{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,22]],"date-time":"2026-03-22T04:06:16Z","timestamp":1774152376785,"version":"3.50.1"},"reference-count":28,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2020,4,8]],"date-time":"2020-04-08T00:00:00Z","timestamp":1586304000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2020,4,8]],"date-time":"2020-04-08T00:00:00Z","timestamp":1586304000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"name":"Ser Cymru National Research Network in Advanced Engineering and Materials under grants","award":["NRNG06"],"award-info":[{"award-number":["NRNG06"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Adv. Model. and Simul. in Eng. Sci."],"published-print":{"date-parts":[[2020,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We develop a novel unfitted finite element solver for composite materials with quasi-1D fibrous reinforcements. The method belongs to the class of mixed-dimensional non-conforming finite element solvers. The fibres are treated as 1D structural elements that may intersect the mesh of the embedding structure in an arbitrary manner. No meshing of the unidimensional elements is required. Instead, fibre solution fields are described using the trace of the background mesh. A regularised \u201ccut\u201d finite element formulation is carefully designed to ensure that analyses using such non-conforming finite element descriptions are stable. We also design a dedicated primal\/dual operator splitting scheme to resolve the coupling between structure and fibrous reinforcements efficiently. The novel computational strategy is applied to the solution of stiff computational models whereby fibrous reinforcements may lose their bond to the embedding material above a certain level of stress. It is shown that the primal-dual 1D\/3D CutFEM scheme is convergent and well-behaved in variety of scenarios involving such highly nonlinear structural computations.<\/jats:p>","DOI":"10.1186\/s40323-020-00154-5","type":"journal-article","created":{"date-parts":[[2020,4,9]],"date-time":"2020-04-09T12:03:27Z","timestamp":1586433807000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["A mixed-dimensional CutFEM methodology for the simulation of fibre-reinforced composites"],"prefix":"10.1186","volume":"7","author":[{"given":"P.","family":"Kerfriden","sequence":"first","affiliation":[]},{"given":"S.","family":"Claus","sequence":"additional","affiliation":[]},{"given":"I.","family":"Mihai","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,4,8]]},"reference":[{"key":"154_CR1","unstructured":"Akula BR, Vignollet J, Yastrebov VA. MorteX method for contact along real and embedded surfaces: coupling X-FEM with the Mortar method. 2019. arXiv preprint\narXiv:1902.04000."},{"issue":"3","key":"154_CR2","doi-asserted-by":"publisher","first-page":"353","DOI":"10.1016\/0045-7825(91)90022-X","volume":"92","author":"P Alart","year":"1991","unstructured":"Alart P, Curnier A. A mixed formulation for frictional contact problems prone to Newton like solution methods. Comput Methods Appl Mech Eng. 1991;92(3):353\u201375.","journal-title":"Comput Methods Appl Mech Eng"},{"key":"154_CR3","doi-asserted-by":"publisher","first-page":"1518","DOI":"10.1002\/nme.2884","volume":"83","author":"O Allix","year":"2010","unstructured":"Allix O, Kerfriden P, Gosselet P. On the control of the load increments for a proper description of multiple delamination in a domain decomposition framework. Int J Numer Methods Eng. 2010;83:1518\u201340.","journal-title":"Int J Numer Methods Eng"},{"issue":"100","key":"154_CR4","first-page":"9","volume":"3","author":"MS Aln\u00e6s","year":"2015","unstructured":"Aln\u00e6s MS, Blechta J, Hake J, Johansson A, Kehlet B, Logg A, Richardson C, Ring J, Rognes ME, Wells GN. The FEniCS project version 1.5. Arch Numer Softw. 2015;3(100):9\u201323.","journal-title":"Arch Numer Softw"},{"key":"154_CR5","doi-asserted-by":"publisher","first-page":"183","DOI":"10.1016\/j.cma.2018.10.023","volume":"345","author":"HP Bui","year":"2019","unstructured":"Bui HP, Tomar S, Bordas SPA. Corotational cut finite element method for real-time surgical simulation: application to needle insertion simulation. Comput Methods Appl Mech Eng. 2019;345:183\u2013211.","journal-title":"Comput Methods Appl Mech Eng"},{"issue":"21\u201322","key":"154_CR6","doi-asserted-by":"publisher","first-page":"1217","DOI":"10.1016\/j.crma.2010.10.006","volume":"348","author":"E Burman","year":"2010","unstructured":"Burman E. Ghost penalty. Compt Rend Math. 2010;348(21\u201322):1217\u201320.","journal-title":"Compt Rend Math"},{"issue":"7","key":"154_CR7","doi-asserted-by":"publisher","first-page":"472","DOI":"10.1002\/nme.4823","volume":"104","author":"E