NeuberNet: a neural operator solving elastic-plastic PDEs at V-notches from low-fidelity elastic simulations

NeuberNet: a neural operator solving elastic-plastic PDEs at V-notches from low-fidelity elastic simulations | 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 Article NeuberNet: a neural operator solving elastic-plastic PDEs at V-notches from low-fidelity elastic simulations Tommaso Grossi, Marco Beghini, Matteo Benedetti This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6113300/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 13 Dec, 2025 Read the published version in Communications Engineering → Version 1 posted You are reading this latest preprint version Abstract We present NeuberNet, a nonlinear manifold decoder that learns a family of operator mappings on the domain of reentrant corners between far-field displacement boundary conditions obtained with low-fidelity elastic simulations and the high-resolution stress and strain fields that stem from the elastic-plastic axisymmetric solid mechanics equations, under the only assumptions of small-scale plasticity and bilinear isotropic hardening. We envision NeuberNet as a data-driven application of the substructuring principle in solid mechanics, engineered to simulate complex geometries by employing plastic material behavior only in the vicinity of stress raisers where nonlinearities are most likely to occur. We provide practical guidelines for mesh resolution in the initial low-fidelity elastic simulations; we show how NeuberNet can detect violations of the small-scale plasticity assumption, signaling the need for full-scale nonlinear models when required; finally, we show that NeuberNet can perform zero-shot inference on 3D problems with axisymmetric geometries and non-symmetric boundary conditions. Physical sciences/Engineering/Mechanical engineering Physical sciences/Mathematics and computing/Computational science Physical sciences/Materials science/Theory and computation/Computational methods Full Text Additional Declarations There is NO Competing Interest. Supplementary Files SupplementaryGrossiBeghiniBenedettiNeuberNetSubmission.pdf Supplementary Material Cite Share Download PDF Status: Published Journal Publication published 13 Dec, 2025 Read the published version in Communications Engineering → 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-6113300","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":421743067,"identity":"c9feccd9-421a-43b4-8744-8590b26b8157","order_by":0,"name":"Tommaso 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