Elements of Continuum Mechanics

  • Ralf Greve
  • Heinz Blatter
Part of the Advances in Geophysical and Environmental Mechanics and Mathematics book series (AGEM)


Continuum mechanics is concerned with the motion and deformation of continuous bodies (for instance, a glacier). A body consists of an infinite number of material elements, called particles. For any time t, each particle is identified by a position vector x (relative to a prescribed origin O) in the physical space ε, and the continuous set of position vectors for all particles of the body is called a configuration κ of the body. If t is the actual time, the corresponding configuration is called the present configuration κ t . In addition, we define a reference configuration κ r which refers to a fixed (or initial) time t 0.


Deformation Gradient Momentum Balance Jump Condition Material Volume Cauchy Stress Tensor 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Ralf Greve
    • 1
  • Heinz Blatter
    • 2
  1. 1.Inst. Low Temperature ScienceHokkaido UniversitySapporoJapan
  2. 2.Inst. Atmospheric & Climate ScienceETH ZürichZürichSwitzerland

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