Effect of Poisson's ratio on bonded rubber blocks

Abstract

A theoretical analysis of bonded rubber blocks with circular cross-section under axial compression is obtained by the use of dynamic-relaxation solutions of classical elastic stress-strain equations. The Poisson's ratio ν for rubber is close to 0.5 which causes difficulties in the analysis because the general stress-strain equations of elasticity contain terms such as ν E/(1 + ν)(1 − 2ν) which approaches infinity when ν approaches a value of 0.5. The range of ν considered varies between 0.45000 and 0.49990 which covers all the natural-rubber compounds used, including pure natural gum which has a ν value of 0.49989 (1)∗. It is shown that the stress distribution within the block is significantly affected by the value of ν and the shape of the block. When a block of material with ν ∼ 0.5, bonded to its end plates, is thin, the stress developed within the block is high and nearly equal in all three directions, which suggests a hydrostatic type of pressure. Such a pressure would confirm the finding in (2) and (3) based on a semi-empirical analysis. When the block is thick this effect is absent. The present paper confirms that these effects follow from the fundamental assumptions of classical elasticity. The investigation also confirms that the dynamic-relaxation method converges satisfactorily even when the Poisson's ratio is very close to the value of 0.5000.