{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,29]],"date-time":"2026-05-29T20:58:34Z","timestamp":1780088314873,"version":"3.54.0"},"reference-count":51,"publisher":"MDPI AG","issue":"21","license":[{"start":{"date-parts":[[2022,10,30]],"date-time":"2022-10-30T00:00:00Z","timestamp":1667088000000},"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>This paper proposed an efficient two-dimensional fatigue crack growth simulation program for linear elastic materials using an incremental crack growth procedure. The Visual Fortran programming language was used to develop the finite element code. The adaptive finite element mesh was generated using the advancing front method. Stress analysis for each increment was carried out using the adaptive mesh finite element technique. The equivalent stress intensity factor is the most essential parameter that should be accurately estimated for the mixed-mode loading condition which was used as the onset criterion for the crack growth. The node splitting and relaxation method advances the crack once the failure mechanism and crack direction have been determined. The displacement extrapolation technique (DET) was used to calculate stress intensity factors (SIFs) at each crack extension increment. Then, these SIFs were analyzed using the maximum circumferential stress theory (MCST) to predict the crack propagation trajectory and the fatigue life cycles using the Paris\u2019 law model. Finally, the performance and capability of the developed program are shown in the application examples.<\/jats:p>","DOI":"10.3390\/ma15217632","type":"journal-article","created":{"date-parts":[[2022,10,30]],"date-time":"2022-10-30T07:26:50Z","timestamp":1667114810000},"page":"7632","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Adaptive Finite Element Modeling of Linear Elastic Fatigue Crack Growth"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1599-8833","authenticated-orcid":false,"given":"Abdulnaser M.","family":"Alshoaibi","sequence":"first","affiliation":[{"name":"Mechanical Engineering Department, Jazan University, P.O. Box 114, Jazan 45142, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Abdullateef H.","family":"Bashiri","sequence":"additional","affiliation":[{"name":"Mechanical Engineering Department, Jazan University, P.O. Box 114, Jazan 45142, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,10,30]]},"reference":[{"key":"ref_1","first-page":"67","article-title":"Mathematical Fundamentals","volume":"Volume 2","author":"Sih","year":"1968","journal-title":"Fracture"},{"key":"ref_2","unstructured":"Hellan, K. (1985). Introduction to Fracture Mechanics, McGraw-Hill."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Barsom, J., and Rolfe, S. (1999). Fracture and Fatigue in Structure: Application of Fracture Mechanics, American Society for Testing and Materials.","DOI":"10.1520\/MNL41_3RD-EB"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"40","DOI":"10.1016\/j.tafmec.2015.04.002","article-title":"Dugdale model for three equal collinear straight cracks: An analytical approach","volume":"78","author":"Hasan","year":"2015","journal-title":"Theor. Appl. Fract. 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