The generalized partial correspondence principle in linear viscoelasticity

A result, referred to as the generalized partial correspondence principle, is proved for noninertial viscoelastic boundary value problems. This states that if $B_u^{\left ( i \right )}\left ( t \right )$, $B_\sigma ^{\left ( i \right )}\left ( t \right )$ are the complementary regions of the boundary of a viscoelastic medium with a unique Poisson’s ratio, on which displacements ${u_i}\left ( {r, t} \right )$ and stresses ${\sigma _{ij}}\left ( {r, t} \right ){n_j}$ are specified, respectively, then if $B_\sigma ^{\left ( i \right )}\left ( {t’} \right ) \subseteq B_\sigma ^{\left ( i \right )}\left ( t \right )$ for all $t’ \le t$, the stresses satisfying this mixed boundary value problem at time $t$ are the stresses for the elastic problem with the same boundary regions and the same specified stresses while known functions take the place of the specified displacements. It is noteworthy that $B_\sigma ^{\left ( i \right )}\left ( {t’} \right )$, $t’ \le t$, is not required to be monotonic increasing.