Axisymmetric rigid punch

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... 

If b is the wetted radius of an axisymmetric rigid punch with a shape y(r), and z is the separation, the G can be computed from the potential energy = - Pz ... 

Theret et al. [1988] analyzed the micropipette experiment with endothelial cell. The cell was interpreted as a linear elastic isotropic half-space, and the pipette was considered as an axisymmetric rigid punch. This approach was later extended to a viscoelastic material of the cell and to the model of the cell as a deformable layer. The solutions were obtained both analytically by using the Laplace transform and numerically by using the finite element method. Spector et al. [1998] analyzed the application of the micropipette to a cylindrical cochlear outer hair cell. The cell composite membrane (wall) was treated as an orthotropic elastic shell, and the corresponding problem was solved in terms of Fourier series. Recently, Hochmuth [2000] reviewed the micropipette technique appHed to the analysis of the cellular properties. 

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]. 

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