{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,17]],"date-time":"2026-09-17T19:02:31Z","timestamp":1789671751320,"version":"4.0.1"},"reference-count":42,"publisher":"National Academy of Sciences","issue":"38","license":[{"start":{"date-parts":[[2026,9,17]],"date-time":"2026-09-17T00:00:00Z","timestamp":1789603200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/"}],"content-domain":{"domain":["www.pnas.org"],"crossmark-restriction":true},"short-container-title":["Proc. Natl. Acad. Sci. U.S.A."],"published-print":{"date-parts":[[2026,9,22]]},"abstract":"<jats:p>\n                    Patterns in soft solids play essential roles across many fields and are created through diverse strategies. Here, we study the complex three-dimensional (3D) patterns which emerge directly from the fractured surfaces of soft stretchable materials. Using polyacrylamide hydrogels as model materials, we investigate the patterns on fractured gels with various crosslinker concentrations. In these systems, the crack front grows with 3D discontinuities that leave distinct step-like traces on the main fracture plane. We characterize the morphology using two geometric parameters: the step height\n                    <jats:italic toggle=\"yes\">t<\/jats:italic>\n                    and step angle\n                    <jats:italic toggle=\"yes\">\u03b8<\/jats:italic>\n                    , which are highly related to material properties as shown by experiments and modelings. We find that for soft stretchable materials, the step height is on the order of the fractocohesive length\n                    <jats:italic toggle=\"yes\">\n                      R\n                      <jats:sub>f<\/jats:sub>\n                    <\/jats:italic>\n                    , rather than the previously claimed elastoadhesive length\n                    <jats:italic toggle=\"yes\">\n                      l\n                      <jats:sub>e<\/jats:sub>\n                    <\/jats:italic>\n                    . The step angle increases with network crosslinker concentration and approaches a plateau of magic ~45\u00b0 at high crosslink densities. This work shows how nonlinear elasticity and fracture energy shape 3D fracture surface topography in soft materials and provides principles for designing functional patterned surfaces with tunable properties.\n                  <\/jats:p>","DOI":"10.1073\/pnas.2613575123","type":"journal-article","created":{"date-parts":[[2026,9,17]],"date-time":"2026-09-17T18:07:04Z","timestamp":1789668424000},"update-policy":"https:\/\/doi.org\/10.1073\/pnas.cm10313","source":"Crossref","is-referenced-by-count":0,"title":["3D patterns on fractured surfaces of soft stretchable materials"],"prefix":"10.1073","volume":"123","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4398-1139","authenticated-orcid":false,"given":"Tenghao","family":"Yin","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/03zx86w41","id-type":"ROR","asserted-by":"publisher"}],"name":"Laboratoire Sciences et Ing\u00e9nierie de la Mati\u00e8re Molle, \u00c9cole sup\u00e9rieure de physique et de chimie industrielles de la Ville de Paris Paris, Paris Sciences et Lettres Universit\u00e9, Sorbonne Universit\u00e9, CNRS","place":["Paris, France"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9797-1908","authenticated-orcid":false,"given":"Etienne","family":"Barthel","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/03zx86w41","id-type":"ROR","asserted-by":"publisher"}],"name":"Laboratoire Sciences et Ing\u00e9nierie de la Mati\u00e8re Molle, \u00c9cole sup\u00e9rieure de physique et de chimie industrielles de la Ville de Paris Paris, Paris Sciences et Lettres Universit\u00e9, Sorbonne Universit\u00e9, CNRS","place":["Paris, France"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chung-Yuen","family":"Hui","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/05bnh6r87","id-type":"ROR","asserted-by":"publisher"}],"name":"Sibley School of Mechanical and Aerospace Engineering, Cornell 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