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The cement lines provide a microstructurally preferable crack path, hence triggering in\u2010plane crack deflection around osteons due to cement line\u2010crack interaction. Inspired by this toughening mechanism and facilitated by a hybrid (3D\u2010printing\/casting) process, the study engineers architected tubular cement\u2010based materials with the stepwise cracking toughening mechanism, that enables a non\u2010brittle fracture. Using experimental and theoretical approaches, the study demonstrates the competition between tube size and shape on stress intensity factor from which engineering stepwise cracking can emerge. Two competing mechanisms, both positively and negatively affected by the growing tube size, arise to significantly enhance the overall fracture toughness by up to 5.6\u2010fold compared to the monolithic brittle counterpart without sacrificing the specific strength. This is enabled by crack\u2010tube interaction and engineering the tube size, shape, and orientation, which promotes rising resistance\u2010curves (R\u2010curve). \u201c\n                    <jats:italic>Disorder<\/jats:italic>\n                    \u201d curves and statistical mechanics parameters are proposed for the first time to quantitatively characterize the degree of disorder for describing the representation of the architected arrangement of materials in lieu of otherwise inadequate \u201c\n                    <jats:italic>periodicity<\/jats:italic>\n                    \u201d classification and misperceived\u00a0disorder parameters (perturbation and Voronoi tessellation methods).\n                  <\/jats:p>","DOI":"10.1002\/adma.202313904","type":"journal-article","created":{"date-parts":[[2024,9,10]],"date-time":"2024-09-10T04:26:32Z","timestamp":1725942392000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["Tough Cortical Bone\u2010Inspired Tubular Architected Cement\u2010Based Material with Disorder"],"prefix":"10.1002","volume":"36","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1192-9603","authenticated-orcid":false,"given":"Shashank","family":"Gupta","sequence":"first","affiliation":[{"name":"Department of Civil and Environmental Engineering Princeton University  Princeton NJ 08544 USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3117-6212","authenticated-orcid":false,"given":"Reza","family":"Moini","sequence":"additional","affiliation":[{"name":"Department of Civil and Environmental Engineering Princeton University  Princeton NJ 08544 USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2024,9,10]]},"reference":[{"key":"e_1_2_10_1_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.pmatsci.2009.05.001"},{"key":"e_1_2_10_2_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.pmatsci.2007.06.001"},{"key":"e_1_2_10_3_1","doi-asserted-by":"publisher","DOI":"10.1038\/nmat2221"},{"key":"e_1_2_10_4_1","doi-asserted-by":"publisher","DOI":"10.1039\/c2ra20218b"},{"key":"e_1_2_10_5_1","doi-asserted-by":"publisher","DOI":"10.1016\/S1359-0294(03)00011-6"},{"key":"e_1_2_10_6_1","doi-asserted-by":"publisher","DOI":"10.1098\/rsif.2007.0218"},{"key":"e_1_2_10_7_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.actbio.2009.11.026"},{"key":"e_1_2_10_8_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.bone.2006.06.033"},{"key":"e_1_2_10_9_1","doi-asserted-by":"publisher","DOI":"10.1126\/science.1220854"},{"key":"e_1_2_10_10_1","doi-asserted-by":"publisher","DOI":"10.1039\/c1ce05572k"},{"key":"e_1_2_10_11_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-009-0563-4_16"},{"key":"e_1_2_10_12_1","doi-asserted-by":"publisher","DOI":"10.1126\/science.1218764"},{"key":"e_1_2_10_13_1","doi-asserted-by":"publisher","DOI":"10.1093\/jmicro\/dfs033"},{"key":"e_1_2_10_14_1","doi-asserted-by":"publisher","DOI":"10.1038\/ncomms3634"},{"key":"e_1_2_10_15_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.asd.2008.11.002"},{"key":"e_1_2_10_16_1","doi-asserted-by":"publisher","DOI":"10.1126\/science.1154117"},{"key":"e_1_2_10_17_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmps.2006.07.007"},{"key":"e_1_2_10_18_1","doi-asserted-by":"publisher","DOI":"10.1557\/jmr.2011.332"},{"key":"e_1_2_10_19_1","doi-asserted-by":"publisher","DOI":"10.1002\/adma.200801256"},{"key":"e_1_2_10_20_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmps.2012.10.004"},{"key":"e_1_2_10_21_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.actbio.2012.12.026"},{"key":"e_1_2_10_22_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.actbio.2009.06.033"},{"key":"e_1_2_10_23_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmbbm.2017.06.010"},{"key":"e_1_2_10_24_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.pmatsci.2019.01.002"},{"key":"e_1_2_10_25_1","doi-asserted-by":"publisher","DOI":"10.1002\/adma.201901561"},{"key":"e_1_2_10_26_1","doi-asserted-by":"publisher","DOI":"10.1038\/s41586-020-2813-8"},{"key":"e_1_2_10_27_1","doi-asserted-by":"publisher","DOI":"10.1038\/nmat3115"},{"key":"e_1_2_10_28_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.mattod.2020.04.009"},{"key":"e_1_2_10_29_1","doi-asserted-by":"publisher","DOI":"10.1002\/adma.200803322"},{"key":"e_1_2_10_30_1","volume-title":"Materials: Engineering, Science, Processing and Design","author":"Ashby M. 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