A three-dimensional phase diagram of growth-induced surface instabilities

Scientific Reports

Volumn 5, Issue , 2015, Pages

  Wang, Qiming ^a,b   Zhao, Xuanhe ^a,b  

^a Massachusetts Institute of Technology Cambridge   (United States)

^b Duke University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ANIMAL; BIOLOGICAL MODEL; COMPUTER SIMULATION; ELASTICITY; HUMAN; MORPHOGENESIS; PHYSIOLOGY; SURFACE PROPERTY;

ANIMALS; COMPUTER SIMULATION; ELASTICITY; HUMANS; MODELS, BIOLOGICAL; MORPHOGENESIS; SURFACE PROPERTIES;

EID: 84924373450     PISSN: None     EISSN: 20452322     Source Type: Journal    
DOI: 10.1038/srep08887     Document Type: Article

References (62)

1. Ball, P. The self-made tapestry: pattern formation in nature (Oxford Univ. Press, Oxford, 1999).
2. Thompson, D. W. On Growth and Form, abridged edition edn (Cambridge Univiversity Press, 1917).
3. Cerda, E. & Mahadevan, L. Geometry and physics of wrinkling. Physical Review Letters 90, 074302 (2003).
4. Yin, J., Gerling, G. J. & Chen, X. Mechanical modeling of a wrinkled fingertip immersed in water. Acta Biomater. 6, 1487-1496 (2010).
5. Kücken, M. & Newell, A. A model for fingerprint formation. Europhys. Lett. 68, 141 (2004).
6. Yin, J. et al. Stress-driven buckling patterns in spheroidal core/shell structures. Proc. Natl. Acad. Sci. U.S.A. 105, 19132-19135 (2008).
7. Katifori, E. et al. Foldable structures and the natural design of pollen grains. Proceedings of the National Academy of Sciences 107, 7635-7639 (2010).
8. Li, B. et al. Surface wrinkling patterns on a core-shell soft sphere. Physical review letters 106, 234301 (2011).
9. Wilking, J. N. et al. Liquid transport facilitated by channels in Bacillus subtilis biofilms. Proceedings of the National Academy of Sciences 110, 848-852 (2012).
10. Asally, M. et al. Localized cell death focuses mechanical forces during 3D patterning in a biofilm. Proceedings of the National Academy of Sciences 109, 18891-18896 (2012).
11. DePas, W. H. et al. Iron induces bimodal population development by Escherichia coli. Proceedings of the National Academy of Sciences 110, 2629-2634 (2013).
12. Hohlfeld, E. & Mahadevan, L. Unfolding the sulcus. Physical review letters 106, 105702 (2011).
13. Tallinen, T., Biggins, J. & Mahadevan, L. Surface Sulci in Squeezed Soft Solids. Physical review letters 110, 024302 (2013).
14. Richman, D. P., Stewart, R. M., Hutchinson, J. W. & Caviness Jr, V. S. Mechanical model of brain convolutional development. Science 189, 18-21 (1975).
15. Kriegstein, A., Noctor, S. & Martínez-Cerdeño, V. Patterns of neural stem and progenitor cell division may underlie evolutionary cortical expansion. Nature Reviews Neuroscience 7, 883-890 (2006).
16. Shyer, A. E. et al. Villification: How the Gut Gets Its Villi. Science 342, 212-218 (2013).
17. Walton, K. D. et al. Hedgehog-responsive mesenchymal clusters direct patterning and emergence of intestinal villi. Proceedings of the National Academy of Sciences 109, 15817-15822 (2012).
18. Amar, M. B. & Jia, F. Anisotropic growth shapes intestinal tissues during embryogenesis. Proceedings of the National Academy of Sciences 110, 10525-10530 (2013).
19. Hannezo, E., Prost, J. & Joanny, J. F. Instabilities of Monolayered Epithelia: Shape and Structure of Villi and Crypts. Physical Review Letters 107, 078104 (2011).
20. Li, B., Cao, Y.-P. & Feng, X.-Q. Growth and surface folding of esophageal mucosa: a biomechanical model. Journal of biomechanics 44, 182-188 (2011).
21. Li, B., Cao, Y.-P., Feng, X.-Q. & Gao, H. Surface wrinkling of mucosa induced by volumetric growth: theory, simulation and experiment. Journal of the Mechanics and Physics of Solids 59, 758-774 (2011).
22. Wiggs, B. R., Hrousis, C. A., Drazen, J. M. & Kamm, R. D. On the mechanism of mucosal folding in normal and asthmatic airways. Journal of Applied Physiology 83, 1814-1821 (1997).
23. Ciarletta, P. Buckling Instability in Growing Tumor Spheroids. Physical review letters 110, 158102 (2013).
24. Dervaux, J., Couder, Y., Guedeau-Boudeville, M.-A. & Amar, M. B. Shape transition in artificial tumors: from smooth buckles to singular creases. Physical review letters 107, 018103 (2011).
25. Eisenhoffer, G. T. et al. Crowding induces live cell extrusion to maintain homeostatic cell numbers in epithelia. Nature 484, 546-549 (2012).
26. Marinari, E. et al. Live-cell delamination counterbalances epithelial growth to limit tissue overcrowding. Nature 484, 542-545 (2012).
27. Wang, L., Castro, C. E. & Boyce, M. C. Growth strain-induced wrinkled membrane morphology of white blood cells. Soft Matter 7, 11319-11324 (2011).
28. Dervaux, J. & Amar, M. B. Mechanical Instabilities of Gels. Annu. Rev. Condens. Matter Phys. 3, 311-332 (2012).
