Abstract
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 0-order shape function can be applied to achieve satisfactory accuracy and efficiency if (i) is guaranteed.
| Original language | English (US) |
|---|---|
| Article number | 61 |
| Journal | Frontiers in Mechanical Engineering |
| Volume | 6 |
| DOIs | |
| State | Published - Aug 28 2020 |
Funding
The authors would like to express sincere gratitude to co-workers at the Center for Surface Engineering and Tribology, Northwestern University, Evanston, IL, USA, for years of research on theoretical derivations of fundamental solutions, ICs, and FRFs, and developments and implementations of the FFT-based methods, especially to Drs. W. W. Chen, X. Q. Jin, W.-S. Kim, D. L. Li, Y. C. Liu, Z. Liu, A. Martini, N. Ren, M. J. Rodgers, X. J. Shi, Z. J. Wang, C. J. Yu, M. Q. Zhang, K. Zhou, and Q. H. Zhou, as well as Mr. H. Yu, Chongqing University, China, for their valuable contributions. The authors would also like to thank Professor L. M. Keer, Northwestern University, for long-term collaboration and research discussion, and the journal editor and reviewers for their valuable suggestions on manuscript revision.
Keywords
- FFT algorithms
- contact of materials
- contact pressure
- contact stress
- fast fourier transform
- tribology
ASJC Scopus subject areas
- General Materials Science
- Mechanical Engineering
- Computer Science Applications
- Industrial and Manufacturing Engineering