Indentor ellipsoidal

It is to be expected that three-dimensional boundary value problems will present greater difficulties than plane problems. In particular, with the far wider choice of boundary regions on which to specify displacement and stress, one rapidly meets problems that are unsolvable - at least analytically. This is true even for elastic materials. In fact, the contact problem with an elliptical contact area is the most general problem that allows an explicit analytic solution - for elastic materials [Galin (1961), Lur e (1964)], in the case of half-space problems. This corresponds to an ellipsoidal indentor, according to classical Hertz theory. The theory can be extended to cover contact between two gently curved bodies. The solution is valid only for quasi-static conditions. 

The problem of a moving indentor has been considered by Golden (1982) in an approximate manner, by simply assuming that the contact region is elliptical for an ellipsoidal or spherical punch. The difficulty is that the physical significance of this assumption is not totally apparent. It is valid at both low and high veloci-... 

We will confine ourselves to axisymmetric indentors, noting of course that fairly explicit results can also be given for an ellipsoidal indentor, by virtue of the classical Hertz solution. For a spherical indentor we may approximately take... 

For low velocities, an expression for /h linear in V can be given, without restriction on the size or nature of viscoelastic effects [Golden (1978)]. Indeed, a complete solution of the problem is possible. We will discuss here the special case of a spherical indentor, though the results may be generalized without difficulty to an ellipsoidal indentor. For steady-state motion in the negative x direction, (5.1.2) may be written in the form... 

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See also in sourсe #XX -- [ , , ]

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