A similarity solution for the Mooney material (Q1601109)

A new static similarity deformation for Mooney-Rivlin incompressible isotropic materials is provided. This similarity solution is not an invariant solution under the action of classical Lie simmetry group of balance equations for isotropic incompressible hyperelastic materials, and for this reason it is not contained in the list provided in the paper [\textit{J. M. Hill}, Q. Appl. Math. 40, 287-291 (1982; Zbl 0507.73032); see also \textit{D. Levi} and \textit{C. Rogers}, J. Elasticity 24, 295-300 (1990; Zbl 0733.73020)]. The deformation maps some families of constant lines in the undeformed configuration in straight lines in the deformed configuration.