Growth instabilities and folding in tubular organs: A variational method in non-linear elasticity

► In this work, we define a variational method for bifurcation analysis of growing soft cylinders. ► We define a set of canonical transformations in mixed polar coordinates, providing a locally isochoric mapping. ► The canonical representation allows transforming a generic boundary value problem into a completely variational formulation. ► The definition of a generating function can also account for the presence of local singularities in the elastic solution. ► Bifurcation analysis is performed for few biomechanical problems, e.g. mucosal folding and surface instabilities in growth.