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Isolated bodies

Any finite elastic body subject to a homogeneous isotropic stress (a negative pressure) $\sigma$ will change its volume by

\begin{displaymath}\Delta V = \sigma V / (\lambda + 2 \mu / 3)
\end{displaymath} (4)

where $(\lambda + 2 \mu / 3)$ is the bulk modulus. In this case, the external forces have an isotropic moment $ M = \sigma V $, and eq. (4) is formally the same as eq. (2). Since uniform shear does not change the volume of an isotropic body, the volume change of any finite body under homogeneous stress is described by eq. (4).

Erhard Wielandt