Wrinkling as a mechanical instability in growing annular hyperelastic plates

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