Figure 1
From: A three-dimensional phase diagram of growth-induced surface instabilities
Illustrations of examples, schematics and potential energies of various growth-induced surface instabilities.
(A) Examples of growth-induced surface instabilities on (i) the pumpkin skin, (ii) the cerebral cortex, (iii) the biofilm and (iv) the dog skin. (B) Schematics of growth-induced surface instabilities: (i) wrinkle, (ii) crease, (iii) delaminated-buckle, (iv) fold, (v) period-double and (vi) ridge. (C) One example pathway to induce the mismatch strain in the film-substrate structure: (i) The film and substrate is first assumed to be detached from each other to form a stress-free state; (ii) the detached stress-free substrate is then pre-stretched by a ratio of Lf/Ls and adhered to the film; (iii) relaxed to length L; and (iv) eventually relaxed to length Ls at the current state. Other pathways to induce mismatch strains are illustrated in Supplementary Figs S5 and S7. (D) Evolution of potential energy of the film-substrate structure with increasing mismatch strain following the pathway in (C). The red dash line denotes the surface patterns with the minimum potential energy. The potential energy of the film-substrate structure with mismatch strain εM is denoted by the black solid circle. Image (Ai) is reprinted with permission from Yin, et al., Proc. Natl. Acad. Sci. U.S.A., 105, 49 (2008). Copyright 2008, National Academy of Sciences, USA. Image (Aii) is reprinted from Bradbury, PLOS Biol., 3, 3 (2005) under Open-Access License. Image (Aiii) is reprinted with permission from Asally, et al., Proc. Natl. Acad. Sci. U.S.A., 109, 46 (2012). Copyright 2012, National Academy of Sciences, USA. Image (Aiv) is reprinted with permission from Alison Ruhe.
