Advances in Theoretical and Mathematical Physics

Volume 26 (2022)

Number 9

Self-gravitating static balls of power-law elastic matter

Pages: 2885 – 2908

DOI: https://dx.doi.org/10.4310/ATMP.2022.v26.n9.a1

Authors

Artur Alho (Center for Mathematical Analysis, Geometry and Dynamical Systems, Instituto Superior Técnico, Universidade de Lisboa, Portugal)

Simone Calogero (Department of Mathematical Sciences, Chalmers University of Technology, University of Gothenburg, Sweden)

Astrid Liljenberg (Department of Mathematical Sciences, Chalmers University of Technology, University of Gothenburg, Sweden)

Abstract

We 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 Lamé type, that depend on no more material parameters than the bulk modulus $\kappa \gt 0$ and the Poisson ratio $-1 \lt \nu \leq 1/2$. 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 provided that some hypotheses in this theorem are necessary, while others are not.

Published 30 October 2023