Spherically symmetric self-gravitating elastic bodies: A numerical investigation
Typ
Examensarbete för masterexamen
Program
Publicerad
2020
Författare
Liljenberg, Astrid
Modellbyggare
Tidskriftstitel
ISSN
Volymtitel
Utgivare
Sammanfattning
We investigate numerically the existence and properties of static self-gravitating
elastic balls in the Euler formulation of continuum mechanics. In this formulation
sufficient conditions for the existence of finite radius balls were recently derived
for the Saint Venant-Kirchhoff, quasi-linear John, and Hadamard material models.
Some problems were left open regarding whether or not the sufficient conditions
for existence are also necessary. We find numerical evidence suggesting that the
hyperbolicity condition at the center is indeed necessary, but that several other
conditions on the central densities are stronger than necessary and can be replaced
by weaker ones. We also find evidence of finite radius balls existing in the quasilinear
Signorini model. Furthermore, the properties of static balls in the recently
introduced polytropic elastic material model are investigated and we find numerical
evidence of the existence of static spherically symmetric balls, shells and multibodies.
Mass-radius diagrams are constructed, some of which admit spiral type
curves. Finally, we investigate numerically the existence and properties of timedependent
homologous solutions to the Cauchy-Poisson system for polytropic elastic
balls and find that solutions exist but do not conserve mass unless static.
Beskrivning
Ämne/nyckelord
Self-gravitating body, euler formulation of continuum mechanics, spherical symmetry, hyperelastic material, homologous collapse, mass-radius diagram, hyperbolicity condition, polytropic elastic material model, polytropic equation of state