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 $(x,...$
1.
Horton
,
J. M.
,
Tupholme
,
G. E.
, and
Gover
,
M. J. C.
, 2002, “