Discrete convolution and FFT method with summation of influence coefficients (DCS–FFT) for three-dimensional contact of inhomogeneous materials

Sun, Linlin; Wang, Q. Jane; Zhang, Mengqi; Zhao, Ning; Keer, Leon M.; Liu, Shuangbiao; Chen, W. Wayne

doi:10.1007/s00466-020-01832-2

Cited by 13 publications

(11 citation statements)

References 39 publications

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“…Algorithm and method Problem to solve DC-FFT (Liu et al, 2000;Liu, 2001) (Liu and Chen, 2012;Liu, 2013) Discrete-convolution and FFT Point-contact problems Cylindrical contact problems, counterformal and conformal CC-FT (Ju and Farris, 1996;Liu, 2001; DCSS-FFT (Sun, 2020) Continuous-convolution and FFT Nominally flat-flat contact problems DCD-FFT (Chen et al, 2008) DC-CC-FFT (Liu et al, 2006) DCS-FFT (Liu and Hua, 2009;Sun et al, 2020) Discrete convolution with duplicated padding and FFT Discrete-convolution, continuous-convolution and FFT Discrete convolution with IC summation and FFT 3D line-contact problems DCR-FFT (Liu and Wang, 2005) Discrete-convolution-correlation and fast-Fourier-transform Materials with residual strains, inclusions and/or inhomogeneities, contact plasticity problems IC conversion (Liu et al, 2000;Liu, 2001; FRFs known, which can be transformed to ICs, followed by the DC-FFT algorithm or other proper ones Layered, viscoelastic, transversely isotropic materials, coupled-stress problems, multifield contact problems…”

Section: Name and Referencesmentioning

confidence: 99%

“…Non-uniform DCS-FFT (Sun et al, 2020) Implementation of DCS-FFT, or others, to segments of different mesh densities Large-scale problems, 3D line-contact problem considering defect, crown, and edge effects SFFT (Wang and Jin, 2004) Discrete-convolution and FFT Sphere-cup contact problems…”

Section: Name and Referencesmentioning

confidence: 99%

“…To explore more detail, we are facing 3D problem with mixed issues. Three FFT-based approaches have been developed, to be discussed below, which are the algorithms of mixed discrete-continuous convolution with duplicated padding and FFT (DCD-FFT) (Chen et al, 2008), the hybrid discrete convolution, continuous convolution and FFT (DC-CC-FFT) (Liu and Hua, 2009), and the discrete-periodic convolution with IC summation and FFT (DCS-FFT) (Liu and Hua, 2009;Sun et al, 2020) to consider the effect of roughness and material inhomogeneity. They are mathematically and numerically the same in the finite direction (x), but different in the other dimension (y).…”

Section: Fft Algorithms For 3d Line-contact Problemsmentioning

confidence: 99%

“…A simple way, with known ICs, described by Sun et al (2020), to build the DC-CC-FFT algorithm is to process the 2D Fourier transform of the ICs sequentially in the y and the x directions to obtain ICs-FRF, where the FRF is from the IC conversion. After the y-direction FFT, the FRFs are calculated from Equations ( 14) and ( 17).…”

Section: Dc-cc-fft With Ic-conversionmentioning

confidence: 99%

“…In this paper, we will discuss the basic issues of the FFT methods for contact analyses from the convolution theorems and the tree of the Fourier-transform algorithms for solving different contact problems, such as (1) the algorithm of discrete-convolution and fast-Fourier-transform (DC-FFT), with double domain extension in each dimension, for non-periodic problems, and the discrete-convolution and fast-Fourier-transform algorithm (DC-FFT) without domain extension for journal bearing problems, (2) the algorithm of continuous-convolution and Fourier-transform (CC-FT) for periodic (or infinite) contact problems, (3) the algorithm of discrete convolution with duplicated padding and FFT (DCD-FFT), that of discrete-continuous convolutions and FFT (DC-CC-FFT), and that of the discrete convolution with IC summation and FFT (DCS-FFT) for 3D line-contact problems that are periodic (or infinite) in one direction but non-periodic in the other direction, (4) the algorithm of discrete-correlation and FFT (DCR-FFT) for inclusion problems, (5) the FRF-IC conversion method, as well as the applications of them to solve the contact problems involving layered materials, anisotropic elastic materials, and viscoelastic polymers, or those subjected to multifields, and (6) a non-uniform DCS-FFT method, recently developed by Sun et al (2020), for solve large-scale contact problems. Most of the contents in this paper are based on the works by Liu et al (2000, , Boucly et al (2005), Chen et al (2008), Liu and Hua (2009), Yu et al (2014Yu et al ( , 2016, Zhang X. et al (2017Zhang X. et al ( , 2018, , Sun (2020), Sun et al (2020), Zhang et al (2020a,b), and Chapter 4 in the book by Wang and Zhu (2019). Table 1 summarizes the FFF-based approaches and their applications.…”

Section: Introductionmentioning

confidence: 99%

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FFT-Based Methods for Computational Contact Mechanics

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Computational contact mechanics seeks for numerical solutions to contact area, pressure, deformation, and stresses, as well as flash temperature, in response to the interaction of two bodies. The materials of the bodies may be homogeneous or inhomogeneous, isotropic or anisotropic, layered or functionally graded, elastic, elastoplastic, or viscoelastic, and the physical interactions may be subjected to a single field or multiple fields. The contact geometry can be cylindrical, point (circular or elliptical), or nominally flat-to-flat. With reasonable simplifications, the mathematical nature of the relationship between a surface excitation and a body response for an elastic contact problem is either in the form of a convolution or correlation, making it possible to formulate and solve the contact problem by means of an efficient Fourier-transform algorithm. Green's function inside such a convolution or correlation form is the fundamental solution to an elementary problem, and if explicitly available, it can be integrated over a region, or an element, to obtain influence coefficients (ICs). Either the problem itself or Green's functions/ICs can be transformed into a space-related frequency domain, via a Fourier transform algorithm, to formulate a frequency-domain solution for contact problems. This approach converts the original tedious integration operation into multiplication accompanied by Fourier and inverse Fourier transforms, and thus a great computational efficiency is achieved. The conversion between ICs and frequency-response functions facilitate the solutions to problems with no explicit space-domain Green's function. This paper summarizes different algorithms involving the fast Fourier transform (FFT), developed for different contact problems, error control, as well as solutions to the problems involving different contact geometries, different types of materials, and different physical issues. The related works suggest that (i) a proper FFT algorithm should be used for each of the cylindrical, point, and nominally flat-flat contact problems, and then (ii) the FFT-based algorithms are accurate and efficient. In most cases, the ICs from the 0order shape function can be applied to achieve satisfactory accuracy and efficiency if (i) is guaranteed.

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