A fractal void/eXplainable Machine Learning analysis of variables affecting initial cracking loads for Mode I cracks emanating from circular voids in multi-void two-dimensional systems subject to uniaxial compression  

A fractal void/eXplainable Machine Learning analysis of variables affecting initial cracking loads for Mode I cracks emanating from circular voids in multi-void two-dimensional systems subject to uniaxial compression | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article A fractal void/eXplainable Machine Learning analysis of variables affecting initial cracking loads for Mode I cracks emanating from circular voids in multi-void two-dimensional systems subject to uniaxial compression A. Ahmed, N. G. Shrive This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8109312/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract While brittle compressive strength is known to depend on material porosity, adequate theoretical explanations have not been presented. The primary limitations have been computational expense and the many variables defining pore structures. The recent development of fractal void analysis (FVA) and maturation of eXplainable machine learning (XML) relieves these limitations. This manuscript thus presents an FVA/XML analysis of normalized stress intensity factors (SIFs, denoted K i1 /K o ) for line cracks of fixed length emanating from void surfaces in two-dimensional, three-void systems in infinite continua subject to distant uniaxial compression. These SIFs correlate to theoretical initial cracking loads. The study aims to identify geometric motifs associated with high K i1 /K o , and quantify the relative importance of void relative size, spacing, and intravoid angles. Large, closely-spaced voids aligned at 30 o angles are a typical motif correlated to 95 th percentile K i1 /K o values. A categorical feature, Void #, identifying void order in an arrangement, is found to encode global configurational effects on K i1 /K o values. The relative importance of void size, spacing, and intravoid angle is determined to vary with Void #. It is not advised to interpret K i1 /K o trends in 95 th percentile arrangements solely via relative void size and pairwise edge distances and angles; higher-order effects are noted. Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-8109312","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":548371143,"identity":"8e8d500d-ddc1-482b-8369-6286c82935ec","order_by":0,"name":"A. 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Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-8109312/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8109312/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eWhile brittle compressive strength is known to depend on material porosity, adequate theoretical explanations have not been presented. The primary limitations have been computational expense and the many variables defining pore structures. The recent development of fractal void analysis (FVA) and maturation of eXplainable machine learning (XML) relieves these limitations. This manuscript thus presents an FVA/XML analysis of normalized stress intensity factors (SIFs, denoted \u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003ei1\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e/K\u003c/em\u003e\u003csub\u003e\u003cem\u003eo\u003c/em\u003e\u003c/sub\u003e) for line cracks of fixed length emanating from void surfaces in two-dimensional, three-void systems in infinite continua subject to distant uniaxial compression. These SIFs correlate to theoretical initial cracking loads. The study aims to identify geometric motifs associated with high \u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003ei1\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e/K\u003c/em\u003e\u003csub\u003e\u003cem\u003eo\u003c/em\u003e\u003c/sub\u003e, and quantify the relative importance of void relative size, spacing, and intravoid angles. Large, closely-spaced voids aligned at 30\u003csup\u003eo\u003c/sup\u003e angles are a typical motif correlated to 95\u003csup\u003eth\u003c/sup\u003e percentile \u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003ei1\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e/K\u003c/em\u003e\u003csub\u003e\u003cem\u003eo\u003c/em\u003e\u003c/sub\u003e values. A categorical feature, Void #, identifying void order in an arrangement, is found to encode global configurational effects on \u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003ei1\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e/K\u003c/em\u003e\u003csub\u003e\u003cem\u003eo\u003c/em\u003e\u003c/sub\u003e values. The relative importance of void size, spacing, and intravoid angle is determined to vary with Void #. It is not advised to interpret \u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003ei1\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e/K\u003c/em\u003e\u003csub\u003e\u003cem\u003eo\u003c/em\u003e\u003c/sub\u003e trends in 95\u003csup\u003eth\u003c/sup\u003e percentile arrangements solely via relative void size and pairwise edge distances and angles; higher-order effects are noted.\u003c/p\u003e","manuscriptTitle":"A fractal void/eXplainable Machine Learning analysis of variables affecting initial cracking loads for Mode I cracks emanating from circular voids in multi-void two-dimensional systems subject to uniaxial compression ","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-11-26 15:59:46","doi":"10.21203/rs.3.rs-8109312/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"20e3882b-e108-4984-bfc5-0a8c1fc25c41","owner":[],"postedDate":"November 26th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2026-02-10T15:58:16+00:00","versionOfRecord":[],"versionCreatedAt":"2025-11-26 15:59:46","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8109312","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8109312","identity":"rs-8109312","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}