Numerical Simulation of Tri-Layered Materials Under Contact Load

Abstract

Various biomedical components, such as dental crowns and hip prostheses, data processing devices, and other numerous mechanical components that transmit load through a mechanical contact, may benefit from a tri-layer design. The coating may be optimized for wear protection and corrosion prevention, whereas the intermediate layer provides increased adhesion between the outer layer and the substrate, and confines the crack propagation. The solution to the contact problem involving tri-layered materials can be pursued numerically with the finite element or the boundary element methods, but semi-analytical techniques benefitting from the efficiency of the fast Fourier transform (FFT) technique have also been successfully applied. At the heart of the FFT-assisted approach lie the frequency response functions (FRFs), which are analytical solutions for fundamental problems of elasticity such as the Boussinesq and Cerruti problems, but expressed in the frequency domain. Considering recent efforts and results in application of FFT to convolution calculations in contact problems, the displacement arising in a tri-layer configuration is computed in the frequency domain, and the contact problem is subsequently solved in the space domain using a state-of-the-art algorithm based on the conjugate gradient method. The method relies on the FRFs derived in the literature for tri-layered materials, and the efficiency and accuracy of computations in the frequency domain is assured by using the Discrete Convolution Fast Fourier Technique (DCFFT) with influence coefficients derived from the FRFs. The computer program reproduces well-known results for bi-layered materials. Numerical simulations are performed for various configurations in which the elastic properties of the layers, as well as the frictional coefficient, are varied. By using the newly advanced simulation technique, design recommendations may be advanced for the optimal configuration of tri-layered materials under contact load.

"Thermoelastic Displacement and Temperature Rise in a Half-Space Due to a Steady-State Heat Flux "

“…Various paths and methods for the application of spectral methods to convolution calculations were explored and compared in [15]. It is noteworthy that the DCFFT extends the types of problems that can be solved to problems with Green's functions derived in closed-form in the frequency domain only, such as the case of multi-layered materials [16], or to contact scenarios involving linear viscoelastic materials [17]. The DCFFT was successfully applied [18] in the study of transient thermoelastic displacement, providing a convenient substitute to time/space domain solutions whose treatment is affected by singularities.…”