{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,24]],"date-time":"2026-01-24T05:53:47Z","timestamp":1769234027826,"version":"3.49.0"},"reference-count":21,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2021,6,18]],"date-time":"2021-06-18T00:00:00Z","timestamp":1623974400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100016775","name":"Politechnika Lubelska","doi-asserted-by":"publisher","award":["FN16\/ILT\/2020"],"award-info":[{"award-number":["FN16\/ILT\/2020"]}],"id":[{"id":"10.13039\/100016775","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Materials"],"abstract":"<jats:p>This paper describes a method of predicting the direction of crack propagation implemented by user subroutines in the Simulia-Abaqus FEA system with the use of the extended finite element method (X-FEM). This method is based on displacements and stresses according to Westergaard\u2019s solution of Griffith\u2019s crack problem. During the calculations, in each crack increment, the algorithm reads the stresses and displacements in the model around the crack tip, calculates the criterion values at the read points, reduces them to a unit distance from the crack tip, fits a polynomial to these points, and finds the minimum of the function closest to the last propagation angle. The algorithm also decides when the crack grows, depending on a chosen criterion. Four criteria have been implemented to predict the direction of failure propagation: the maximum principal stress criterion, the Ottosen\u2013Podg\u00f3rski criterion, the new criterion described here based on the minimum component values of the displacement vector, and the maximum circumferential tensile stress (MTS). These criteria were verified in two tests: the three-point bending test of the notched beam and the anchor pull-out test. For these tests, the criterion built into Simulia Abaqus does not correctly define the crack path, which causes the crack propagation direction to \u201crotate\u201d when simulating the fracture. The criteria developed here, in most cases, determine the crack path and the maximum force very well compared to real laboratory tests.<\/jats:p>","DOI":"10.3390\/ma14123382","type":"journal-article","created":{"date-parts":[[2021,6,18]],"date-time":"2021-06-18T11:19:20Z","timestamp":1624015160000},"page":"3382","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Comparison of Various Criteria Determining the Direction of Crack Propagation Using the UDMGINI User Procedure Implemented in Abaqus"],"prefix":"10.3390","volume":"14","author":[{"given":"Jakub","family":"Gontarz","sequence":"first","affiliation":[{"name":"Department of Structural Mechanics, Faculty of Civil Engineering and Architecture, Lublin University of Technology, Nadbystrzycka 40, 20-618 Lublin, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4745-7705","authenticated-orcid":false,"given":"Jerzy","family":"Podg\u00f3rski","sequence":"additional","affiliation":[{"name":"Department of Structural Mechanics, Faculty of Civil Engineering and Architecture, Lublin University of Technology, Nadbystrzycka 40, 20-618 Lublin, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,6,18]]},"reference":[{"key":"ref_1","unstructured":"(2020, November 13). 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