{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T09:44:18Z","timestamp":1753868658823,"version":"3.41.2"},"reference-count":51,"publisher":"Wiley","issue":"11","license":[{"start":{"date-parts":[[2024,10,7]],"date-time":"2024-10-07T00:00:00Z","timestamp":1728259200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"funder":[{"DOI":"10.13039\/501100002858","name":"China Postdoctoral Science Foundation","doi-asserted-by":"publisher","award":["2023M732568"],"award-info":[{"award-number":["2023M732568"]}],"id":[{"id":"10.13039\/501100002858","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12002309","52275164"],"award-info":[{"award-number":["12002309","52275164"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Numer Methods Biomed Eng"],"published-print":{"date-parts":[[2024,11]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We develop a cluster\u2010based model order reduction (called C\u2010pRBMOR) approach for efficient homogenization of bones, compatible with a large variety of generalized standard material (GSM) models. To this end, the pRBMOR approach based on a mixed incremental potential formulation is extended to a clustered version for a significantly improved computational efficiency. The microscopic modeling of bones falls into a mixed incremental class of the GSM framework, originating from two potentials. An offline phase of the C\u2010pRBMOR approach includes both a clustering analysis spatially decomposing the micro\u2010domain within an RVE and a space\u2013time decomposition of the microscopic plastic strain fields. A comparative study on two different clustering approaches and two algorithms for mode identification is additionally conducted. For an online analysis, a cluster\u2010enhanced version of evolution equations for the reduced variables is derived from an effective incremental variational formulation, rendering a very small set of nonlinear equations to be numerically solved. Several numerical examples show the effectiveness of the C\u2010pRBMOR approach. A striking acceleration rate beyond 10<jats:sup>4<\/jats:sup> against conventional FE computations and that beyond 10<jats:sup>3<\/jats:sup> against the original pRBMOR approach are observed.<\/jats:p>","DOI":"10.1002\/cnm.3872","type":"journal-article","created":{"date-parts":[[2024,10,8]],"date-time":"2024-10-08T04:20:00Z","timestamp":1728361200000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A cluster\u2010based incremental potential approach for reduced order homogenization of bones"],"prefix":"10.1002","volume":"40","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4670-632X","authenticated-orcid":false,"given":"Xiaozhe","family":"Ju","sequence":"first","affiliation":[{"name":"Taizhou Hospital of Zhejiang Province  Linhai China"},{"name":"College of Mechanical Engineering Zhejiang University of Technology  Hangzhou China"},{"name":"School of Aeronautics and Astronautics Zhejiang University  Hangzhou China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chunli","family":"Xu","sequence":"additional","affiliation":[{"name":"Taizhou Hospital of Zhejiang Province  Linhai China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yangjian","family":"Xu","sequence":"additional","affiliation":[{"name":"College of Mechanical Engineering Zhejiang University of Technology  Hangzhou China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lihua","family":"Liang","sequence":"additional","affiliation":[{"name":"College of Mechanical Engineering Zhejiang University of Technology  Hangzhou China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Junbo","family":"Liang","sequence":"additional","affiliation":[{"name":"Taizhou Hospital of Zhejiang Province  Linhai China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Weiming","family":"Tao","sequence":"additional","affiliation":[{"name":"School of Aeronautics and Astronautics Zhejiang University  Hangzhou China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2024,10,7]]},"reference":[{"key":"e_1_2_8_2_1","doi-asserted-by":"publisher","DOI":"10.1016\/S1350-4533(98)00007-1"},{"key":"e_1_2_8_3_1","doi-asserted-by":"publisher","DOI":"10.1142\/S1758825120500817"},{"key":"e_1_2_8_4_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11914-020-00631-1"},{"key":"e_1_2_8_5_1","doi-asserted-by":"publisher","DOI":"10.1002\/cnm.2739"},{"key":"e_1_2_8_6_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10237-015-0741-6"},{"key":"e_1_2_8_7_1","doi-asserted-by":"publisher","DOI":"10.1002\/cnm.3188"},{"key":"e_1_2_8_8_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jbiomech.2017.10.002"},{"key":"e_1_2_8_9_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10237-019-01254-x"},{"key":"e_1_2_8_10_1","doi-asserted-by":"publisher","DOI":"10.1002\/cnm.3211"},{"issue":"1","key":"e_1_2_8_11_1","first-page":"39","article-title":"Sur les mat\u00e9riaux standard g\u00e9n\u00e9ralis\u00e9s","volume":"14","author":"Halphen B","year":"1975","journal-title":"Journal de