29. Li, B., Cao, Y.-P., Feng, X.-Q. & Gao, H. Mechanics of morphological instabilities and surface wrinkling in soft materials: a review. Soft Matter 8, 5728-5745 (2012).
30. Burgess, D. R. Morphogenesis of intestinal villi II. Mechanism of formation of previllous ridges. J. Embryol. Eep. Morph. 34, 723-740 (1975).
31. Ben Amar, M. & Goriely, A. Growth and instability in elastic tissues. Journal of the Mechanics and Physics of Solids 53, 2284-2319 (2005).
32. Bradbury, J. Molecular insights into human brain evolution. PLoS Biol. 3, e50 (2005).
33. Akey, J. M. et al. Tracking footprints of artificial selection in the dog genome. Proc. Natl. Acad. Sci. U.S.A. 107, 1160-1165 (2010).
34. Kim, J., Yoon, J. & Hayward, R. C. Dynamic display of biomolecular patterns through an elastic creasing instability of stimuli-responsive hydrogels. Nat. Mater. 9, 159-164 (2010).
35. Shivapooja, P. et al. Bioinspired Surfaces with Dynamic Topography for Active Control of Biofouling. Advanced Materials 25, 1430-1434 (2013).
36. Zang, J. et al . Multifunctionality and control of the crumpling and unfolding of large-area graphene. Nat. Mater. 12, 321-325 (2013).
37. Jiang, H. et al. Finite deformation mechanics in buckled thin films on compliant supports. Proceedings of the National Academy of Sciences 104, 15607-15612 (2007).
38. Khang, D. Y., Jiang, H., Huang, Y. & Rogers, J. A. A stretchable form of single-crystal silicon for high-performance electronics on rubber substrates. Science 311, 208-212 (2006).
39. Wang, Q. & Zhao, X. Phase Diagrams of Instabilities in Compressed Film-Substrate Systems. J. Appl. Mech. 81, 051004 (2014).
40. Thompson, J. M. T. & Hunt, G. W. Elastic instability phenomena (Wiley Chichester etc., 1984).
41. Ericksen, J. L. Introduction to the Thermodynamics of Solids (Springer, 1998).
42. Abeyaratne, R. Evolution of phase transitions: a continuum theory (Cambridge University Press, 2006).
43. Hong, W., Zhao, X. & Suo, Z. Formation of creases on the surfaces of elastomers and gels. Applied Physics Letters 95, 111901-111901-111903 (2009).
44. Wang, Q., Zhang, L. & Zhao, X. Creasing to Cratering Instability in Polymers under Ultrahigh Electric Fields. Physical review letters 106, 118301 (2011).
45. Brau, F. et al. Multiple-length-scale elastic instability mimics parametric resonance of nonlinear oscillators. Nature Physics 7, 56-60 (2010).
46. Sun, J. Y. et al. Folding wrinkles of a thin stiff layer on a soft substrate. Proc. R. Soc. A 468, 932-953 (2012).
47. Vella, D. et al. The macroscopic delamination of thin films from elastic substrates. Proceedings of the National Academy of Sciences 106, 10901-10906 (2009).
48. Cai, S., Chen, D., Suo, Z. & Hayward, R. C. Creasing instability of elastomer films. Soft Matter 8, 1301-1304 (2012).
49. Cao, Y. & Hutchinson, J. W. Wrinkling phenomena in neo-Hookean film/substrate bilayers. Journal of applied mechanics 79, 1019 (2012).
50. Chen, X. & Hutchinson, J.W. Herringbone buckling patterns of compressed thin films on compliant substrates. Journal of applied mechanics 71, 597-603 (2004).
51. Chen, D., Cai, S., Suo, Z. & Hayward, R. C. Surface Energy as a Barrier to Creasing of Elastomer Films: An Elastic Analogy to Classical Nucleation. Physical review letters 109, 38001 (2012).
52. Yoon, J., Kim, J. & Hayward, R. C. Nucleation, growth, and hysteresis of surface creases on swelled polymer gels. Soft Matter 6, 5807-5816 (2010).
53. Trujillo, V., Kim, J. & Hayward, R. C. Creasing instability of surface-attached hydrogels. Soft Matter 4, 564-569 (2008).
54. Velankar, S. S., Lai, V. & Vaia, R. A. Swelling-Induced Delamination Causes Folding of Surface-Tethered Polymer Gels. ACS Appl. Mater. Interfaces 4, 24-29 (2012).
55. Sultan, E. & Boudaoud, A. The Buckling of a Swollen Thin Gel Layer Bound to a Compliant Substrate. J. Appl. Mech. 75, 051002-051002 (2008).
56. Tanaka, T. et al.Mechanical instability of gels at the phase transition. Nature 325, 796-798 (1987).
57. Breid, D. & Crosby, A. J. Effect of stress state on wrinkle morphology. Soft Matter 7, 4490-4496 (2011).
58. Tallinen, T., Chung, J. Y., Biggins, J. S. & Mahadevan, L. Gyrification from constrained cortical expansion. Proceedings of the National Academy of Sciences 111, 12667-12672 (2014).
59. Grason, G. M. & Davidovitch, B. Universal collapse of stress and wrinkle-to-scar transition in spherically confined crystalline sheets. Proceedings of the National Academy of Sciences 110, 12893-12898 (2013).
60. Wu, Z., Bouklas, N. & Huang, R. Swell-induced surface instability of hydrogel layers with material properties varying in thickness direction. International Journal of Solids and Structures 50, 578-587 (2013).
61. Song, Z. et al. Origami lithium-ion batteries. Nat. Comm. 5, 3140 (2014).
62. Kendall, K. The adhesion and surface energy of elastic solids. J. Phys. D: Appl. Phys. 4, 1186 (1971).