  The combination of Dirac physics and elasticity has been explored at length
in graphene where the so--called "elastic gauge fields" have given rise to an
entire new field of research and applications: Straintronics. The fact that
these elastic fields couple to fermions as the electromagnetic field, implies
that many electromagnetic responses will have elastic counterparts not explored
before. In this work we will first show that the presence of elastic gauge
fields will be the rule rather than the exception in most of the topologically
non--trivial materials in two and three dimensions. In particular we will
extract the elastic gauge fields associated to the recently observed Weyl
semimetals, the "three dimensional graphene". As it is known, quantum
electrodynamics suffers from the chiral anomaly whose consequences have been
recently explored in matter systems. We will show that, associated to the
physics of the anomalies, and as a counterpart of the Hall conductivity,
elastic materials will have a Hall viscosity in two and three dimensions with a
coefficient orders of magnitude bigger than the previously studied response.
The magnitude and generality of the new effect will greatly improve the chances
for the experimental observation of this topological, non dissipative response.
