Evaluation of the incremental compliances of non-elliptical contacts by treating them as external cracks

The incremental normal compliance of a contact of “irregular” (non-elliptical) shape between two elastic half spaces is considered. The contact is modeled as external crack. An approximate expression for the stress intensity factor (SIFs) around its boundary, in conjunction with Rice (1975) theorem that interrelates SIFs and crack compliances, are used to evaluate the crack compliance. The results cover a broad class of contact shapes, including – but not limited to - all convex ones. Bounds, similar to Hill's comparison theorem in micromechanics, are formulated for the compliances of contacts. The cross-property elasticity-conductivity relation yields similar results for contact conductance. The methodology is illustrated on several examples. •A methodology for evaluation of contact compliances by treating contacts as external cracks is suggested.•Compliances of contacts of irregular shapes are evaluated.•Rigorous bounds for contact compliances are derived.