Modelling Forces in Continuum Mechanics

  • Jean Salençon


In Sect. 6 of the previous chapter we set out some general results which follow from the principle of virtual work, expressed in terms of wrenches. These require, for any model:

• The law of mutual actions, equivalent to the statement (4.1) in Chap. IV, expressing the fact that the virtual rate of work by internal forces must be zero in any rigid body motion
$$\left\{ {\begin{array}{*{20}{c}} {forS,\left[ {{{F}_{i}}} \right] = 0,} \\ {\forall S',\left[ {{{F}_{i}}} \right] = 0.} \\ \end{array} } \right.$$
The fundamental law of dynamics
$$\left\{ {\begin{array}{*{20}{c}} {{\text{in a Galilean frame }}\mathcal{R},} \hfill \\ {{\text{for }}S,\left[ {{{\mathcal{F}}_{e}}} \right] = \left[ {\mathcal{M}a} \right],} \hfill \\ {\forall S',\left[ {{{{\mathcal{F}'}}_{e}}} \right] = \left[ {\mathcal{M}a'} \right].} \hfill \\ \end{array} } \right.$$

Key Work

Body forces Surface forces Pressure Perfect fluid Viscous fluid Hydrostatics Cauchy stress tensor Contact forces Stress vector Facet Equations of motion Piola-Kirchhoff stress tensor 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Jean Salençon
    • 1
  1. 1.Laboratoire de Mécanique des SolidesÉcole PolytechniquePalaiseau CedexFrance

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