A Fourier-accelerated volume integral method for elastoplastic contact

Abstract

The contact of solids with rough surfaces plays a fundamental role in physical phenomena such as friction, wear, sealing, and thermal transfer. However, its simulation is a challenging problem due to surface asperities covering a wide range of length-scales. In addition, non-linear local processes, such as plasticity, are expected to occur even at the lightest loads. In this context, robust and efficient computational approaches are required. We therefore present a novel numerical method, based on integral equations, capable of handling the large discretization requirements of real rough surfaces as well as the non-linear plastic flow occurring below and at the contacting asperities. This method is based on a new derivation of the Mindlin fundamental solution in Fourier space, which leverages the computational efficiency of the fast Fourier transform. The use of this Mindlin solution allows a dramatic reduction of the memory imprint (as the Fourier coefficients are computed on-the-fly), a reduction of the discretization error, and the exploitation of the structure of the functions to speed up computation of the integral operators. We validate our method against an elasticplastic FEM Hertz normal contact simulation and showcase its ability to simulate contact of rough surfaces with plastic flow.

Adhesive wear mechanisms in the presence of weak interfaces: Insights from an amorphous model system

“…Second, in a previous study [9], it was found that the wear coefficient cannot simply be derived only from the assumption that contact spots larger than a critical value form wear particles, while smaller ones deform plastically [16]. Indeed, this view misses important complexities, such as interactions between contact spots [68], plastic deformations due to the normal load [25,[69][70][71][72], and, as the present paper indicates, slip. This slip depends on the strength of the adhesive bond and the sharpness of the interface, and as such is subject to time-dependent phenomena such as aging [73][74][75] and interface creep [76][77][78][79].…”

A review of recent advances in tribology

“…The conjugate gradient method (CGM) has been widely accepted for the minimization, providing that the influence coefficient (IC) or the Green's function, defined as the response of displacement to a point load, has been obtained in advance. To accelerate the calculation of deformation, fast Fourier transform (FFT) technique has been employed and efforts have been made to further improve its computational efficiency [629]. A numerical scheme known as the Sami-analytical method (SAM) has been developed in last decades, in which the ICs are derived analytically in frequency space and deformations are calculated by the FFT technique.…”

Tamaas: a library for elastic-plastic contact of periodic rough surfaces

“…In this case, volume integral methods can be employed to account for plastic deformation (Telles & Brebbia, 1979). These enjoy properties analogous to boundary integral methods and can also be accelerated with a Fourier approach (Frérot et al, 2019b).…”

“…Tamaas is a C++ library with a Python interface (Jakob, Rhinelander, & Moldovan, 2017), developed in the Computational Solid Mechanics Laboratory at EPFL, that implements a unique Fourier-accelerated volume integral formulation of equilibrium (Frérot et al, 2019b) for the solution of elastic-plastic rough contact problems. The use of C++ allows for a particular focus on performance: most loops are parallelized using Thrust/OpenMP and the fast-Fourier transforms are computed with FFTW3/OpenMP.…”

“…The use of C++ allows for a particular focus on performance: most loops are parallelized using Thrust/OpenMP and the fast-Fourier transforms are computed with FFTW3/OpenMP. Thanks to this, it can handle simulations with upwards of 100 million degrees of freedom on a single compute node (Frérot et al, 2019b). Tamaas is aimed at researchers and practitioners wishing to compute realistic contact solutions for the study of interface phenomena.…”