Numerical Analysis of Elastic Contact between Coated Bodies

Substrate protection by means of a hard coating is an efficient way of extending the service life of various mechanical, electrical, or biomedical elements. The assessment of stresses induced in a layered body under contact load may advance the understanding of the mechanisms underlying coating performance and improve the design of coated systems. The iterative derivation of contact area and contact tractions requires repeated displacement evaluation; therefore the robustness of a contact solver relies on the efficiency of the algorithm for displacement calculation. The fast Fourier transform coupled with the discrete convolution theorem has been widely used in the contact modelling of homogenous bodies, as an efficient computational tool for the rapid evaluation of convolution products that appear in displacements and stresses calculation. The extension of this technique to layered solids is tantalizing given that the closed-form analytical functions describing the response of layered solids to load are only available in the frequency domain. Whereas the false problem periodization can be treated as in the case of homogenous solids, the aliasing phenomenon and the handling of the frequency response function in origin require adapted techniques. The proposed algorithm for displacement calculation is coupled with a state-of-the-art contact solver based on the conjugate gradient method. The predictions of the newly advanced computer program are validated against existing results derived by a different method. Multiple contact cases are simulated aiming to assess the influence of coating thickness and of its elastic properties on the contact parameters and the strass state. The performed simulations prove that the advanced algorithm is an efficient tool for the contact analysis of coated bodies, which can be used to further understand the mechanical behavior of the coated system and to optimize its design.