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Non-axisymmetric frictionless JKR-type adhesive contact between a rigid body and a thin incompressible elastic layer bonded to a rigid base is considered in the framework of the leading-order asymptotic model, which has the form of an overdetermined boundary value problem. Based on the first-order perturbation of the Neumann operator in the Dirichlet problem for Poisson's equation, the decohesion initiation problem is formulated in the form of a variational inequality. The asymptotic model assumes that the contact zone and its boundary contour during the detachment process are unknown. The absence of the solvability theorem is illustrated by an example of the instability of an axisymmetric flat circular contact. [ABSTRACT FROM AUTHOR]

Unilateral adhesive contact between a rigid indenter and a uniformly stretched membrane of arbitrary shape is considered. The generalized Johnson– Kendall–Roberts (JKR)-type and Derjaguin– Muller–Toporov (DMT)-type models of nonaxisymmetric adhesive contact are presented for short- and long-range adhesion, respectively, and the JKR–DMT transition is established in the framework of the generalized Maugis–Dugdale model. A refined method of matched asymptotic expansions is applied to construct the leading-order asymptotic model for indentation mapping of freestanding twodimensional materials with an axisymmetric probe, using the approximate analytical solution obtained in explicit form for an infinite membrane in the limit of short-range adhesive contact with an indenter in the form of an elliptic paraboloid. The cases of a spherical indenter and a rectangular membrane are studied in detail. [ABSTRACT FROM AUTHOR]

To describe properly interactions between contacting solids at micro/nanometre scales, one needs to know both adhesive and mechanical properties of the solids. Borodich and Galanov have introduced an effective method (the BG method) for identifying both characteristics from a single experiment on depth-sensing indentation by a spherical indenter using optimal fitting of the experimental data. Unlike traditional indentation techniques involving sharp indenters, the Borodich-Galanov methodology intrinsically takes adhesion into account. It is essentially a non-destructive approach. These features extend the scope of the method to important applications beyond the capabilities of conventional indentation. The scope of the original BG method was limited to the classic JKR and DMT theories. Recently, this restriction has been overcome by introducing the extended BG (eBG) method, where a new objective functional based on the concept of orthogonal distance curve fitting has been introduced. In the present work, questions related to theoretical development of the eBG method are discussed. Using the data for elastic bulk samples, it is shown that the eBG method is at least as good as the original BG method. It is shown that the eBG can be applied to adhesive indentation of coated, multilayered, functionally graded media. [ABSTRACT FROM AUTHOR]