Burman","year":"2015","unstructured":"Burman E, Claus S, Hansbo P, Larson MG, Massing A. CutFEM: Discretizing geometry and partial differential equations. Int J Numer Methods Eng. 2015;104(7):472\u2013501.","journal-title":"Int J Numer Methods Eng"},{"issue":"1","key":"154_CR8","doi-asserted-by":"publisher","first-page":"173","DOI":"10.1051\/m2an\/2018047","volume":"53","author":"E Burman","year":"2019","unstructured":"Burman E, Hansbo P, Larson MG. Augmented Lagrangian finite element methods for contact problems. ESAIM Math Model Numer Anal. 2019;53(1):173\u201395.","journal-title":"ESAIM Math Model Numer Anal"},{"issue":"1","key":"154_CR9","doi-asserted-by":"publisher","first-page":"189","DOI":"10.1007\/s10596-018-9792-y","volume":"23","author":"E Burman","year":"2019","unstructured":"Burman E, Hansbo P, Larson MG. A simple finite element method for elliptic bulk problems with embedded surfaces. Comput Geosci. 2019;23(1):189\u201399.","journal-title":"Comput Geosci"},{"issue":"6","key":"154_CR10","doi-asserted-by":"publisher","first-page":"2247","DOI":"10.1051\/m2an\/2018038","volume":"52","author":"E B\u00fcrman","year":"2018","unstructured":"B\u00fcrman E, Hansbo P, Larson MG, Massing Ae. Cut finite element methods for partial differential equations on embedded manifolds of arbitrary codimensions. ESAIM Math Model Numer Anal. 2018;52(6):2247\u201382.","journal-title":"ESAIM Math Model Numer Anal"},{"issue":"5","key":"154_CR11","doi-asserted-by":"publisher","first-page":"B1444","DOI":"10.1137\/18M1185697","volume":"40","author":"S Claus","year":"2018","unstructured":"Claus S, Bigot S, Kerfriden P. CutFEM method for Stefan\u2013Signorini problems with application in pulsed laser ablation. SIAM J Sci Comput. 2018;40(5):B1444\u201369.","journal-title":"SIAM J Sci Comput"},{"issue":"6","key":"154_CR12","doi-asserted-by":"publisher","first-page":"938","DOI":"10.1002\/nme.5694","volume":"113","author":"S Claus","year":"2018","unstructured":"Claus S, Kerfriden P. A stable and optimally convergent LaTIn-CutFEM algorithm for multiple unilateral contact problems. Int J Numer Methods Eng. 2018;113(6):938\u201366.","journal-title":"Int J Numer Methods Eng"},{"key":"154_CR13","doi-asserted-by":"publisher","first-page":"185","DOI":"10.1016\/j.cma.2019.01.009","volume":"348","author":"S Claus","year":"2019","unstructured":"Claus S, Kerfriden P. A CutFEM method for two-phase flow problems. Comput Methods Appl Mech Eng. 2019;348:185\u2013206.","journal-title":"Comput Methods Appl Mech Eng"},{"issue":"2","key":"154_CR14","doi-asserted-by":"publisher","first-page":"465","DOI":"10.1051\/m2an\/2011148","volume":"46","author":"C D\u2019Angelo","year":"2012","unstructured":"D\u2019Angelo C, Scotti A. A mixed finite element method for Darcy flow in fractured porous media with non-matching grids$${_\\ast }$$. ESAIM: Math Model Numer Anal. 2012;46(2):465\u201389.","journal-title":"ESAIM: Math Model Numer Anal"},{"key":"154_CR15","doi-asserted-by":"publisher","first-page":"80","DOI":"10.1016\/j.finel.2016.12.001","volume":"130","author":"F Duboeuf","year":"2017","unstructured":"Duboeuf F, B\u00e9chet E. Embedded solids of any dimension in the X-FEM. Part I\u2014building a dedicated P1 function space. Finite Elem Anal Design. 2017;130:80\u2013101.","journal-title":"Finite Elem Anal Design"},{"issue":"4","key":"154_CR16","doi-asserted-by":"publisher","first-page":"1089","DOI":"10.1051\/m2an\/2013132","volume":"48","author":"L Formaggia","year":"2014","unstructured":"Formaggia L, Fumagalli A, Scotti A, Ruffo P. A reduced model for Darcy\u2019s problem in networks of fractures$${_\\ast }$$. ESAIM Math Model Numer Anal. 2014;48(4):1089\u2013116.","journal-title":"ESAIM Math Model Numer Anal"},{"issue":"4","key":"154_CR17","doi-asserted-by":"publisher","first-page":"257","DOI":"10.1016\/S0965-9978(00)00093-4","volume":"32","author":"HM Gomes","year":"2001","unstructured":"Gomes HM, Awruch AM. Some aspects on three-dimensional numerical modelling of reinforced concrete structures using the finite element method. Adv Eng Softw. 2001;32(4):257\u201377.","journal-title":"Adv Eng Softw"},{"issue":"33\u201335","key":"154_CR18","doi-asserted-by":"publisher","first-page":"3523","DOI":"10.1016\/j.cma.2003.12.041","volume":"193","author":"A Hansbo","year":"2004","unstructured":"Hansbo A, Hansbo P. A finite element method for the simulation of strong and weak discontinuities in solid mechanics. Comput Methods Appl Mech Eng. 2004;193(33\u201335):3523\u201340.","journal-title":"Comput Methods Appl Mech Eng"},{"key":"154_CR19","doi-asserted-by":"publisher","first-page":"28","DOI":"10.1016\/j.finel.2015.08.003","volume":"107","author":"M Hirmand","year":"2015","unstructured":"Hirmand M, Vahab M, Khoei AR. An augmented Lagrangian contact formulation for frictional discontinuities with the extended finite element method. Finite Elem Anal Design. 