{
  "id": "2010.08398",
  "version": "v1",
  "published": "2020-10-15T09:11:52.000Z",
  "updated": "2020-10-15T09:11:52.000Z",
  "title": "Neutron star crust in Voigt approximation: general symmetry of the stress-strain tensor and an universal estimate for the effective shear modulus",
  "authors": [
    "Andrey Chugunov"
  ],
  "comment": "5 pages, accepted for publication in MNRAS:Letters",
  "categories": [
    "astro-ph.HE",
    "astro-ph.SR",
    "cond-mat.mtrl-sci",
    "nucl-th",
    "physics.plasm-ph"
  ],
  "abstract": "I discuss elastic properties of neutron star crust in the framework of static Coulomb solid model when atomic nuclei are treated as non-vibrating point charges; electron screening is neglected. The results are also applicable for solidified white dwarf cores and other materials, which can be modeled as Coulomb solids (dusty plasma, trapped ions, etc.). I demonstrate that the Coulomb part of the stress-strain tensor has additional symmetry: contraction $B_{ijil}=0$. It does not depend on the structure (crystalline or amorphous) and composition. I show as a result of this symmetry the effective (Voigt averaged) shear modulus of the polycrystalline or amorphous matter to be equal to $-2/15$ of the Coulomb (Madelung) energy density at undeformed state. This result is general and exact within the model applied. Since the linear mixing rule and the ion sphere model are used, I can suggest a simple universal estimate for the effective shear modulus: $\\sum_Z 0.12\\, n_Z Z^{5/3}e^2 /a_\\mathrm{e}$. Here summation is taken over ion species, $n_Z$ is number density of ions with charge $Ze$. Finally $a_\\mathrm{e}=(4 \\pi n_\\mathrm{e}/3)^{-1/3}$ is electron sphere radius. Quasineutrality condition $n_\\mathrm{e}=\\sum_Z Z n_Z$ is assumed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-10-15T09:11:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "neutron star crust",
      "effective shear modulus",
      "stress-strain tensor",
      "universal estimate",
      "general symmetry"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}