New classes of linearizable hyperelastic compressible materials

The governing equations for plane deformations of isotropic compressible hyperelastic materials are highly nonlinear, and consequently, very few exact solutions are known. At present, there are only two classes of material in which the governing equations are known to be linearizable. The first is the harmonic material, and the second is a class of material recently introduced by the authors. In this paper, we show new materials exist where the governing equations are linearizable.