Surface of Discontinuity in Anisotropic Reduced Cosserat Continuum: Uniqueness Theorem for Dynamic Problems with Discontinuities

Abstract

An isolated surface that moves relative to the micropolar media and across which the first derivatives of variables are discontinuous is considered. The reduced Cosserat continuum is an elastic medium where all translations and rotations are independent. Moreover, the force stress tensor is asymmetric and the couple stress tensor is equal to zero. Continuity conditions were established and it is shown that the first derivative of the rotation vector cannot have discontinuities. It is demonstrated that the solution in this case is unique.

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Correspondence to A. E. Anisimov or E. V. Zdanchuk or V. V. Lalin.

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Translated by E. Oborin

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Anisimov, A.E., Zdanchuk, E.V. & Lalin, V.V. Surface of Discontinuity in Anisotropic Reduced Cosserat Continuum: Uniqueness Theorem for Dynamic Problems with Discontinuities. Mech. Solids 55, 1051–1056 (2020). https://doi.org/10.3103/S0025654420070031

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Keywords:

  • micropolar continuum
  • reduced Cosserat continuum
  • surface of strong discontinuity
  • granular materials
  • kinematic and dynamic conditions
  • uniqueness theorem