2015;107:28\u201343.","journal-title":"Finite Elem Anal Design"},{"issue":"5","key":"154_CR20","doi-asserted-by":"publisher","first-page":"795","DOI":"10.1016\/j.cemconres.2010.01.004","volume":"40","author":"A Jefferson","year":"2010","unstructured":"Jefferson A, Joseph C, Lark R, Isaacs B, Dunn S, Weager B. A new system for crack closure of cementitious materials using shrinkable polymers. Cem Concr Res. 2010;40(5):795\u2013801.","journal-title":"Cem Concr Res"},{"issue":"3","key":"154_CR21","doi-asserted-by":"publisher","first-page":"343","DOI":"10.1007\/s00466-009-0378-3","volume":"44","author":"P Kerfriden","year":"2009","unstructured":"Kerfriden P, Allix O, Gosselet P. A three-scale domain decomposition method for the 3D analysis of debonding in laminates. Comput Mech. 2009;44(3):343\u201362.","journal-title":"Comput Mech"},{"key":"154_CR22","doi-asserted-by":"publisher","first-page":"4869","DOI":"10.1016\/S0045-7825(02)00406-1","volume":"191","author":"P Ladev\u00e8ze","year":"2002","unstructured":"Ladev\u00e8ze P, Nouy A, Loiseau O. A multiscale computational approach for contact problems. Comput Methods Appl Mech Eng. 2002;191:4869\u201391.","journal-title":"Comput Methods Appl Mech Eng"},{"key":"154_CR23","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.finel.2017.01.002","volume":"128","author":"B L\u00e9","year":"2017","unstructured":"L\u00e9 B, Legrain G, Mo\u00ebs N. Mixed dimensional modeling of reinforced structures. Finite Elem Anal Design. 2017;128:1\u201318.","journal-title":"Finite Elem Anal Design"},{"key":"154_CR24","doi-asserted-by":"publisher","unstructured":"Maddalena R, Bonanno L, Balzano B, Sweeney J, Mihai I. A crack closure system for cementitious composite materials using knotted shape memory polymer (k-SMP) fibres. Cement Concr Composi. 2019. https:\/\/doi.org\/10.17035\/d.2019.0078702279","DOI":"10.17035\/d.2019.0078702279"},{"issue":"10","key":"154_CR25","doi-asserted-by":"publisher","first-page":"1273","DOI":"10.1002\/nme.2861","volume":"83","author":"C Miehe","year":"2010","unstructured":"Miehe C, Welschinger F, Hofacker M. Thermodynamically consistent phase-field models of fracture: Variational principles and multi-field FE implementations. Int J Numer Methods Eng. 2010;83(10):1273\u2013311.","journal-title":"Int J Numer Methods Eng"},{"key":"154_CR26","first-page":"1","volume":"2018","author":"JM Navarro-Jim\u00e9nez","year":"2018","unstructured":"Navarro-Jim\u00e9nez JM, Tur M, Albelda J, R\u00f3denas JJ. Large deformation frictional contact analysis with immersed boundary method. Comput Mech. 2018;2018:1\u201318.","journal-title":"Comput Mech"},{"issue":"9","key":"154_CR27","doi-asserted-by":"publisher","first-page":"931","DOI":"10.1002\/nag.357","volume":"28","author":"M Sadek","year":"2004","unstructured":"Sadek M, Shahrour I. A three dimensional embedded beam element for reinforced geomaterials. Int J Numer Anal Methods Geomech. 2004;28(9):931\u201346.","journal-title":"Int J Numer Anal Methods Geomech"},{"key":"154_CR28","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1061\/JSDEAG.0003416","volume":"99","author":"M Suidan","year":"1973","unstructured":"Suidan M, Schnobrich WC. Finite element analysis of reinforced concrete. J Struct Div. 1973;99:1.","journal-title":"J Struct Div"}],"container-title":["Advanced Modeling and Simulation in Engineering Sciences"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1186\/s40323-020-00154-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1186\/s40323-020-00154-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1186\/s40323-020-00154-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,4,7]],"date-time":"2021-04-07T23:26:08Z","timestamp":1617837968000},"score":1,"resource":{"primary":{"URL":"https:\/\/amses-journal.springeropen.com\/articles\/10.1186\/s40323-020-00154-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,4,8]]},"references-count":28,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2020,12]]}},"alternative-id":["154"],"URL":"https:\/\/doi.org\/10.1186\/s40323-020-00154-5","relation":{},"ISSN":["2213-7467"],"issn-type":[{"value":"2213-7467","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,4,8]]},"assertion":[{"value":"2 December 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"28 March 2020","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"8 April 2020","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"Not applicable","order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}],"article-number":"18"}}