On a non-symmetrical plane strain deformation for hyperelastic materials. (Q2746247)

The paper is devoted to the study of a non-symmetrical plane deformation which generalizes the inflation of a long circular incompressible tube. The authors have previously shown [\textit{J. M. Hill} and \textit{A. M. Milan}, Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 455, No. 1983, 1067--1082 (1999; Zbl 0937.74011)] that the deformation of the solution considered here satisfies balance equations when the constitutive equations are of Varga type or of perfectly elastic Mooney kind. Now they ask which is the largest sub-class of isotropic incompressible materials for which the considered deformation is a solution of balance equations. The authors solve this problem and found that only in a special class of materials it is possible to find nontrivial solutions in the class of deformations considered.