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Application of the Wiener–Hopf technique in contact problems

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Problems involving the contact interaction between two elastic bodies, or between an elastic body (called substrate) and a rigid body (called indenter), have occupied the attention of engineering researchers for well over a century. In recent years much attention has been paid to mechanical aspects of contact and adhesion in biological systems, which has resulted in formulating new contact problems, in particular, for a thin elastic layer on a substrate being indented by an indenter of non-canonical shape. Since problems in contact mechanics belong to the class of mixed boundary value problems and can be usually reduced to solving integral equations, it is natural to expect that the Wiener–Hopf method will one of the powerful analytical tools for their investigation. The Wiener–Hopf technique in combination with asymptotic methods has the advantage of universality in obtaining solutions in the analytical form as well as of simplicity for further qualitative analysis. In the present talk we briefly overview the application of the Wiener–Hopf technique to a representative range of contact problems, emphasizing the need of using complementarity asymptotic techniques to cover a larger space of the problem parameters.

This talk is part of the Isaac Newton Institute Seminar Series series.

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