Axial Loading of Bonded Rubber Blocks

Axially loaded rubber blocks of long, thin rectangular and circular cross section whose ends are bonded to rigid plates are studied. Closed-form expressions, which satisfy exactly the governing equations and conditions based upon the classical theory of elasticity, are derived for the total axial deflection and stress distribution using a superposition approach. The corresponding relations are presented for readily calculating the apparent Young’s modulus, $Ea,$ the modified modulus, $Ea′,$ and the deformed lateral profiles of the blocks. From these, improved approximate elementary expressions for evaluating $Ea$ and $Ea′$ are deduced. These estimates, and the precisely found values, agree for large values of the shape factor, S, with those previously suggested, but also fit the experimental data more closely for small values of S. Confirmation is provided that the assumption of a parabolic lateral profile is invalid for small values of S.