{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T04:23:04Z","timestamp":1777350184438,"version":"3.51.4"},"reference-count":29,"publisher":"Springer Science and Business Media LLC","issue":"10","license":[{"start":{"date-parts":[[2022,10,24]],"date-time":"2022-10-24T00:00:00Z","timestamp":1666569600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2022,10,24]],"date-time":"2022-10-24T00:00:00Z","timestamp":1666569600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Nat Comput Sci"],"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Many biological structures exhibit intriguing morphological patterns adapted to environmental cues, which contribute to their important biological functions and also inspire material designs. Here, we report a chiral wrinkling topography in shrinking core\u2013shell spheres, as observed in excessively dehydrated passion fruit and experimentally demonstrated in silicon core\u2013shells under air extraction. Upon shrinkage deformation, the surface initially buckles into a buckyball pattern (periodic hexagons and pentagons) and then transforms into a chiral mode. The neighbouring chiral cellular patterns can further interact with each other, resulting in secondary symmetry breaking and the formation of two types of topological network. We develop a core\u2013shell model and derive a universal scaling law to understand the underlying morphoelastic mechanism and to effectively describe and predict such chiral symmetry breaking far beyond the critical instability threshold. Moreover, we show experimentally that the chiral characteristic adapted to local perturbation can be harnessed to effectively and stably grasp small-sized objects of various shapes and made of different stiff and soft materials. Our results not only reveal chiral instability topographies, providing fundamental insights into the surface morphogenesis of the deformed core\u2013shell spheres that are ubiquitous in the real world, but also demonstrate potential applications of adaptive grasping based on delicate chiral localization.<\/jats:p>","DOI":"10.1038\/s43588-022-00332-y","type":"journal-article","created":{"date-parts":[[2022,10,24]],"date-time":"2022-10-24T15:03:04Z","timestamp":1666623784000},"page":"632-640","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":45,"title":["Chiral topographic instability in shrinking spheres"],"prefix":"10.1038","volume":"2","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3910-5398","authenticated-orcid":false,"given":"Fan","family":"Xu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yangchao","family":"Huang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shichen","family":"Zhao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6894-7979","authenticated-orcid":false,"given":"Xi-Qiao","family":"Feng","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2022,10,24]]},"reference":[{"key":"332_CR1","doi-asserted-by":"publisher","first-page":"19132","DOI":"10.1073\/pnas.0810443105","volume":"105","author":"J Yin","year":"2008","unstructured":"Yin, J., Cao, Z., Li, C., Sheinman, I. & Chen, X. Stress-driven buckling patterns in spheroidal core\/shell structures. Proc. Natl Acad. Sci. USA 105, 19132\u201319135 (2008).","journal-title":"Proc. Natl Acad. Sci. USA"},{"key":"332_CR2","doi-asserted-by":"publisher","first-page":"1470","DOI":"10.1016\/j.jmps.2009.06.002","volume":"57","author":"J Yin","year":"2009","unstructured":"Yin, J., Chen, X. & Sheinman, I. Anisotropic buckling patterns in spheroidal film\/substrate systems and their implications in some natural and biological systems. J. Mech. Phys. Solids 57, 1470\u20131484 (2009).","journal-title":"J. Mech. Phys. Solids"},{"key":"332_CR3","doi-asserted-by":"publisher","first-page":"234301","DOI":"10.1103\/PhysRevLett.106.234301","volume":"106","author":"B Li","year":"2011","unstructured":"Li, B., Jia, F., Cao, Y. P., Feng, X. Q. & Gao, H. Surface wrinkling patterns on a core\u2013shell soft sphere. Phys. Rev. Lett. 106, 234301 (2011).","journal-title":"Phys. Rev. Lett."},{"key":"332_CR4","doi-asserted-by":"publisher","first-page":"068101","DOI":"10.1103\/PhysRevLett.101.068101","volume":"101","author":"J Dervaux","year":"2008","unstructured":"Dervaux, J. & Ben Amar, M. Morphogenesis of growing soft tissues. Phys. Rev. Lett. 101, 068101 (2008).","journal-title":"Phys. Rev. Lett."