  Many manmade and naturally occurring materials form viscoelastic solids. The
increasing use of biologically inspired elastomeric material and the extreme
mechanical response these elastomers offer drive the need for a better, more
intuitive and quantitative understanding of the mechanical response of such
continua. This is in particular important in determining the stability of
viscoelastic structure over time where in lieu of robust rules we often must
resort to simulations. In this work we put forward a metric description of
viscoelasticity in which the continua is characterized by temporally evolving
reference lengths quantified by a rest reference metric. This rest reference
metric serves as a state variable describing the result of the viscoelastic
flow in the system, and allows us to provide robust claims regarding stability
of incompressible isotropic viscoelastic media. We demonstrate these claims for
a simple bistable systems of three standard-linear-solid spring dashpot
assemblies where the predicted rules can be verified by explicit calculations,
and also show quantitative agreement with recent experiments in viscoelastic
silicone rubber shells that display delayed stability loss.
