General theory of deformation of viscoelastic substances

The general theory of the deformation of viscoelastic substances developed in two previous papers for the one-dimensional case is now extended to three dimensions. The integro-differential equations obtained are generalizations of the well-known Navier-Cauchy equations and, like these, only apply to small deformations. Some special cases are considered in detail and lead to interesting conclusions. In particular, the theory predicts that for incompressible high polymers, one should obtain the same creep and relaxation functions when the material is subjected to extension, torsion, or bending.