Milling matter in a crusher: modeling based on extended micropolar theory

  • Mariia Fomicheva
  • Elena N. VilchevskayaEmail author
  • Wolfgang H. Müller
  • Nikolay Bessonov
Original Article


This paper presents a new aspect in generalized continuum theory, namely micropolar media showing structural change. Initially, the necessary theoretical framework for a micropolar continuum is presented. To this end, the standard macroscopic equations for mass and linear and angular momentum are complemented by a recently proposed kinetic equation for the moment of inertia tensor containing a production term. An example for this term is studied: A continuous stream of matter through a crusher is considered. The matter is milled, and consequently, the total number of particles will change. This structural change is the reason for the production of microinertia. The matter is modeled as a Hookean as well as a linear viscous material. The equations are solved numerically based on a finite difference technique.


Micropolar media Production of microinertia Viscous material Crusher 


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Support of this work by a Grant from the Russian Foundation for Basic Research (16-01-00815) is gratefully acknowledged.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Mariia Fomicheva
    • 2
  • Elena N. Vilchevskaya
    • 1
    • 2
    Email author
  • Wolfgang H. Müller
    • 3
  • Nikolay Bessonov
    • 1
    • 2
  1. 1.Institute for Problems in Mechanical Engineering of the Russian Academy of SciencesSt. PetersburgRussia
  2. 2.Peter the Great Saint-Petersburg Polytechnic UniversitySt. PetersburgRussia
  3. 3.Institut für Mechanik, Kontinuumsmechanik und MaterialtheorieTechnische Universität BerlinBerlinGermany

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