Memory-dependent and size-dependent effects on nonlinear electro-magneto-thermo-viscoelastic vibration analysis of a polymer spherical microshell with fractional order strain

Memory-dependent and size-dependent effects on nonlinear electro-magneto-thermo-viscoelastic vibration analysis of a polymer spherical microshell with fractional order strain | 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 Memory-dependent and size-dependent effects on nonlinear electro-magneto-thermo-viscoelastic vibration analysis of a polymer spherical microshell with fractional order strain Wei Peng, Jingsong Luan, Ashraf M. Zenkour This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7281323/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 9 You are reading this latest preprint version Abstract The stress-strain prediction for viscoelastic materials using integer-order thermoviscoelastic models faces challenges due to the limitations of integer-order derivatives.With the miniaturization of devices, size-dependent effects on elastic deformation become more significant. Additionally, experiments and theories indicate that thermal conductivity in materials should not be treated as a constant in practical analyses. This study develops a fractional-order thermoviscoelastic model by integrating the fractional three-phase-lag heat conduction model, the fractional strain model and the nonlocal elasticity theory. The proposed model is then applied to analyze the nonlinear electro-magneto-thermo-viscoelastic response of a polymer spherical microshell under ramp-type heating and an external magnetic field. Taking into account the variable thermal conductivity, the nonlinear governing equations are derived. The Laplace and Kirchhoff transformations are employed to derive and solve the governing equations. The dimensionless temperature, induced magnetic field, displacement and stress are obtained and illustrated graphically. The results show that the nonlinear thermoviscoelastic response of the polymer spherical shell can be adjusted by the suitably modified parameters, which strongly depend on the size-dependent effect, memory-dependent effect and the variable thermal conductivity. Nonlinear electro-magneto-thermo-viscoelastic vibration response spherical microshell size-dependent effect fractional-order strain variable thermal conductivity Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 21 Sep, 2025 Reviews received at journal 31 Aug, 2025 Reviews received at journal 12 Aug, 2025 Reviewers agreed at journal 06 Aug, 2025 Reviewers agreed at journal 05 Aug, 2025 Reviewers invited by journal 05 Aug, 2025 Editor assigned by journal 04 Aug, 2025 Submission checks completed at journal 04 Aug, 2025 First submitted to journal 03 Aug, 2025 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. 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Additionally, experiments and theories indicate that thermal conductivity in materials should not be treated as a constant in practical analyses. This study develops a fractional-order thermoviscoelastic model by integrating the fractional three-phase-lag heat conduction model, the fractional strain model and the nonlocal elasticity theory. The proposed model is then applied to analyze the nonlinear electro-magneto-thermo-viscoelastic response of a polymer spherical microshell under ramp-type heating and an external magnetic field. Taking into account the variable thermal conductivity, the nonlinear governing equations are derived. The Laplace and Kirchhoff transformations are employed to derive and solve the governing equations. The dimensionless temperature, induced magnetic field, displacement and stress are obtained and illustrated graphically. 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