Elastic instabilities in a model cerebral cortex

Soft and biological systems exhibit elastic instabilities, such as buckling, folding and wrinkling, in the presence of external loads, growth, or both. The modeling of such systems calls for a continuum approach to account for the interplay between local elastic stresses and global growth profiles. It is this interplay that can lead to non-trivial geometries. We propose a model of the cerebral cortex, described as an anisotropic multi-layered material with two basic components (white matter and grey matter) undergoing differential growth. We explore the nature of buckling instabilities, assuming a compatibility between the growth and geometric deformation, by solving a nonlinear variational problem with a free interface. We expect that this simplified approach, based on a combination of geometry and elasticity, could give insight into the formation and splitting of folds observed during the development of the cerebral cortex.