},{"key":"332_CR5","doi-asserted-by":"publisher","first-page":"12359","DOI":"10.1073\/pnas.1811296115","volume":"115","author":"C Huang","year":"2018","unstructured":"Huang, C., Wang, Z., Quinn, D., Suresh, S. & Hsia, K. J. Differential growth and shape formation in plant organs. Proc. Natl Acad. Sci. USA 115, 12359\u201312364 (2018).","journal-title":"Proc. Natl Acad. Sci. USA"},{"key":"332_CR6","doi-asserted-by":"publisher","first-page":"038003","DOI":"10.1103\/PhysRevLett.124.038003","volume":"124","author":"F Xu","year":"2020","unstructured":"Xu, F., Fu, C. & Yang, Y. Water affects morphogenesis of growing aquatic plant leaves. Phys. Rev. Lett. 124, 038003 (2020).","journal-title":"Phys. Rev. Lett."},{"key":"332_CR7","doi-asserted-by":"publisher","first-page":"10525","DOI":"10.1073\/pnas.1217391110","volume":"110","author":"M Ben Amar","year":"2013","unstructured":"Ben Amar, M. & Jia, F. Anisotropic growth shapes intestinal tissues during embryogenesis. Proc. Natl Acad. Sci. USA 110, 10525\u201310530 (2013).","journal-title":"Proc. Natl Acad. Sci. USA"},{"key":"332_CR8","doi-asserted-by":"publisher","first-page":"248101","DOI":"10.1103\/PhysRevLett.113.248101","volume":"113","author":"P Ciarletta","year":"2014","unstructured":"Ciarletta, P., Balbi, V. & Kuhl, E. Pattern selection in growing tubular tissues. Phys. Rev. Lett. 113, 248101 (2014).","journal-title":"Phys. Rev. Lett."},{"key":"332_CR9","doi-asserted-by":"publisher","first-page":"158102","DOI":"10.1103\/PhysRevLett.110.158102","volume":"110","author":"P Ciarletta","year":"2013","unstructured":"Ciarletta, P. Buckling instability in growing tumor spheroids. Phys. Rev. Lett. 110, 158102 (2013).","journal-title":"Phys. Rev. Lett."},{"key":"332_CR10","doi-asserted-by":"publisher","first-page":"588","DOI":"10.1038\/nphys3632","volume":"12","author":"T Tallinen","year":"2016","unstructured":"Tallinen, T. et al. On the growth and form of cortical convolutions. Nat. Phys. 12, 588\u2013593 (2016).","journal-title":"Nat. Phys."},{"key":"332_CR11","doi-asserted-by":"publisher","first-page":"56","DOI":"10.1038\/nphys1806","volume":"7","author":"F Brau","year":"2011","unstructured":"Brau, F. et al. Multiple-length-scale elastic instability mimics parametric resonance of nonlinear oscillators. Nat. Phys. 7, 56\u201360 (2011).","journal-title":"Nat. Phys."},{"key":"332_CR12","doi-asserted-by":"publisher","first-page":"337","DOI":"10.1038\/nmat4202","volume":"14","author":"N Stoop","year":"2015","unstructured":"Stoop, N., Lagrange, R., Terwagne, D., Reis, P. M. & Dunkel, J. Curvature-induced symmetry breaking determines elastic surface patterns. Nat. Mater. 14, 337\u2013342 (2015).","journal-title":"Nat. Mater."},{"key":"332_CR13","doi-asserted-by":"publisher","first-page":"7635","DOI":"10.1073\/pnas.0911223107","volume":"107","author":"E Katifori","year":"2010","unstructured":"Katifori, E., Alben, S., Cerda, E., Nelson, D. R. & Dumais, J. Foldable structures and the natural design of pollen grains. Proc. Natl Acad. Sci. USA 107, 7635\u20137639 (2010).","journal-title":"Proc. Natl Acad. Sci. USA"},{"key":"332_CR14","doi-asserted-by":"publisher","first-page":"228002","DOI":"10.1103\/PhysRevLett.121.228002","volume":"121","author":"M Holland","year":"2018","unstructured":"Holland, M., Budday, S., Goriely, A. & Kuhl, E. Symmetry breaking in wrinkling patterns: Gyri are universally thicker than sulci. Phys. Rev. Lett. 121, 228002 (2018).","journal-title":"Phys. Rev. Lett."},{"key":"332_CR15","doi-asserted-by":"publisher","first-page":"146","DOI":"10.1038\/30193","volume":"393","author":"N Bowden","year":"1998","unstructured":"Bowden, N., Brittain, S., Evans, A. G., Hutchinson, J. W. & Whitesides, G. M. Spontaneous formation of ordered structures in thin films of metals supported on an elastomeric polymer. Nature 393, 146\u2013149 (1998).","journal-title":"Nature"},{"key":"332_CR16","doi-asserted-by":"publisher","first-page":"1603","DOI":"10.1126\/science.1182383","volume":"327","author":"JA Rogers","year":"2010","unstructured":"Rogers, J. A., Someya, T. & Huang, Y. Materials and mechanics for stretchable electronics. Science 327, 1603\u20131607 (2010).","journal-title":"Science"},{"key":"332_CR17","doi-asserted-by":"publisher","first-page":"948","DOI":"10.1038\/s41567-018-0193-x","volume":"14","author":"L Pocivavsek","year":"2018","unstructured":"Pocivavsek, L. et al. Topography-driven surface renewal. Nat. Phys. 14, 948\u2013953 (2018).","journal-title":"Nat. Phys."},{"key":"332_CR18","doi-asserted-by":"publisher","first-page":"210","DOI":"10.1126\/science.aan5627","volume":"358","author":"JH Pikul","year":"2017","unstructured":"Pikul, J. H. et al. Stretchable surfaces with programmable 3D texture morphing for synthetic camouflaging skins. Science 358, 210\u2013214 (2017).","journal-title":"Science"},{"key":"332_CR19","doi-asserted-by":"publisher","first-page":"24","DOI":"10.1038\/s41563-018-0219-x","volume":"18","author":"E Si\u00e9fert","year":"2019","unstructured":"Si\u00e9fert, E., Reyssat, E., Bico, J. & Roman, B. Bio-inspired pneumatic shape-morphing elastomers. Nat. Mater. 