Engineering stress ($\sigma =F/A_0$)

Engineering stress is axial force divided by the initial cross-sectional area $A_0$:It uses a fixed geometric reference even as a specimen stretches. The axial Cauchy stress tensor, by contrast, is $F/A$ for a uniform current cross-section $A$. During extension with decreasing area, the two quantities diverge.

For uniform deformation at approximately constant volume, $AL=A_0{L}_0$. With engineering strain $e=(L-L_0)/L_0$, the relation is ${\sigma }_{\mathrm{Cauchy}}=(1+e){\sigma }_{\mathrm{eng}}$. It assumes a uniform axial stress state and fails as a local conversion after pronounced necking unless the local geometry is measured. In a tensile modulus experiment, engineering stress versus engineering strain gives the initial Young's modulus. Its later maximum identifies a maximum load per original area, rather than a universal local failure stress.