  While determining the stability of an unconstrained elastic structure is a
straightforward task, this is not the case for viscoelastic structures.
Seemingly elastically stable conformations of viscoelastic structures may
gradually creep until stability is lost, and conversely, creeping does not
necessarily imply that a structure will eventually become unstable.
Understanding instabilities in viscoelastic structures requires a more
intuitive description of viscoelasticity to allow analytical results and
quantitative predictions. In this work we put forward a metric description of
viscoelasticity in which the continua is characterized by temporally evolving
reference lengths with respect to which elastic strains are measured.
Formulating the three dimensional theory using metric tensors we are able to
predict which structures will exhibit delayed instability due to viscoelastic
flow. We also quantitatively describe the viscoelastic relaxation in free
standing structures including cases where the relaxation leads to no apparent
motion. We demonstrate these results and the power of the metric approach by
elucidating the subtle mechanism of delayed instability in elastomer shells
showing quantitative agreement with experimental measurements.
