Engineering stress
= Engineering stress
{title2=$\sigma=F/A_0$}
<Engineering stress> is axial <force> divided by the initial cross-sectional <area> $A_0$:
$$
\sigma_{\mathrm{eng}}=F/A_0.
$$
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>, $AL=A_0L_0$. 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>.