Non-Euclidean surface growth

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In the field of surface growth, there are growth processes that result in the surface of an object changing shape over time. As the object grows, its surface may change from flat to curved, or change curvature. Two points on the surface may also change in distance as a result of deformations of the object or accretion of new matter onto the object. The shape of the surface and its changes can be described in terms of non-Euclidean geometry and in particular, Riemannian geometry with a space- and time-dependent curvature. [1] [2]

Examples of non-Euclidean surface growth are found in the mechanics of growing gravitational bodies, [3] [4] [5] [6] [7] [8] propagating fronts of phase transitions, [9] epitaxial growth of nanostructures and additive 3D printing, [10] growth of plants, [11] and cell motility [12]

References

  1. ↑ Truskinovsky, Lev; Zurlo, Giuseppe (2019-05-03). "Nonlinear elasticity of incompatible surface growth". Physical Review E. 99 (5). American Physical Society (APS): 053001. arXiv: 1901.06182 . Bibcode:2019PhRvE..99e3001T. doi:10.1103/physreve.99.053001. ISSN   2470-0045. PMID   31212512.
  2. ↑ Zurlo, Giuseppe; Truskinovsky, Lev (2017-07-26). "Printing Non-Euclidean Solids". Phys. Rev. Lett. 119 (4). American Physical Society (APS): 048001. arXiv: 1703.03082 . Bibcode:2017PhRvL.119d8001Z. doi:10.1103/PhysRevLett.119.048001. ISSN   2470-0045. PMID   29341729.
  3. ↑ E. I. Rashba, Construction sequence dependent stresses in massive bodies due to their weight, Proc. Inst. Struct. Mech. Acad. Sci. Ukrainian SSR 18, 23 (1953).
  4. ↑ Brown, C. B.; Goodman, L. E. (1963-12-17). "Gravitational stresses in accreted bodies". Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences. 276 (1367). The Royal Society: 571–576. Bibcode:1963RSPSA.276..571B. doi:10.1098/rspa.1963.0227. ISSN   2053-9169.
  5. ↑ V. E. Naumov, Mechanics of growing deformable solids: A review, J. Eng. Mech. 120, 207 (1994).
  6. ↑ J. G. Bentler and J. F. Labuz, Performance of a Cantilever retaining wall, J. Geotech. Geoenviron. Eng. 132, 1062 (2006).
  7. ↑ Bacigalupo, Andrea; Gambarotta, Luigi (2012). "Effects of Layered Accretion on the Mechanics of Masonry Structures". Mechanics Based Design of Structures and Machines. 40 (2). Informa UK Limited: 163–184. doi:10.1080/15397734.2011.628622. ISSN   1539-7734.
  8. ↑ S. A. Lychev, Geometric aspects of the theory of incompatible deformations in growing solids, in Mechanics for Materials and Technologies, ed. by H. Altenbach, R. Goldstein, and E.Murashkin, Advanced Structured Materials, 46 (Springer, New York, 2017).
  9. ↑ Wildeman, Sander; Sterl, Sebastian; Sun, Chao; Lohse, Detlef (2017-02-23). "Fast Dynamics of Water Droplets Freezing from the Outside In". Physical Review Letters. 118 (8). American Physical Society (APS): 084101. arXiv: 1701.06818 . Bibcode:2017PhRvL.118h4101W. doi:10.1103/physrevlett.118.084101. ISSN   0031-9007. PMID   28282160.
  10. ↑ Ge, Qi; Sakhaei, Amir Hosein; Lee, Howon; Dunn, Conner K.; Fang, Nicholas X.; Dunn, Martin L. (2016-08-08). "Multimaterial 4D Printing with Tailorable Shape Memory Polymers". Scientific Reports. 6 (1). Springer Science and Business Media LLC: 31110. Bibcode:2016NatSR...631110G. doi: 10.1038/srep31110 . ISSN   2045-2322. PMC   4976324 . PMID   27499417.
  11. ↑ R. R. Archer, Growth Stresses and Strains in Trees, Springer Series in Wood Science (Springer-Verlag, Berlin, 1987)
  12. ↑ Dafalias, Yannis F.; Pitouras, Zacharias (2007-12-06). "Stress field in actin gel growing on spherical substrate". Biomechanics and Modeling in Mechanobiology. 8 (1). Springer Science and Business Media LLC: 9–24. doi:10.1007/s10237-007-0113-y. ISSN   1617-7959. PMID   18058144.

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