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Buckling of a thick slab
Figure 30.1
An incompressible, elastic slab of length  , thickness  and of infinite width is placed between two rigid blocks on which the slab remains strongly bonded. The slab is compressed axially by applying stress  at its end, because of which, the length of the slab decreases to  and its thickness increases to  . The elastic slab behaves like a rubber like material and follows the stress-strain relations as in equation 13.55. Depending on the geometry we can consider two different situations. For example, we can consider that the slab is restrained from deforming along the direction perpendicular to the plane of the paper, so that,  and due to incompressibility,  . The compressive stress can then be related as,
And the incremental modulus is
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