Static Self-gravitating Newtonian Elastic Balls

Alho, Artur; Calogero, Simone

doi:10.1007/s00205-020-01551-1

Cited by 6 publications

(35 citation statements)

References 11 publications

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“…In [2] we have written (2.2) in a slightly different form, namely we expressed the exponents of η as θ j = 1 3 γ j . This notation was particularly useful for the examples considered in [2] but here is no longer necessary. Moreover in [2] we used the Lamé material parameters λ, µ instead of κ, ν.…”

Section: Power-law Hyperelastic Constitutive Functionsmentioning

confidence: 99%

“…This notation was particularly useful for the examples considered in [2] but here is no longer necessary. Moreover in [2] we used the Lamé material parameters λ, µ instead of κ, ν. The relation between these two sets of parameters is…”

Section: Power-law Hyperelastic Constitutive Functionsmentioning

confidence: 99%

“…Remark. Examples of well-known hyperelastic models with power-law stored energy function are the Saint Venant-Kirchhoff model, the Signorini model, the John model and the Hadamard model, see [2] and Section 2.2 below.…”

Section: Power-law Hyperelastic Constitutive Functionsmentioning

confidence: 99%

“…The existence of static Newtonian self-gravitating elastic bodies, without any symmetry assumption, has been studied in [4,5] using the Lagrangian formulation of elasticity theory. The first theorem proving the existence of static self-gravitating multibody elastic matter distributions with regular boundaries and arbitrarily large strain has been given in [1] for the Seth model in spherical symmetry and it was later extended to more general elastic models for static self-gravitating balls in [2]. One purpose of this paper is to present numerical evidence showing that some of the assumptions made in [2] are necessary, while other are not, see Section 3.…”

Section: Introductionmentioning

confidence: 99%

“…The first theorem proving the existence of static self-gravitating multibody elastic matter distributions with regular boundaries and arbitrarily large strain has been given in [1] for the Seth model in spherical symmetry and it was later extended to more general elastic models for static self-gravitating balls in [2]. One purpose of this paper is to present numerical evidence showing that some of the assumptions made in [2] are necessary, while other are not, see Section 3. In the next section we define and discuss some general properties of power-law stored energy functions.…”

Section: Introductionmentioning

confidence: 99%

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Self-gravitating static balls of power-law elastic matter

Alho,

Calogero,

Liljenberg

2021

Preprint

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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 κ > 0 and the Poisson ratio −1 < ν ≤ 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.

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Section: Power-law Hyperelastic Constitutive Functionsmentioning

confidence: 99%

Section: Power-law Hyperelastic Constitutive Functionsmentioning

confidence: 99%

Section: Power-law Hyperelastic Constitutive Functionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Self-gravitating static balls of power-law elastic matter

Alho,

Calogero,

Liljenberg

2021

Preprint

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On Self-Gravitating Polytropic Elastic Balls

Calogero

2022

Ann. Henri Poincaré

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Spherically symmetric elastic bodies in general relativity

Alho,

Natário,

Pani

et al. 2024

Class. Quantum Grav.

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The purpose of this review it to present a renewed perspective of the problem of self-gravitating elastic bodies under spherical symmetry. It is also a companion to the papers [Phys. Rev. D105, 044025 (2022)], [Phys. Rev. D106, L041502 (2022)], and [arXiv:2306.16584 [gr-qc]], where we introduced a new definition of spherically symmetric elastic bodies in general relativity, and applied it to investigate the existence and physical viability, including radial stability, of static self-gravitating elastic balls. We focus on elastic materials that generalize fluids with polytropic, linear, and affine equations of state, and discuss the symmetries of the energy density function, including homogeneity and the resulting scale invariance of the TOV equations. By introducing invariant characterizations of physical admissible initial data, we numerically construct mass-radius-compactness diagrams, and conjecture about the maximum compactness of stable physically admissible elastic balls.

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Static Self-gravitating Newtonian Elastic Balls

Cited by 6 publications

References 11 publications

Self-gravitating static balls of power-law elastic matter

Self-gravitating static balls of power-law elastic matter

On Self-Gravitating Polytropic Elastic Balls

Spherically symmetric elastic bodies in general relativity

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