{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,23]],"date-time":"2026-01-23T07:09:49Z","timestamp":1769152189895,"version":"3.49.0"},"reference-count":27,"publisher":"MDPI AG","issue":"20","license":[{"start":{"date-parts":[[2022,10,13]],"date-time":"2022-10-13T00:00:00Z","timestamp":1665619200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Materials"],"abstract":"<jats:p>To investigate the influence of addition amount and length of steel fibers on the bearing capacity of a concrete beam, this study simulated the crack propagation process of a concrete beam in a four-point bending experiment. The extended finite element method (XFEM) using the ABAQUS software was adopted. Additionally, stress distribution trends for the concrete under loading and load\u2013displacement curves at the stressed points were obtained. The simulation results for a concrete beam with different amounts and lengths of steel fibers were compared and analyzed, and conclusions were drawn. The experiment shows that the flexural performance of the concrete improves with increases in the length and amount of steel fibers, but the reinforcement effects produced by different amounts and lengths of steel fibers are different. When the steel fiber content is 1.5% and the length is 20\u201325 mm, the reinforcement effect in the concrete is significantly improved, and its flexural strength is nearly doubled.<\/jats:p>","DOI":"10.3390\/ma15207146","type":"journal-article","created":{"date-parts":[[2022,10,13]],"date-time":"2022-10-13T22:21:11Z","timestamp":1665699671000},"page":"7146","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Simulation of Four-Point Bending Fracture Test of Steel-Fiber-Reinforced Concrete"],"prefix":"10.3390","volume":"15","author":[{"given":"Wenguang","family":"Kan","sequence":"first","affiliation":[{"name":"College of Aerospace and Civil Engineering, Harbin Engineering University, Harbin 150001, China"},{"name":"School of Water Conservancy and Civil Engineering, Northeast Agricultural University, Harbin 150030, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zailin","family":"Yang","sequence":"additional","affiliation":[{"name":"College of Aerospace and Civil Engineering, Harbin Engineering University, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Weilong","family":"Yin","sequence":"additional","affiliation":[{"name":"School of Astronautics, Harbin Institute of Technology, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,10,13]]},"reference":[{"key":"ref_1","unstructured":"He, S., Xiong, Z., and Zhu, J. (2021, January 23\u201325). Academic Committee of the National Symposium on modern structural engineering. Proceedings of the 21st National Symposium on Modern Structural Engineering, Tianjin, China."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"619","DOI":"10.1007\/s11029-010-9118-1","article-title":"FRP-strengthened reinforced concrete beams: A review and the assessment of cracking and deflection models","volume":"45","author":"Ombres","year":"2009","journal-title":"Mech. Compos. Mater."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Barris, C., Zubillaga, P., and Torres, L. (2019, January 27\u201329). A review on experimental flexural cracking in FRP reinforced concrete members. Proceedings of the IABSE Symposium, Guimaraes 2019: Towards a Resilient Built Environment Risk and Asset Management, Guimaraes, Portugal.","DOI":"10.2749\/guimaraes.2019.0088"},{"key":"ref_4","unstructured":"Zhao, Y.X., Xu, H., and Jin, W.L. (2013, January 11\u201313). Concrete cracking process induced by steel corrosion\u2014A review. Proceedings of the 13th East Asia-Pacific, Conference on Structural Engineering and Construction, EASEC (2013), Sapporo, Japan."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1227","DOI":"10.1061\/(ASCE)0733-9399(1985)111:10(1227)","article-title":"Two-Parameter fracture model for concrete","volume":"111","author":"Jenq","year":"1985","journal-title":"J. Eng. Mech."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1016\/j.compositesb.2018.04.020","article-title":"Synergy assessment of hybrid reinforcements in concrete","volume":"147","author":"Vantadori","year":"2018","journal-title":"Compos. Part B Eng."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"542","DOI":"10.1016\/j.prostr.2018.12.089","article-title":"Contribution of date-palm fibres reinforcement to mortar fracture toughness","volume":"13","author":"Zanichelli","year":"2018","journal-title":"Procedia Struct. Integr."},{"key":"ref_8","first-page":"100","article-title":"Size-effect independence of hybrid fiber-reinforced roller-compacted concrete fracture toughness","volume":"9","author":"Scorza","year":"2022","journal-title":"Compos. Part C"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1111\/ffe.13107","article-title":"A refined diffuse cohesive approach for the failure analysis in quasibrittle materials\u2014Part I: Theoretical formulation and numerical calibration","volume":"43","author":"Greco","year":"2020","journal-title":"Fatigue Fract. Eng. Mater. Struct."