FFT-BASED IMPLEMENTATION OF THE MDR TRANSFORMATIONS FOR HOMOGENEOUS AND POWER-LAW GRADED MATERIALS

Abstract

It is shown how the Abel transform solution to the general axisymmetric normal contact problem for homogeneous and power-law graded elastic materials, which is paramount for the solution of different classes of tribological problems with the help of the method of dimensionality reduction (MDR), can be written in terms of explicit convolutions. These can be very efficiently evaluated with the 1D Fast Fourier Transform (FFT), which reduces the numerical complexity of the transformations from the order of N2 for the standard matrix-vector-multiplication (MVM) algorithm to the order of N. Convergence and performance of the proposed method are studied in detail. As an illustrative example a fretting wear simulation based on the new implementation is shown, the results of which are compared to the standard MVM implementation.