Discussion: “Axial Loading of Bonded Rubber Blocks” (Horton, J. M., Tupholme, G. E., and Gover, M. J. C., 2002, ASME J. Appl. Mech., 69, pp. 836–843)

The paper by Horton, Tupholme, and Gover (1) analyzes the deformation behavior of rubber using the isotropic, infinitesimal strain theory of elasticty for an incompressible material. Accordingly, the Poisson’s ratio $ν=1∕2$ and Young’s modulus is three times the shear modulus $(E=3μ)$⁠. In this setting, the stresses $σij$ determine the (infinitesimal) strains $ϵij$⁠, but the strains only determine the stresses up to a hydrostatic pressure. Hence, the strains determine the shear stresses and also determine the normal stress differences. The strains follow from the displacements $ui$ in the usual fashion $ϵij=(ui,j+uj,i)∕2$⁠. In their analysis of a rectangular block with Cartesian coordinates $(x,y,z)$ and associated displacement components $(...$