In bulk metal forming, a solid billet or workpiece undergoes large plastic shape change while remaining essentially solid and nearly incompressible.

For plastic deformation of metals, volume is commonly approximated as constant:

$$A_0L_0\approx A_1L_1.$$

If a cylindrical billet is compressed so its height falls from $h_0$ to $h_1$, a convenient logarithmic measure of compressive deformation magnitude is

$$\varepsilon=\ln\left(\frac{h_0}{h_1}\right).$$

For $h_0=100$ mm and $h_1=60$ mm,

$$\varepsilon=\ln(100/60)\approx0.511.$$

Because volume is nearly constant, the cross-sectional area must increase as height decreases.

This same conservation idea appears in rolling, forging, extrusion and drawing: material is redirected rather than removed. Tooling geometry and friction determine how uniformly the material flows and how much additional deformation is required beyond the ideal homogeneous shape change.

Large-deformation strain measures are useful because ordinary engineering strain does not add conveniently over successive large forming steps. Logarithmic strain does: two sequential reductions can be represented by adding their logarithmic strains.

Bulk forming is therefore governed by plastic flow, approximate volume conservation and contact mechanics rather than by chip generation or melting.