Wrinkles, creases, and cusps in growing soft matter

The buckling of a material surface subject to compression or growth is a ubiquitous phenomenon, arising in materials science contexts such as the swelling of gels as well as in biological contexts such as morphogenesis and embryogenesis. A complete understanding of the creases and sharp cusps that commonly accompany buckling requires nonlinear elasticity theory. This review presents a modern treatment of the Biot instability, integrating many standard techniques of nonlinear physics and solid mechanics, such as bifurcation theory, conformal mapping, and $J$ and $M$ integrals.