  Inspired by experiments on dynamic extensile gels of biofilaments and motors,
we propose a model of a network of linear springs with a kinetics consisting of
growth at a prescribed rate, death after a lifetime drawn from a distribution,
and birth at a randomly chosen node. The model captures features such as the
build-up of self-stress, that are not easily incorporated into hydrodynamic
theories. We study the model numerically and show that our observations can
largely be understood through a stochastic effective-medium model. The
resulting dynamically extending force-dipole network displays many features of
yielded plastic solids, and offers a way to incorporate strongly non-affine
effects into theories of active solids. A rather distinctive form for the
stress distribution, and a Herschel-Bulkley dependence of stress on activity,
are our major predictions.
