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Solving the Problem of Gravitational Compression of a Layered Sphere (by the Example of the Earth)

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Abstract

The problem of spherically symmetric, gravitational compression of an isotropic hyperelastic layered sphere which modeling the region of the Earth below the Mohorovičič boundary is solved. The known mechanical characteristics of the Earth in the compressed state are used to find its characteristics in the unstrained state obtained by adiabatic or isothermal stress relief. The stress state differs significantly from the state of purely hydrostatic compression. The minimum bulk compression and maximum radial tension occur not on the boundary of the sphere but in depth at certain distances from the boundary.

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REFERENCES

  1. K. E Bullen, The Earth Density, Wiley, New York (1975).

    Google Scholar 

  2. Sir H. Jeffreys, The Earth, Cambridge Univ. Press, Cambridge (1970).

    Google Scholar 

  3. A. M. Dziewonsky and F. Gilbert, “Observations of normal modes from 84 recordings of the Alaskan earthquakes of 1964 March 28, II. Further remarks based on new spheroidal overtone data,” Geophys. J. Astr. Soc., 35, 401-437 (1973).

    Google Scholar 

  4. T. N. Jordan and D. L. Anderson, “Earth structure from free oscillations and travel times,” Geophys. J. Astr. Soc., 36, 411-459 (1974).

    Google Scholar 

  5. V. N. Solodovnikov, “Constitutive equations of an isotropic hyperelastic body,” J. Appl. Mech. Tech. Phys., 41, No. 6, 1118-1123 (2000).

    Google Scholar 

  6. V. N. Solodovnikov, “Stability of deformation of isotropic hyperelastic bodies,” J. Appl. Mech. Tech. Phys., 42, No. 6, 1043-1052 (2001).

    Google Scholar 

  7. V. N. Solodovnikov, “On the theory of deformation of isotropic hyperelastic bodies,” J. Appl. Mech. Tech. Phys., 45, No. 1, 99-106 (2004).

    Google Scholar 

  8. F. Birch, “Elasticity and constitution of the Earth's interior,” Geophys. Res., 57, 227-286 (1952).

    Google Scholar 

  9. F. D. Murnaghan, Finite Deformation of Unelastic Solid, John Wiley and Sons, New York (1951).

    Google Scholar 

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Authors and Affiliations

  1. Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk, 630090, Russia

    L. V. Baev & V. N. Solodovnikov

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  1. L. V. Baev
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  2. V. N. Solodovnikov
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Baev, L.V., Solodovnikov, V.N. Solving the Problem of Gravitational Compression of a Layered Sphere (by the Example of the Earth). Journal of Applied Mechanics and Technical Physics 45, 860–870 (2004). https://doi.org/10.1023/B:JAMT.0000046035.96555.d6

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  • DOI: https://doi.org/10.1023/B:JAMT.0000046035.96555.d6

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