The finite compression of elastic solid cylinders in the presence of gravity

Abstract

The deformation induced by gravity in a solid cylinder is considered. The cylinder is placed on a horizontal frictionless surface with the axis vertical and is treated as an isotropic incompressible elastic material. Further distortion is produced by finite axial compression. Thus the overall deformation is predominantly uniform with a small perturbation superimposed to account for the gravity effects. A particular case is when there is no finite axial compression. The solution then describes the shortening and general infinitesimal deformation associated with the gravitational body force. The results may be used for determining the material constants of soft elastic materials. In particular, the equivalent of Young’s modulus for gelatin has been found by measuring the changes in height of cylindrical specimens when removed from rigid containers and using the appropriate formula derived in the analysis. The results obtained were extremely consistent. In addition, the behaviour of gelatin under finite compression has been examined. By comparing the theoretical predictions with the experimental measurements it is shown that gelatin behaves more as a Mooney material than as a material which has a quadratic form for the associated strain energy function. Values of the two material constants occurring in the Mooney form of the strain energy function are obtained.