Existence of solutions for the anti-plane stress for a new class of “strain-limiting” elastic bodies
KAUST Grant NumberKUS-C1-016-04
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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.
CitationBulíček M, Málek J, Rajagopal KR, Walton JR (2015) Existence of solutions for the anti-plane stress for a new class of “strain-limiting” elastic bodies. Calc Var 54: 2115–2147. Available: http://dx.doi.org/10.1007/s00526-015-0859-5.
SponsorsM. Bulíček and J. Málek acknowledge the support of the project LL1202 in the programme ERC-CZ funded by the Ministry of Education, Youth and Sports of the Czech Republic. M. Bulíček is a researcher in the Charles University Centre for Mathematical Modelling, Applied Analysis and Computational Mathematics (Math MAC). K. R. Rajagopal thanks the National Science Foundation and the Office of Naval Research for their support of his work. He and J. R. Walton acknowledge support by Award No. KUS-C1-016-04 from King Abdullah University of Science and Technology.We are thankful to Emilio Acerbi for several valuable comments and suggestions.
PublisherSpringer Science + Business Media