{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,25]],"date-time":"2026-02-25T12:14:46Z","timestamp":1772021686007,"version":"3.50.1"},"reference-count":46,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2024,1,5]],"date-time":"2024-01-05T00:00:00Z","timestamp":1704412800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Fundamental Research Funds of Southwest University of Science and Technology","award":["23zx7156"],"award-info":[{"award-number":["23zx7156"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Materials"],"abstract":"<jats:p>Fracture failure in quasi-brittle materials poses a persistent challenge in materials science and engineering. This study presents a thorough investigation of the Boundary Effect Model (BEM), offering a nuanced understanding of the size effect on fracture properties. The conceptual framework, evolutionary process, and applicability scope of BEM are elucidated, highlighting its accuracy and reliability in calculating fracture properties across various quasi-brittle materials. Through the integration of BEM with diverse fracture tests\u2014such as three-point bending, four-point bending, and wedge-splitting\u2014a linear correlation between maximum failure loads and material fracture properties is established. Notably, the study demonstrates that fracture properties, determined by BEM, can be regarded as consistent material constants across specimens of varying sizes, initial notch lengths, geometries, and microstructures. Validation of the BEM\u2019s reliability encompasses the analysis of 140 fracture test results involving concrete, hard rocks, and bamboo scrimber. The synergy of non-linear and linear BEM analyses emerges as a robust approach for accurately predicting the fracture behavior of quasi-brittle materials. This comprehensive exploration sheds light on the potential of the Boundary Effect Model as a valuable tool for predicting and understanding fracture mechanics in diverse materials and scenarios. This research serves as an effective approach to accurately evaluating the fracture properties of quasi-brittle materials, which is of great practical significance for material design, engineering construction, and various industrial applications.<\/jats:p>","DOI":"10.3390\/ma17020282","type":"journal-article","created":{"date-parts":[[2024,1,5]],"date-time":"2024-01-05T07:38:31Z","timestamp":1704440311000},"page":"282","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Application of a Closed-Form Model in Analyzing the Fracture of Quasi-Brittle Materials"],"prefix":"10.3390","volume":"17","author":[{"given":"Xiangyu","family":"Han","sequence":"first","affiliation":[{"name":"School of Civil Engineering and Architecture, Southwest University of Science and Technology, Mianyang 621010, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Peng","family":"Li","sequence":"additional","affiliation":[{"name":"China Railway 17th Bureau Group Co., Ltd., Taiyuan 030006, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jianguo","family":"Liu","sequence":"additional","affiliation":[{"name":"China Railway 17th Bureau Group Co., Ltd., Taiyuan 030006, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,1,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"4191","DOI":"10.1016\/S0020-7683(97)00309-0","article-title":"Characteristic strength of quasi-brittle materials","volume":"35","author":"Labuz","year":"1998","journal-title":"Int. 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