{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,18]],"date-time":"2026-08-18T05:03:05Z","timestamp":1787029385600,"version":"build-2736575974"},"reference-count":33,"publisher":"MDPI AG","issue":"19","license":[{"start":{"date-parts":[[2021,10,1]],"date-time":"2021-10-01T00:00:00Z","timestamp":1633046400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100006754","name":"Army Research Laboratory","doi-asserted-by":"publisher","award":["W911NF1520026"],"award-info":[{"award-number":["W911NF1520026"]}],"id":[{"id":"10.13039\/100006754","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Polymers"],"abstract":"<jats:p>Linear elastic fracture modeling coupled with empirical material tensile data result in good quantitative agreement with the experimental determination of mode I fracture for both brittle and toughened epoxy nanocomposites. The nanocomposites are comprised of diglycidyl ether of bisphenol A cured with Jeffamine D-230 and some were filled with core-shell rubber nanoparticles of varying concentrations. The quasi-static single-edge notched bending (SENB) test is modeled using both the surface-based cohesive zone (CZS) and extended finite element methods (XFEM) implemented in the Abaqus software. For each material considered, the critical load predicted by the simulated SENB test is used to calculate the mode I fracture toughness. Damage initiates in these models when nodes at the simulated crack tip attain the experimentally measured yield stress. Prediction of fracture processes using a generalized truncated linear traction\u2013separation law (TSL) was significantly improved by considering the case of a linear softening function. There are no adjustable parameters in the XFEM model. The CZS model requires only optimization of the element displacement at the fracture parameter. Thus, these continuum methods describe these materials in mode I fracture with a minimum number of independent parameters.<\/jats:p>","DOI":"10.3390\/polym13193387","type":"journal-article","created":{"date-parts":[[2021,10,8]],"date-time":"2021-10-08T21:26:20Z","timestamp":1633728380000},"page":"3387","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Modeling Brittle Fractures in Epoxy Nanocomposites Using Extended Finite Element and Cohesive Zone Surface Methods"],"prefix":"10.3390","volume":"13","author":[{"given":"John J. S.","family":"Biswakarma","sequence":"first","affiliation":[{"name":"Department of Chemical Engineering, Northeastern University, 360 Huntington Avenue, Boston, MA 02115, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Dario A.","family":"Cruz","sequence":"additional","affiliation":[{"name":"Department of Chemical Engineering, Northeastern University, 360 Huntington Avenue, Boston, MA 02115, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Erich D.","family":"Bain","sequence":"additional","affiliation":[{"name":"Engineering Systems, Inc., 10338 Miller Rd., Dallas, TX 75238, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Joseph M.","family":"Dennis","sequence":"additional","affiliation":[{"name":"Materials and Manufacturing Science Division, CCDC, U.S. Army Research Laboratory, 4600 Deer Creek Loop, Aberdeen Proving Ground, MD 21005, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jan W.","family":"Andzelm","sequence":"additional","affiliation":[{"name":"Department of Chemical Engineering, Northeastern University, 360 Huntington Avenue, Boston, MA 02115, USA"},{"name":"Materials and Manufacturing Science Division, CCDC, U.S. Army Research Laboratory, 4600 Deer Creek Loop, Aberdeen Proving Ground, MD 21005, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5030-852X","authenticated-orcid":false,"given":"Steven R.","family":"Lustig","sequence":"additional","affiliation":[{"name":"Department of Chemical Engineering, Northeastern University, 360 Huntington Avenue, Boston, MA 02115, USA"},{"name":"Materials and Manufacturing Science Division, CCDC, U.S. Army Research Laboratory, 4600 Deer Creek Loop, Aberdeen Proving Ground, MD 21005, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2021,10,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1371","DOI":"10.1002\/(SICI)1099-0488(199806)36:8<1371::AID-POLB11>3.0.CO;2-4","article-title":"The effect of network architecture on the thermal and mechanical behavior of epoxy resins","volume":"36","author":"Crawford","year":"1998","journal-title":"J. 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