Compression of an elastic film sandwiched between two rigid parallel plates:

The stress equilibrium relations for a compressible elastic film of thickness and width sandwiched between two rigid substrates is given in plane strain approximation by,

(11.1)

Where is the Poisson ratio and and are the displacements in the film along the and directions respectively. We can write equations 11.1 in terms of the following dimensionless quantities:

Here is the film thickness and is a characteristic spatial length scale, such that . Equation 11.1 then transforms into

	(11.2a)
	(11.2b)

Notice that the first term in the right hand side of equation 11.2b is smaller than the rest of the terms, so that we can neglect it, yielding,

(11.3)