An FFT-Based Method for Rough Surface Contact

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Abstract
Elastic contact between a rigid plane and a halfspace whose surface height is described by a bandwidth-limited Fourier series is considered. The surface normal displacements and contact pressures are found by a numerical technique that exploits the structure of the Fast Fourier Transform (FFT) and an exact result in linear elasticity. The multiscale nature of rough surface contact is implicit to the method, and features such as contact agglomeration and asperity interaction—a source of difficulty for asperity-based models—evolve naturally. Both two-dimensional (2-D) and three-dimensional (3-D) contact are handled with equal ease. Finally, the implementation is simple, compact, and fast.