{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,11]],"date-time":"2026-09-11T05:33:22Z","timestamp":1789104802841,"version":"build-2803163510"},"reference-count":56,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2023,1,16]],"date-time":"2023-01-16T00:00:00Z","timestamp":1673827200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)","award":["492535144"],"award-info":[{"award-number":["492535144"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Materials"],"abstract":"<jats:p>Many concrete structures, such as bridges and wind turbine towers, fail mostly due to the fatigue rapture and bending, where the cracks are initiated and propagate under cyclic loading. Modeling the fracture process zone (FPZ) is essential to understanding the cracking behavior of heterogeneous, quasi-brittle materials such as concrete under monotonic and cyclic actions. The paper aims to present a numerical modeling approach for simulating crack growth using a scaled boundary finite element model (SBFEM). The cohesive traction law is explored to model the stress field under monotonic and cyclic loading conditions. In doing so, a new constitutive law is applied within the cohesive response. The cyclic damage accumulation during loading and unloading is formulated within the thermodynamic framework of the constitutive concrete model. We consider two common problems of three-point bending of a single-edge-notched concrete beam subjected to different loading conditions to validate the developed method. The simulation results show good agreement with experimental test measurements from the literature. The presented analysis can provide a further understanding of crack growth and damage accumulation within the cohesive response, and the SBFEM makes it possible to identify the fracture behavior of cyclic crack propagation in concrete members.<\/jats:p>","DOI":"10.3390\/ma16020863","type":"journal-article","created":{"date-parts":[[2023,1,16]],"date-time":"2023-01-16T04:57:19Z","timestamp":1673845039000},"page":"863","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":25,"title":["Modeling Cyclic Crack Propagation in Concrete Using the Scaled Boundary Finite Element Method Coupled with the Cumulative Damage-Plasticity Constitutive Law"],"prefix":"10.3390","volume":"16","author":[{"given":"Omar","family":"Alrayes","sequence":"first","affiliation":[{"name":"Institute of Structural Mechanics, Bauhaus Weimar University, Marienstra\u00dfe 15, 99423 Weimar, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6008-511X","authenticated-orcid":false,"given":"Carsten","family":"K\u00f6nke","sequence":"additional","affiliation":[{"name":"Institute of Structural Mechanics, Bauhaus Weimar University, Marienstra\u00dfe 15, 99423 Weimar, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ean Tat","family":"Ooi","sequence":"additional","affiliation":[{"name":"School of Science, Engineering and Information Technology, Federation University, Ballarat, VIC 3350, Australia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9898-8421","authenticated-orcid":false,"given":"Khader M.","family":"Hamdia","sequence":"additional","affiliation":[{"name":"Institute of Continuum Mechanics, Leibniz Universit\u00e4t Hannover, 30167 Hannover, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,1,16]]},"reference":[{"key":"ref_1","first-page":"390","article-title":"Size effect in fatigue fracture of concrete","volume":"88","author":"Bazant","year":"1991","journal-title":"ACI Mater. 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