Axisymmetric flat punch

The case of an axisymmetric flat punch of radius a on an elastic half-space was solved by KendalK7) by evaluating the elastic energy = iPb and the potential energy Up = —from the elastic displacement under the load P ... 

Adherence of spheres and flat punches was studied by Johnson et al. (3), Kendall (5), and Maugis and Barquins (2,6). For an axisymmetric rigid punch contacting an elastic half-space, under a load P, over an area of radius a, it can be shown (7,4) that... 

The most basic configuration for an elastic contact is the indentation of an elastic halfspace by a rigid axisymmetric frictionless punch. Frictionless means that we assume that no shear stress can develop between the punch and the half-space. While historically the first solution of such a problem was given by Hertz for the case of a spherical indenter [846], we will start with a flat rigid cylindrical punch (Figure 8.3) that was first worked out by Boussinesq in 1885 [847] and solved in all details by Sneddon in 1946 [848]. 

Van Landigham et al. reviewed nanoindentation of polymers, [40, 41] including a summary of the most common analyses of load-indentation data. Chief among these methods is an analysis of indentation load-penetration curves according to the Oliver-Pharr method. [42] This method is based on relationships developed by Sneddon for the penetration of a flat elastic half space by different probes with particular axisymmetric shapes (e.g., aflat-ended cylindrical punch, a paraboloid of revolution, or a cone) [43], More recently, Withers and Aston discussed indentation in the context of plasticity and viscoelasticity [44]. 

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