Definitions of Continuum Mechanics

  • Sergey P. Kiselev
  • Evgenii V. Vorozhtsov
  • Vasily M. Fomin
Part of the Modeling and Simulation in Science, Engineering and Technology book series (MSSET)


The purpose of the present chapter is to provide a systematic introduction of the basic concepts and definitions of the tensors of strains and stress. The presentation begins with a section, in which we briefly present the elements of tensor analysis. Tensor analysis enables one to present in a simple and elegant form the fundamantals of continuum mechanics, and it is used systematically subsequently throughout the book. We then introduce the definition of the tensors of strains and stress, which characterize a continuum, in a reference frame and in an actual frame without any assumptions on the smallness of strains.


Reference Frame Stress Tensor Basis Vector Strain Tensor Vortex Line 
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Copyright information

© Springer Science+Business Media New York 1999

Authors and Affiliations

  • Sergey P. Kiselev
    • 1
  • Evgenii V. Vorozhtsov
    • 1
  • Vasily M. Fomin
    • 1
  1. 1.Institute of Theoretical and Applied MechanicsRussian Academy of SciencesNovosibirskRussia

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