bulk-modulus-turns-volume-strain-into-pressure - Elasticity: Stress, Strain, and Material Response Step by Step

Bulk response uses positive pressure and volume-change magnitudes. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Bulk response starts from volume and volume change

The book uses positive compression magnitudes. Volume and volume change are checked before pressure is accepted.

V=6\ \text{m}^{3}\qquad \Delta V=1\ \text{m}^{3}

Pressure follows the volume-change ratio

Hold the starting volume and bulk modulus fixed. The pressure column follows the checked volume change.

\begin{array}{c|c|c|c}V&\Delta V&K&\Delta P\\6\ \text{m}^{3}&\tfrac{1}{2}\ \text{m}^{3}&12\ \text{Pa}&1\ \text{Pa}\\6\ \text{m}^{3}&1\ \text{m}^{3}&12\ \text{Pa}&2\ \text{Pa}\\6\ \text{m}^{3}&2\ \text{m}^{3}&12\ \text{Pa}&4\ \text{Pa}\\\end{array}

Bulk modulus turns volume strain into pressure change

This checked ledger uses positive compression magnitudes; sign conventions are outside this training surface.

\Delta P=K\frac{\Delta V}{V}=12\ \text{Pa}\cdot\frac{1\ \text{m}^{3}}{6\ \text{m}^{3}}=2\ \text{Pa}