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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. [ABSTRACT FROM AUTHOR]

• Cracks of "zig-zag" shapes consisting of two rectilinear links are considered. • Their compliances and stress intensity factors and far field asymptotics are examined. • A simple and reasonably accurate computational procedure is developed. Cracks of kinked, or "zig-zag" shapes (that are common in brittle materials, particularly in polycrystalline ones) consisting of two rectilinear links are considered. Their compliances, as well as stress intensity factors, are examined using a simple and reasonably accurate procedure that is based on approximating the original configuration by rectilinear cracks separated by a very small ligament. Full stress fields and their far-field asymptotics are also examined. [ABSTRACT FROM AUTHOR]

Abstract The compliance contribution of a penny-shaped crack having multiple contacts between crack faces is analyzed. In order to reduce the number of parameters involved, regular lattices of circular contacts are considered. It is found, in particular, that, at the same total area of contacts, a large number of small contacts produces stronger stiffening effect than a small number of large contacts; hence the total contact area is not the parameter controlling the crack compliance contribution. The effects of contacts on both the normal and the shear crack compliances are found to be very close. In the case of moderately non-regular contact lattices, the results were found to be only marginally different from the results for regular ones. Results are conveniently expressed in terms of "Holm's radius"—the radius of a single contact that would have produced the same effect. Being applied to multiple cracks with contacts, our results yield the "adjusted", for the presence of contacts, value of crack density. [ABSTRACT FROM AUTHOR]