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

Miroslav Bulíček, Josef Málek, K. R. Rajagopal, Jay R. Walton

Research output: Contribution to journalArticlepeer-review

24 Scopus citations

Abstract

© 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.
Original languageEnglish (US)
Pages (from-to)2115-2147
Number of pages33
JournalCalculus of Variations and Partial Differential Equations
Volume54
Issue number2
DOIs
StatePublished - Apr 21 2015
Externally publishedYes

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