  Cell proliferation, apoptosis, and myosin-dependent contraction can generate
elastic stress and strain in living tissues, which may be dissipated by tissue
rearrangement through cell topological transition and cytoskeletal
reorganization. The present work demonstrates significant nonlinear effects in
macroscopic tissue mechanics arising from the competition between
force-generating and dissipating processes. We develop a mathematical model to
describe the coupled dynamics of tissue activities and mechanics in the
nonlinear regime. The model exhibits multi-timescale behavior when the
timescale of rearrangement is much shorter than that of growth and
constriction. Under this condition, tissue behaves like an active viscoelastic
solid at the shorter timescale and like an active viscous fluid at the longer
timescale. The accumulated prestrain due to growth and constriction can
regulate its viscosity. We solve the full nonlinear system considering the
local growth rate coupled with a chemical gradient within a 2D radially
symmetric tissue region. We find that the elastic properties and rearrangement
rate can regulate tissue size as a higher-order effect due to advection in
tissue flow. Furthermore, we show that tissue mechanics' nonlinear effects can
increase tissue size control sensitivity via mechanical feedback mechanisms.
