Green’s Functions in Contact Mechanics

Definitions

Hills and colleagues (1996) define a Green’s function as “the response of a system to a standard input or, in elasticity theory, the stress/strains induced in a body in response to, for example, a point force.” Results derived from Fourier transforms are also presented in Mura (1993).

Scientific Fundamentals

History

Problems in elasticity theory can be solved using potentials. In particular, the definition of a Green’s function given above can be used mathematically to derive solutions to point load problems, either within the elastic body or on its surface. Such problems were treated by Boussinesq (1885) and later reproduced by Green and Zerna (1968). This history and excellent examples are given by Barber (2010). Using the potentials, Green’s functions for some common concentrated loadings can be derived. Since the objective of this section is not to derive the Green’s functions, some of them will be written out in full.

Formulae for Common Examples

The examples used here...