  Mechanical forces influence the development and behavior of biological
tissues. In many situations these forces are exerted or resisted by elastic
compliant structures such as the own-tissue cellular matrix or other
surrounding tissues. This kind of tissue-elastic body interactions are also at
the core of many state-of-the-art {\it in situ} force measurement techniques
employed in biophysics. This creates the need to model tissue interaction with
the surrounding elastic bodies that exert these forces, raising the question:
which are the minimum ingredients needed to describe such interactions? We
conduct experiments where migrating cell monolayers push on carbon fibers as a
model problem. Although the migrating tissue is able to bend the fiber for some
time, it eventually recoils before coming to a stop. This stop occurs when
cells have performed a fixed mechanical work on the fiber, regardless of its
stiffness. Based on these observations we develop a minimal active-fluid model
that reproduces the experiments and predicts quantitatively relevant features
of the system. This minimal model points out the essential ingredients needed
to describe tissue-elastic solid interactions: an effective inertia and viscous
stresses.
