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=12 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, “
Axial Loading of Bonded Rubber Blocks
,”
ASME J. Appl. Mech.
0021-8936,
69
, pp.
836
843
.
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