Surface growth, i.e. the accretion of a solid onto a surface, occurs in several contexts of physical, technological, and biological interest. One of the most common examples of surface growth is the solidification of water at the ice–water interface near the freezing temperature; other examples include technological processes such as chemical vapor deposition or, in biology, the growth of hard tissues like bones and teeth. More recent example include applications to 3D printing. 1
In all these case The formation of a new material surface is strongly dependent chemo-mechanically coupled processes that occur within the material, which may involve thermal or diffusion effects.
Surface growth body may induce mechanical instability, which play a crucial role in morphogenesis. Most description of this kind of instabilities start from a prescribed growth process
Tomassetti, G., Cohen, T., & Abeyaratne, R. (2016). Steady accretion of an elastic body on a hard spherical surface and the notion of a four-dimensional reference space. Journal of the Mechanics and Physics of Solids, 96, 333–352. https://doi.org/10.1016/j.jmps.2016.05.015↩