m\u00e9canique"},{"key":"e_1_2_8_12_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.compositesb.2014.08.024"},{"key":"e_1_2_8_13_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0045-7825(98)00219-9"},{"key":"e_1_2_8_14_1","doi-asserted-by":"publisher","DOI":"10.1002\/nme.515"},{"key":"e_1_2_8_15_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmps.2010.11.001"},{"key":"e_1_2_8_16_1","article-title":"Elements of homogenization for inelastic solid mechanics","author":"Suquet P.","year":"1987","journal-title":"Homogenization Techniques Composite Media"},{"key":"e_1_2_8_17_1","doi-asserted-by":"publisher","DOI":"10.1016\/0022-5096(63)90036-X"},{"key":"e_1_2_8_18_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0045-7825(99)00224-8"},{"key":"e_1_2_8_19_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0045-7825(97)00218-1"},{"key":"e_1_2_8_20_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2016.12.025"},{"key":"e_1_2_8_21_1","doi-asserted-by":"publisher","DOI":"10.1002\/nme.4473"},{"issue":"1900","key":"e_1_2_8_22_1","first-page":"291","article-title":"On transformation strains and uniform fields in multiphase elastic media","volume":"437","author":"Dvorak G","year":"1992","journal-title":"Proceedings of the Royal Society of London"},{"key":"e_1_2_8_23_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0020-7683(03)00346-9"},{"key":"e_1_2_8_24_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmps.2016.02.005"},{"key":"e_1_2_8_25_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2006.09.019"},{"key":"e_1_2_8_26_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00466-012-0706-x"},{"key":"e_1_2_8_27_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2003.12.071"},{"key":"e_1_2_8_28_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.compscitech.2007.10.032"},{"key":"e_1_2_8_29_1","doi-asserted-by":"publisher","DOI":"10.1002\/nme.2920"},{"key":"e_1_2_8_30_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijsolstr.2021.111103"},{"key":"e_1_2_8_31_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.mechmat.2016.01.007"},{"key":"e_1_2_8_32_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2022.115199"},{"key":"e_1_2_8_33_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.compstruct.2022.115699"},{"key":"e_1_2_8_34_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.compstruct.2021.114209"},{"key":"e_1_2_8_35_1","doi-asserted-by":"publisher","DOI":"10.1002\/nme.6696"},{"key":"e_1_2_8_36_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00419-022-02356-2"},{"key":"e_1_2_8_37_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2016.04.004"},{"key":"e_1_2_8_38_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00466-018-1573-x"},{"key":"e_1_2_8_39_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2019.01.019"},{"key":"e_1_2_8_40_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2013.03.007"},{"key":"e_1_2_8_41_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2014.05.006"},{"key":"e_1_2_8_42_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4471-6599-6"},{"key":"e_1_2_8_43_1","doi-asserted-by":"publisher","DOI":"10.1002\/nme.5450"},{"key":"e_1_2_8_44_1","doi-asserted-by":"publisher","DOI":"10.1002\/cnm.3784"},{"issue":"72","key":"e_1_2_8_45_1","first-page":"300","article-title":"Computational micro\u2010to\u2010macro transitions of discretized microstructures undergoing small strains","volume":"2002","author":"Koch A","year":"2002","journal-title":"Archiv Appl Mech"},{"key":"e_1_2_8_46_1","doi-asserted-by":"publisher","DOI":"10.1002\/nme.6209"},{"key":"e_1_2_8_47_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.commatsci.2011.10.017"},{"key":"e_1_2_8_48_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2020.113621"},{"key":"e_1_2_8_49_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00466-023-02290-2"},{"key":"e_1_2_8_50_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.compstruct.2021.114365"},{"key":"e_1_2_8_51_1","doi-asserted-by":"publisher","DOI":"10.3390\/electronics9081295"},{"key":"e_1_2_8_52_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10237-022-01615-z"}],"container-title":["International Journal for Numerical Methods in Biomedical Engineering"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/cnm.3872","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,1,3]],"date-time":"2025-01-03T09:51:46Z","timestamp":1735897906000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/cnm.3872"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,10,7]]},"references-count":51,"journal-issue":{"issue":"11","published-print":{"date-parts":[[2024,11]]}},"alternative-id":["10.1002\/cnm.3872"],"URL":"https:\/\/doi.org\/10.1002\/cnm.3872","archive":["Portico"],"relation":{},"ISSN":["2040-7939","2040-7947"],"issn-type":[{"type":"print","value":"2040-7939"},{"type":"electronic","value":"2040-7947"}],"subject":[],"published":{"date-parts":[[2024,10,7]]},"assertion":[{"value":"2024-03-08","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2024-09-01","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2024-10-07","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"e3872"}}