From the onset of creasing as a Kosterlitz-Thouless transition to "buckling without bending" in morphogenesis

Cusped inward folds, known as creases, form on a free surface of a soft disordered solid under compression at critical strains below that of buckling. Harnessing a model for composite elastic materials, quasi-particle excitations termed ghost shear lag fibers serve as surface stress localizers to initiate this creasing transition. The mathematics of these stress localizers maps to charges on the free surface of the solid. This mapping, combined with the presence of fluctuations due to the underlying disordered material under compression, point to the creasing transition as a Kosterlitz-Thouless transition. For the sake of contrast, a new shape-changing mechanism, termed "buckling without bending", involving not only solid material but a proliferating fluid layer under mechanical constraints will also be presented. The implications of creasing, buckling, and "buckling without bending" for the cerebrum, the cerebellum, and brain organoids will be addressed along the way.