Collected Works of H. S. Tsien (1938-1956)

A Generalization of Alfrey’s Theorem for Visco-elastic Media

H.S. Tsien

(California Institute of Technology)

1. Introduction

For the non-homogeneous stresses in isotropic incompressible viscoelastic media characterized by linear relations between the components of stress, strain and their derivatives with respect to time, T. Alfrey has shown^[1] that in the case of the first boundary value problem, the stress distribution is identical with that in an incompressible elastic material under the same instantaneous surface forces. A similar result was obtained for the second boundary value problem where the displacements at the boundary are specified. It is the purpose of the present note to generalize this theorem to isotropic compressible media ...