Existence of solutions for the anti-plane stress for a new class of “strain-limiting” elastic bodies | Zendy

Miroslav Bulíček | Zendy; Josef Málek | Zendy; Κ. R. Rajagopal | Zendy; Jay R. Walton | Zendy

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Existence of solutions for the anti-plane stress for a new class of “strain-limiting” elastic bodies

Author(s) -

Miroslav Bulíček,

Josef Málek,

Κ. R. Rajagopal,

Jay R. Walton

Publication year - 2015

Publication title -

calculus of variations and partial differential equations

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.329

H-Index - 76

eISSN - 1432-0835

pISSN - 0944-2669

DOI - 10.1007/s00526-015-0859-5

Subject(s) - mathematics , limiting , class (philosophy) , surface (topology) , plane (geometry) , plane stress , range (aeronautics) , boundary (topology) , stress (linguistics) , mathematical analysis , boundary value problem , deformation (meteorology) , geometry , finite element method , computer science , physics , artificial intelligence , linguistics , philosophy , mechanical engineering , materials science , meteorology , engineering , composite material , thermodynamics

© 2015, Springer-Verlag Berlin Heidelberg. The main purpose of this study is to establish the existence of a weak solution to the anti-plane stress problem on V-notch domains for a class of recently proposed new models that could describe elastic materials in which the stress can increase unboundedly while the strain yet remains small. We shall also investigate the qualitative properties of the solution that is established. Although the equations governing the deformation that are being considered share certain similarities with the minimal surface problem, the boundary conditions and the presence of an additional model parameter that appears in the equation and its specific range makes the problem, as well as the result, different from those associated with the minimal surface problem

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