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Physical Mesomechanics

, Volume 20, Issue 3, pp 250–262 | Cite as

Micropolar theory with production of rotational inertia: A farewell to material description

  • W. H. MüllerEmail author
  • E. N. Vilchevskaya
  • W. Weiss
Article

Abstract

This paper takes a new look at micropolar media. Initially the necessary theoretical framework for a micropolar continuum is presented. To this end the standard macroscopic equations for mass, linear and angular momentum are complemented by a recently proposed kinetic equation for the moment of inertia tensor containing a production term. The main purpose of this paper is to study possible forms of this production term and its effects. For this reason two examples are investigated. In the first example we study a continuum of hollow particles subjected to an external pressure and gravity, such that the number of particles does not change. In the second example a continuous stream of matter through a crusher is considered so that the total number of particles will change. In context with these examples it will also become clear that the traditional Lagrangian way of describing the motion of solids is no longer adequate and should be superseded by an Eulerian approach.

Keywords

micropolar media spatial description characteristics transport equations 

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References

  1. 1.
    Eringen, A.C. and Kafadar, C.B., Polar Field Theories, Continuum Physics IV, London: Academic Press, 1976.Google Scholar
  2. 2.
    Eringen, C., Nonlocal Continuum Field Theories, New York: Springer, 2002.zbMATHGoogle Scholar
  3. 3.
    Eremeyev, V.A., Lebedev, L.P., and Altenbach, H., Foundations of Micropolar Mechanics, Heidelberg: Springer, 2012.zbMATHGoogle Scholar
  4. 4.
    Ivanova, E.A. and Vilchevskaya, E.N., Micropolar Continuum in Spatial Description, Cont. Mech. Thermodyn., 2016, vol. 28, no. 6, pp. 1759–1780.MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Eringen, A.C., Mechanics of Continua, Robert E. Krieger Publishing Company, 1980.zbMATHGoogle Scholar
  6. 6.
    Müller, I., Thermodynamics, Boston: Pitman, 1985.zbMATHGoogle Scholar
  7. 7.
    NISTFiPy Package, 2017. http://www.ctcms.nist.gov/fipy/index.html.Google Scholar
  8. 8.
    Guyer, J.E., Wheeler, D., and Warren, J.A., FiPy: Partial Differential Equations with Python, Cont. Mech. Thermodyn., 2009, vol. 11, no. 3, pp. 6–15.Google Scholar
  9. 9.
    Mitchell, A.R., Recent Developments in the Finite Element Method, Computational Techniques and Applications: CTAC. V. 83, New York: Elsevier North-Holland, 1984, pp. 6–15.Google Scholar
  10. 10.
    Courant, R. and Hilbert, D., Methods of Mathematical Physics. V. II: Partial Differential Equations, New York: Wiley Interscience, 1962.zbMATHGoogle Scholar
  11. 11.
    Müller, I. and Ruggeri, T., Rational Extended Thermodynamics. V. 37, New York: Springer, 2013.zbMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2017

Authors and Affiliations

  • W. H. Müller
    • 1
    Email author
  • E. N. Vilchevskaya
    • 2
    • 3
  • W. Weiss
    • 1
  1. 1.Institute of MechanicsTechnische Universität BerlinBerlinGermany
  2. 2.Institute for Problems in Mechanical EngineeringRussian Academy of SciencesSt. PetersburgRussia
  3. 3.Peter the Great Saint-Petersburg Polytechnic UniversitySt. PetersburgRussia

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