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
Article

Abstract

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.

Mathematics subject classifications

35Q74 74B20 49Q05 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Miroslav Bulíček
    • 1
  • Josef Málek
    • 1
  • K. R. Rajagopal
    • 2
  • Jay R. Walton
    • 3
  1. 1.Faculty of Mathematics and Physics, Mathematical InstituteCharles University in PraguePrague 8Czech Republic
  2. 2.Department of Mechanical EngineeringTexas A&M UniversityCollege StationUSA
  3. 3.Department of MathematicsTexas A&M UniversityCollege StationUSA

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