2020/01/01 by Andrey Chugunov, A. I. Chugunov · 11 citations
Earth and Planetary Sciences · Mathematics · Medicine · Physics and Astronomy · #Astrophysics #Cauchy stress tensor #Classical mechanics #Composite material #Crust #Finite element method #Geometry #Geophysics #High-pressure geophysics and materials #Infinitesimal strain theory #Materials science #Mathematics #Mechanics #Medicine #Neutron star #Physics #Pulsars and Gravitational Waves Research #Shear (geology) #Shear modulus #Shear stress #Strain (injury) #Symmetry (geometry) #Tensor (intrinsic definition) #Thermodynamics #astro-ph.HE #astro-ph.SR #cond-mat.mtrl-sci #earthquake and tectonic studies #nucl-th #physics.plasm-ph
paper · pdf · doi:10.1093/mnrasl/slaa173
published in Monthly Notices of the Royal Astronomical Society Letters 500(1), L17-L21 (Oxford University Press) · 5 pages, accepted for publication in MNRAS:Letters
openalex publication_date 2020/01/01 · arxiv created 2020/10/15 · openalex created_date 2020/10/22 · arxiv updated 2020/11/20 · openalex updated_date 2026/08/05
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 modelled as Coulomb solids (dusty plasma, trapped ions, etc.). I demonstrate that the Coulomb part of the stress–strain tensor has additional symmetry: contraction Bijil = 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: ∑ Z 0.12 nZ Z5/3e2 /ae. Here summation is taken over ion species, nZ is number density of ions with charge Ze. Finally, ae = (4πne/3)−1/3 is electron sphere radius. Quasi-neutrality condition ne = ∑ZZnZ is assumed.