The approach integrates the interface finite element method (FEM) for modelling interface interactions at the macro-scale with a boundary element method (BEM) for the solution of the contact problem at the micro-scale. The BEM is used at each integration point to determine the normal contact traction and the normal contact stiffness, allowing to take into account any desirable kind of rough topology, either real, e.g. obtained from profilometric data, or artificial, evaluated with the most suitable numerical or analytical approach. Different numerical strategies to accelerate coupling between FEM and BEM are discussed in relation to a selected benchmark test.

Algebraic multigrid methods for saddle point systems arising from mortar contact formulations

“…That is, since the second block row in the error matrices (10) or (11) does not vanish, the Uzawa smoother by definition cannot exactly fulfill the contact constraints, but adds a systematic error for the contact constraints. This might have a negative impact on the overall performance of the iterative linear solver.…”

“…Therefore, it is not surprising that recent years have seen significant progress in modeling and simulation of contact interaction and its associated phenomena, such as friction, [1][2][3] wear, [4][5][6][7] adhesion, 8,9 or multiscale contact phenomena. 10,11 This is particularly true with regard to robust finite element based discretization techniques for finite deformations and efficient nonlinear solution algorithms. Above all, mortar finite element methods-originally introduced in the context of domain decomposition 12,13 -are meanwhile well established as a basis for state-of-the-art contact formulations and widely accepted among researchers as being superior to more classical discretization techniques, such as the node-to-segment (NTS) method, the Gauss-point-to-segment (GPTS) method, and other collocation based approaches.…”

“…Many engineering applications require the simulation of large‐scale contact problems. Therefore, it is not surprising that recent years have seen significant progress in modeling and simulation of contact interaction and its associated phenomena, such as friction, 1‐3 wear, 4‐7 adhesion, 8,9 or multiscale contact phenomena 10,11 . This is particularly true with regard to robust finite element based discretization techniques for finite deformations and efficient nonlinear solution algorithms.…”

Generating fractal rough surfaces with the spectral representation method

“…Müser et al, 9 Borri and Paggi, 30 and Zhang et al 15 used the FFT filtering method as well. Besides the FFT filtering method and the W-M function, the RMD is another common choice in studies, for example, Pei et al, 31 Bonari et al, 32 and Vakis et al 33 simulated fractal surfaces by the RMD for contact analysis. In addition to the methods above, Papangelo et al 13 and Putignano et al 34 developed a spectral method, which is similar to the FFT filtering method, for simulating fractal surfaces.…”

Algebraic multigrid methods for saddle point systems arising from mortar contact formulations

“…Many engineering applications require the simulation of large-scale contact problems. Therefore, it is not surprising that recent years have seen significant progress in modelling and simulation of contact interaction and its associated phenomena, such as friction [24,46,59], wear [12,20,39,42], adhesion [40,58], or multi-scale contact phenomena [6,66]. This is particularly true with regard to robust finite element based discretization techniques for finite deformations and efficient nonlinear solution algorithms.…”