Mathematical study of boundary-value problems within the framework of Steigmann-Ogden model of surface elasticity

DOI10.1007/S00161-015-0439-0zbMath1348.35260OpenAlexW349108900MaRDI QIDQ332489

Victor A. Eremeyev, Leonid P. Lebedev

Publication date: 8 November 2016

Published in: Continuum Mechanics and Thermodynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00161-015-0439-0

zbMATH Keywords

weak solutionsexistence of solutionseigenfrequency analysisnanomechanicsSteigmann-Ogden modelsurface stresses

Mathematics Subject Classification ID

Classical linear elasticity (74B05) Weak solutions to PDEs (35D30) PDEs in connection with mechanics of deformable solids (35Q74)

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Cites Work

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• On effective properties of materials at the nano- and microscales considering surface effects
• Solvability of boundary value problems in a theory of plane-strain elasticity with boundary reinforcement
• A continuum theory of elastic material surfaces
• Addenda to our paper: A continuum theory of elastic material surfaces
• Edge contact forces and quasi-balanced power
• How contact interactions may depend on the shape of Cauchy cuts in \(N\)th gradient continua: approach ``à la d'Alembert
• Asymptotic Behaviour of the Elastic Solution near the Tip of a Crack Situated at a Nonideal Interface
• Effect of surface elasticity on an interface crack in plane deformations
• On the spectrum and stiffness of an elastic body with surface stresses
• A scaling law for properties of nano-structured materials
• Generalized Hooke's law for isotropic second gradient materials
• Integral equation methods in plane-strain elasticity with boundary reinforcement
• Elastic surface—substrate interactions
• Plane deformations of elastic solids with intrinsic boundary elasticity
• Functional Analysis in Mechanics
• A clarification of the role of crack-tip conditions in linear elasticity with surface effects
• Existence of weak solutions in elasticity
• On the existence of solution in the linear elasticity with surface stresses
• The effect of surface stress on an interface crack in linearly elastic materials

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