Deep drawing forms a flat sheet blank into a hollow cup-like shape by pushing material into a die with a punch.

A blank holder controls the flange surrounding the die opening. If holding force is too low, compressive circumferential stress can make the flange wrinkle. If it is too high, friction prevents material from feeding inward and the wall can tear.

A common severity measure is the drawing ratio

$$DR=\frac{D_0}{D_p},$$

where $D_0$ is initial blank diameter and $D_p$ is punch diameter.

For a $100$ mm blank drawn by a $60$ mm punch,

$$DR=\frac{100}{60}=1.67.$$

Larger drawing ratio means more material must be pulled from the flange into the cup in one operation and therefore increases difficulty.

The sheet does not deform uniformly. Material in the flange experiences radial tension and circumferential compression; the cup wall carries tensile load; contact at punch and die radii changes direction under friction.

Tool radii, lubrication, material anisotropy and sheet thickness all influence failure. Complex deep parts may require several drawing and redrawing stages rather than one severe operation.

Deep drawing demonstrates why sheet forming must be understood as controlled material flow under multiaxial stress, not simply as pressing sheet against a shape.