Encasement as a morphogenetic mechanism: The case of bending

• Mechanics offers attractive avenues for the explanation of shape in living matter.
• We consider here a new mechanism for bio-morphogenesis, i.e. encasement.
• In encasement, a growing bulk is surrounded/protected by a closed growing surface layer.
• The coat and the bulk have different mechanical and growth properties.
• We illustrate the simplest example of a bending instability triggered by encasement.

We study how the encasement of a growing elastic bulk within a possibly differently growing elastic coat may induce mechanical instabilities in the equilibrium shape of the combined body. The inhomogeneities induced in an incompressible bulk during growth are also discussed. These effects are illustrated through a simple example in which a growing elastic cylinder may undergo a shape transition towards a bent configuration.