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2764","DOI":"10.1111\/ffe.13115","article-title":"A refined diffuse cohesive approach for the failure analysis in quasibrittle materials\u2014Part II: Application to plain and reinforced concrete structures","volume":"42","author":"Greco","year":"2019","journal-title":"Fatigue Fract. Eng. Mater. Struct."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"601","DOI":"10.1002\/(SICI)1097-0207(19990620)45:5<601::AID-NME598>3.0.CO;2-S","article-title":"Elastic crack growth in finite elements with minimal remeshing","volume":"45","author":"Belytschkot","year":"1999","journal-title":"Int. J. Numer. Methods Eng."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"106683","DOI":"10.1016\/j.compstruc.2021.106683","article-title":"Generalized beam theory-based advanced beam finite elements for linear buckling analyses of perforated thin-walled members","volume":"259","author":"Duan","year":"2022","journal-title":"Comput. Struct."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"110299","DOI":"10.1016\/j.matdes.2021.110299","article-title":"Understanding fracture mechanisms via validated virtual tests of encapsulation-based self-healing concrete beams","volume":"213","author":"Dai","year":"2021","journal-title":"Mater. Des."},{"key":"ref_14","first-page":"113522","article-title":"A computational multi-scale model for the stiffness degradation of short-fiber reinforced plastics subjected to fatigue loading","volume":"373","author":"Magino","year":"2020","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"103736","DOI":"10.1016\/j.ijnonlinmec.2021.103736","article-title":"A three-dimensional beam formulation for large deformation and an accurate implementation of the free boundary","volume":"134","author":"Huang","year":"2021","journal-title":"Int. J. Non-Linear Mech."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"347","DOI":"10.1016\/j.engfracmech.2008.10.015","article-title":"An Abaqus implementation of the extended finite element method","volume":"76","author":"Giner","year":"2009","journal-title":"Eng. Fract. Mech."},{"key":"ref_17","first-page":"74","article-title":"Experimental study on mechanical properties of steel fiber reinforced concrete under freeze-thaw conditions","volume":"45","author":"Li","year":"2019","journal-title":"Sichuan Archit. Sci. Res."},{"key":"ref_18","first-page":"133","article-title":"Effect of nano-SiO2 on mechanical properties and microstructure of steel fiber\/concrete after high temperature","volume":"30","author":"Yan","year":"2013","journal-title":"J. Compos. Mater."},{"key":"ref_19","first-page":"409","article-title":"Mechanical properties of corroded steel fiber and steel fiber concrete","volume":"18","author":"Zhao","year":"2015","journal-title":"J. Build. Mater."},{"key":"ref_20","first-page":"2084","article-title":"Study on the improvement of mechanical properties and microstructure of concrete by steel fiber","volume":"32","author":"Bai","year":"2013","journal-title":"Silic. Bull."},{"key":"ref_21","first-page":"495","article-title":"Numerical simulation of cracking of reinforced concrete beams based on XFEM","volume":"47","author":"Yang","year":"2013","journal-title":"J. Zhejiang Univ."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"943","DOI":"10.1002\/nme.201","article-title":"Modelling crack growth by level sets in the extended finite element method","volume":"51","author":"Stolarska","year":"2001","journal-title":"Int. J. Numer. Methods Eng."},{"key":"ref_23","first-page":"1307","article-title":"Study on fracture parameters of concrete based on extended finite element method","volume":"36","author":"Tang","year":"2019","journal-title":"J. Appl. Mech."},{"key":"ref_24","first-page":"254","article-title":"Investigation into static properties of damaged plasticity model for concrete in ABAQUS","volume":"3","author":"Fang","year":"2007","journal-title":"J. PLA Univ. Sci. Technol."},{"key":"ref_25","unstructured":"Powers, T.C. (1960, January 2\u20137). Physical Properties of Cement Paste. Proceedings of the Fourth International Symposium on the Chemistry of Cement, Washington, DC, USA."},{"key":"ref_26","first-page":"61","article-title":"Experimental study on strengthening concrete beams with carbon fiber mesh and chopped strand","volume":"1","author":"Lei","year":"2021","journal-title":"Concr. Cem. Prod."},{"key":"ref_27","first-page":"1","article-title":"Effects of single and hybrid steel fiber lengths and fiber contents on the mechanical properties of high-strength fiber-reinforced concrete","volume":"1","author":"Kim","year":"2018","journal-title":"Adv. Civ. Eng."}],"container-title":["Materials"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1996-1944\/15\/20\/7146\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:53:41Z","timestamp":1760144021000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1996-1944\/15\/20\/7146"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,10,13]]},"references-count":27,"journal-issue":{"issue":"20","published-online":{"date-parts":[[2022,10]]}},"alternative-id":["ma15207146"],"URL":"https:\/\/doi.org\/10.3390\/ma15207146","relation":{},"ISSN":["1996-1944"],"issn-type":[{"value":"1996-1944","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,10,13]]}}}