Symmetry-induced collapse of elastic polarization in a strain–energy Hilbert space

Symmetry-induced collapse of elastic polarization in a strain–energy Hilbert space | 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 Symmetry-induced collapse of elastic polarization in a strain–energy Hilbert space Hong Jae Kim, Hyeon Sik Won, Hong Min Seung, Joo Hwan Oh, Chung Il Park This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9306751/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 7 You are reading this latest preprint version Abstract Elastic waves intrinsically support multiple symmetry-distinct deformation channels, rendering polarization control fundamentally more complex than in scalar or purely transverse wave systems. While polarization in electromagnetic waves is uniquely defined by the orientation of a transverse field vector, elastic polarization arises from the coexistence of volumetric and deviatoric strain representations that may occupy the same frequency and wavevector. Here we reformulate elastic polarization as an admissibility problem in a strain–energy Hilbert space endowed with a metric defined by the elastic stiffness tensor. We show that symmetry and Bloch periodicity can collapse this Hilbert space, enforcing a unique admissible strain representation within finite frequency windows of a three-dimensional elastic metamaterial. Using a meta-atom that engineers the hierarchy of strain–energy metrics through directional bending inertia, we demonstrate complete non-admissibility of competing elastic polarizations along all principal directions of the Brillouin zone. We further show that the identity of the admissible elastic polarization is governed by the preservation or breakdown of this strain–energy hierarchy, independent of absolute resonance frequency. These results establish elastic polarization as a symmetry-governed state-space phenomenon and introduce Hilbert-space collapse as a general mechanism for deterministic elastic wave control. Physical sciences/Materials science Physical sciences/Physics Full Text Additional Declarations No competing interests reported. Supplementary Files SupplementaryNotesCIParkEPv2.docx Cite Share Download PDF Status: Under Review Version 1 posted Reviewers agreed at journal 07 May, 2026 Reviewers agreed at journal 27 Apr, 2026 Reviewers invited by journal 26 Apr, 2026 Editor invited by journal 21 Apr, 2026 Editor assigned by journal 08 Apr, 2026 Submission checks completed at journal 08 Apr, 2026 First submitted to journal 02 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. 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-9306751","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":630856368,"identity":"bf6fe27c-df53-4bc7-bbbf-3c8955136865","order_by":0,"name":"Hong Jae Kim","email":"","orcid":"","institution":"Samsung (South Korea)","correspondingAuthor":false,"prefix":"","firstName":"Hong","middleName":"Jae","lastName":"Kim","suffix":""},{"id":630856369,"identity":"d81620f9-4cb9-4d3a-8cf9-a87712e239d6","order_by":1,"name":"Hyeon Sik Won","email":"","orcid":"","institution":"Kangwon National 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