Self-gravitating static balls of power-law elastic matter

Ve study a class of power-law stored energy functions for spherically symmetric elastic bodies that includes well-known material models, such as the Saint Venant-Kirchhoff, Hadamard. Signorini and John models. We identify a finite subclass of these stored energy functions, which we call Lamn type, that depend on no more material parameters than the bulk modulus kappa > 0 and the Poisson ratio -1 < nu <= 1/2. A general theorem proving the existence of static self-gravitating elastic balls for some power-law materials has been given elsewhere. In this paper numerical evidence is providel that some hypotheses in this theorem are necessary, while others are not.