Hybrid Constitutive Law with Machine Learning for Sintering of Advanced Ceramics

Hybrid Constitutive Law with Machine Learning for Sintering of Advanced Ceramics | 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 Hybrid Constitutive Law with Machine Learning for Sintering of Advanced Ceramics Baber SALEEM, Peter POLAK, Ran HE, Savvaki Savva, Jonathan PHILLIPS, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9359299/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 12 You are reading this latest preprint version Abstract Predictive simulation of sintering-induced distortion remains challenging for ceramic components subjected to gravity and mechanical constraint. Classical constitutive sintering laws reproduce free densification reliably but lack the flexibility required to accurately capture stress-driven deformation within finite-element (FE) frameworks when calibrated solely from dilatometer data. This study presents a hybrid machine-learning-assisted constitutive framework for modelling constrained sintering of an industrial ceramic material. Dilatometer densification data and a gravity-loaded beam-bending experiments were obtained for the same material system, enabling simultaneous evaluation of volumetric sintering kinetics and part-level deformation. Two independently calibrated parameter sets of an Olevsky-type constitutive law reproduce densification behaviour but underpredict gravity-driven curvature (A) when applied within FE simulations, highlighting an inherent trade-off between densification fitting and deformation prediction. To overcome this limitation, the analytical volumetric strain-rate term is replaced by an artificial neural network (ANN) trained directly on experimental densification data, while analytical formulations for mean and deviatoric stress response are retained. This hybrid framework decouples densification kinetics from shear-dominated deformation, enabling modulation of the effective viscous stiffness governing beam bending without compromising physical interpretability or numerical robustness. The results establish a simple, computationally efficient, and physically interpretable pathway toward predictive modelling of constrained sintering, providing a scalable foundation for industrial process optimisation and future digital-twin development. Physical sciences/Engineering Physical sciences/Materials science Physical sciences/Mathematics and computing sintering deformation constrained sintering hybrid constitutive modelling artificial neural networks finite element analysis Full Text Additional Declarations No competing interests reported. Supplementary Files FInalGraphicalAbstractUpdated.pdf Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 28 Apr, 2026 Reviews received at journal 24 Apr, 2026 Reviews received at journal 24 Apr, 2026 Reviews received at journal 23 Apr, 2026 Reviewers agreed at journal 17 Apr, 2026 Reviewers agreed at journal 14 Apr, 2026 Reviewers agreed at journal 14 Apr, 2026 Reviewers invited by journal 14 Apr, 2026 Editor invited by journal 14 Apr, 2026 Editor assigned by journal 09 Apr, 2026 Submission checks completed at journal 09 Apr, 2026 First submitted to journal 08 Apr, 2026 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. 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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-9359299","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":624812604,"identity":"8f16d467-8a55-468a-bfd5-642d77074c37","order_by":0,"name":"Baber 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Classical constitutive sintering laws reproduce free densification reliably but lack the flexibility required to accurately capture stress-driven deformation within finite-element (FE) frameworks when calibrated solely from dilatometer data.\u003c/p\u003e \u003cp\u003eThis study presents a hybrid machine-learning-assisted constitutive framework for modelling constrained sintering of an industrial ceramic material. Dilatometer densification data and a gravity-loaded beam-bending experiments were obtained for the same material system, enabling simultaneous evaluation of volumetric sintering kinetics and part-level deformation. Two independently calibrated parameter sets of an Olevsky-type constitutive law reproduce densification behaviour but underpredict gravity-driven curvature (A) when applied within FE simulations, highlighting an inherent trade-off between densification fitting and deformation prediction.\u003c/p\u003e \u003cp\u003eTo overcome this limitation, the analytical volumetric strain-rate term is replaced by an artificial neural network (ANN) trained directly on experimental densification data, while analytical formulations for mean and deviatoric stress response are retained. This hybrid framework decouples densification kinetics from shear-dominated deformation, enabling modulation of the effective viscous stiffness governing beam bending without compromising physical interpretability or numerical robustness. 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