{"paper_id":"3aeb8518-0e9d-45dd-ad37-8a16e703ba08","body_text":"Dynamic Normal Stress Determination at the Rigid Sphere-Elastic Half-Space Interface: A Particle Dynamics Approach | 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 Dynamic Normal Stress Determination at the Rigid Sphere-Elastic Half-Space Interface: A Particle Dynamics Approach Hong Xie, Zhiping Zeng, Miao Su, Jun Luo, Hao Ge, Gonglian Dai This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5019862/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 The Hertz theory provides a foundation for understanding the contact behavior between elastic bodies. However, the theory's reliance on static equilibrium assumptions limits its applicability to dynamic scenarios, particularly where the contact interface experiences rapid changes in stress due to impact or vibration. This paper addresses the gap in the literature regarding the dynamic normal stress at the contact interface between a rigid sphere and an elastic half-space based on the theory of particle dynamics. Our approach begins by establishing a system of particle dynamics equations for the interface contact zone. By decoupling these equations based on the lateral and tangential motion characteristics of the particles, we derive a unified normal dynamics equation that describes the relative relationship between the normal strain of each particle and the center point of the interface. Utilizing the dynamic equation of the interface collision center and the motion equation of the small ball, we determine the absolute values of the normal strain of each particle in the interface contact zone. The research results demonstrate that the lateral and tangential strains (forces) prior to collision do not directly affect the sphere motion in the normal direction, while the incremental strains (forces) post-collision significantly do. By analyzing the normal dynamic equations of the contact zone, we obtain the lateral stress increment, tangential stress increment, and the distribution law of normal stress for each particle at the interface. In conclusion, the normal strain values obtained using our proposed method, when compared with those from Hertz theory at the maximum collision depth, are significantly greater. This indicates that our method is more effective in explaining contact interface damage phenomena, which are not adequately addressed by Hertz theory. The findings have implications for understanding and predicting contact interface failure in engineering applications, particularly under dynamic loading conditions. Physical sciences/Physics/Statistical physics, thermodynamics and nonlinear dynamics/Nonlinear phenomena Physical sciences/Physics/Applied physics Rigid small sphere Elastic half-space Collision Hertz theory Interface contact stress Particle dynamics Full Text Additional Declarations There is NO Competing Interest. 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. 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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-5019862\",\"acceptedTermsAndConditions\":true,\"allowDirectSubmit\":true,\"archivedVersions\":[],\"articleType\":\"Article\",\"associatedPublications\":[],\"authors\":[{\"id\":353128357,\"identity\":\"304e6564-95c3-4b79-b377-c3948a5a4d32\",\"order_by\":0,\"name\":\"Hong 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