Modelling Forces in Continuum Mechanics

Abstract

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

$$\left\{ {\begin{array}{*{20}{c}} {forS,\left[ {{{F}_{i}}} \right] = 0,} \\ {\forall S',\left[ {{{F}_{i}}} \right] = 0.} \\ \end{array} } \right.$$

(1.1)

The fundamental law of dynamics

$$\left\{ {\begin{array}{*{20}{c}} {{\text{in a Galilean frame }}\mathcal{R},} \hfill \\ {{\text{for }}S,\left[ {{{\mathcal{F}}_{e}}} \right] = \left[ {\mathcal{M}a} \right],} \hfill \\ {\forall S',\left[ {{{{\mathcal{F}'}}_{e}}} \right] = \left[ {\mathcal{M}a'} \right].} \hfill \\ \end{array} } \right.$$

(1.2)