Mechanics of Solids (about journal) Mechanics of Solids
A Journal of Russian Academy of Sciences
 Founded
in January 1966
Issued 6 times a year
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IssuesArchive of Issues2024-3pp.1823-1831

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E.A. Lyamina, "Expansion of a Spherical Cavity in an Infinite Dilatant Medium Obeying the Drucker–Prager Yield Criterion and a Non-Associated Plastic Flow Rule," Mech. Solids. 59 (3), 1823-1831 (2024)
Year 2024 Volume 59 Number 3 Pages 1823-1831
DOI 10.1134/S0025654424604014
Title Expansion of a Spherical Cavity in an Infinite Dilatant Medium Obeying the Drucker–Prager Yield Criterion and a Non-Associated Plastic Flow Rule
Author(s) E.A. Lyamina (Ishlinsky Institute for Problems in Mechanics RAS, Moscow, 119526 Russia, lyamina@inbox.ru)
Abstract The distributions of the principal stresses, the radial velocity, and the relative density are determined in an infinite dilatant medium in which a spherical cavity expands from a zero radius. The medium obeys the Drucker–Prager yield criterion. The plastic potential is also of Drucker–Prager type but differs from the yield criterion. Moreover, it involves the relative density and results in the incompressibility equation at a certain relative density value. A detailed analysis of the solution is provided for a specific dependence of the plastic potential on the relative density. It is shown that the qualitative behavior of the solution near the cavity’s surface depends on a constitutive parameter involved in this dependence. A numerical example illustrates the general solution.
Keywords spherical cavity, dilatant material, non-associated plastic flow rule, rigid plasticity
Received 29 May 2024Revised 17 June 2024Accepted 18 June 2024
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