18, 24\u201328 (2019).","journal-title":"Nat. Mater."},{"key":"332_CR20","doi-asserted-by":"publisher","first-page":"6608","DOI":"10.1002\/adma.201401403","volume":"26","author":"D Terwagne","year":"2014","unstructured":"Terwagne, D., Brojan, M. & Reis, P. M. Smart morphable surfaces for aerodynamic drag control. Adv. Mater. 26, 6608\u20136611 (2014).","journal-title":"Adv. Mater."},{"key":"332_CR21","doi-asserted-by":"publisher","first-page":"036102","DOI":"10.1103\/PhysRevLett.100.036102","volume":"100","author":"G Cao","year":"2008","unstructured":"Cao, G., Chen, X., Li, C., Ji, A. & Cao, Z. Self-assembled triangular and labyrinth buckling patterns of thin films on spherical substrates. Phys. Rev. Lett. 100, 036102 (2008).","journal-title":"Phys. Rev. Lett."},{"key":"332_CR22","doi-asserted-by":"crossref","first-page":"3624","DOI":"10.1039\/c3sm27331h","volume":"9","author":"D Breid","year":"2013","unstructured":"Breid, D. & Crosby, A. J. Curvature-controlled wrinkle morphologies. Soft Matter 9, 3624\u20133630 (2013).","journal-title":"Soft Matter"},{"key":"332_CR23","doi-asserted-by":"publisher","first-page":"103892","DOI":"10.1016\/j.jmps.2020.103892","volume":"137","author":"F Xu","year":"2020","unstructured":"Xu, F., Zhao, S., Lu, C. & Potier-Ferry, M. Pattern selection in core\u2013shell spheres. J. Mech. Phys. Solids 137, 103892 (2020).","journal-title":"J. Mech. Phys. Solids"},{"key":"332_CR24","unstructured":"van der Heijden, A. M. A. W.T. Koiter\u2019s Elastic Stability of Solids and Structures (Cambridge Univ. Press, 2009)."},{"key":"332_CR25","doi-asserted-by":"publisher","first-page":"A1","DOI":"10.1115\/1.4008739","volume":"4","author":"MA Biot","year":"1937","unstructured":"Biot, M. A. Bending of an infinite beam on an elastic foundation. J. Appl. Mech. 4, A1\u2013A7 (1937).","journal-title":"J. Appl. Mech."},{"key":"332_CR26","doi-asserted-by":"crossref","unstructured":"Allen, H. G. Analysis and Design of Structural Sandwich Panels (Pergamon, 1969).","DOI":"10.1016\/B978-0-08-012870-2.50006-7"},{"key":"332_CR27","doi-asserted-by":"publisher","first-page":"212","DOI":"10.1016\/j.jmps.2014.09.005","volume":"73","author":"Y Zhao","year":"2014","unstructured":"Zhao, Y., Cao, Y., Feng, X. Q. & Ma, K. Axial compression-induced wrinkles on a core-shell soft cylinder: Theoretical analysis, simulations and experiments. J. Mech. Phys. Solids 73, 212\u2013227 (2014).","journal-title":"J. Mech. Phys. Solids"},{"key":"332_CR28","doi-asserted-by":"publisher","first-page":"394","DOI":"10.1016\/j.cma.2017.12.001","volume":"331","author":"RMJ Groh","year":"2018","unstructured":"Groh, R. M. J., Avitabile, D. & Pirrera, A. Generalised path-following for well-behaved nonlinear structures. Comput. Methods Appl. Mech. Eng. 331, 394\u2013426 (2018).","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"332_CR29","doi-asserted-by":"publisher","unstructured":"Xu, F., Huang, Y., Zhao, S. & Feng, X. Q. Chiral topographic instability in shrinking spheres. Zenodo https:\/\/doi.org\/10.5281\/zenodo.7025830 (2022).","DOI":"10.5281\/zenodo.7025830"}],"container-title":["Nature Computational Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.nature.com\/articles\/s43588-022-00332-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/s43588-022-00332-y","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/s43588-022-00332-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,10,24]],"date-time":"2022-10-24T16:08:31Z","timestamp":1666627711000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.nature.com\/articles\/s43588-022-00332-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,10,24]]},"references-count":29,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2022,10]]}},"alternative-id":["332"],"URL":"https:\/\/doi.org\/10.1038\/s43588-022-00332-y","relation":{},"ISSN":["2662-8457"],"issn-type":[{"value":"2662-8457","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,10,24]]},"assertion":[{"value":"23 April 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 September 2022","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 October 2022","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"The authors declare that they have no competing interests.","order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}]}}