  Growth-induced instabilities are ubiquitous in biological systems and lead to
diverse morphologies in the form of wrinkling, folding, and creasing. The
current work focusses on the mechanics behind growth-induced wrinkling
instabilities in an incompressible annular hyperelastic plate. The governing
differential equations for a two-dimensional plate system are derived using a
variational principle with no apriori kinematic assumptions in the thickness
direction. A linear bifurcation analysis is performed to investigate the
stability behaviour of the growing hyperelastic annular plate by considering
both axisymmetric and asymmetric perturbations. The resulting differential
equations are then solved numerically using the compound matrix method to
evaluate the critical growth factor that leads to wrinkling. The effect of
boundary constraints, thickness, and radius ratio of the annular plate on the
critical growth factor is studied. For most of the considered cases, an
asymmetric bifurcation is the preferred mode of instability for an annular
plate. Our results are useful to model the physics of wrinkling phenomena in
growing planar soft tissues, swelling hydrogels, and pattern transition in
two-dimensional films growing on an elastic substrate.
