Modeling of problems with small-scale liquid inclusions - Influence of initial stress state

Modeling of problems with small-scale liquid inclusions - Influence of initial stress state | 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 Modeling of problems with small-scale liquid inclusions - Influence of initial stress state Sofia G. Mogilevskaya, Zhilin Han, Henryk K. Stolarski This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9278770/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 problem of a small liquid inclusion within an elastic matrix subjected to initial stress and external load is considered. To evaluate the elastic fields in the material system, the two-stage process is proposed. In each stage, the inclusion/matrix interface is described by the Gurtin-Murdoch model of material surface. Stage I is designed to estimate the initial stresses that develop in all parts of the material system, e.g., during the fabrication process. Stage II represents the analysis of deformations and stresses due to external load. In that stage, the effects of initial stresses are included. The governing equations for the second stage problem are derived by linearization of the non-linear formulation. Three-dimensional equations for the two stages are provided and specified for two-dimensions. To illustrate the approach, the isotropic matrix is considered, the plane strain assumptions are made, and an inclusion is assumed to be of circular shape. Closed-form solutions for the elastic fields in the material system are obtained under two different descriptions of the matrix material. Those expressions are compared with solutions previously reported in the literature. Small liquid inclusions Initial stresses Surface effects Gurtin-Murdoch theory Zaremba-Jaumann rate Full Text Additional Declarations The authors declare no competing interests. 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-9278770","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":615216469,"identity":"65c12ea3-4257-4a9d-b9b5-e41e97234405","order_by":0,"name":"Sofia G. 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