True stress and engineering stress

Engineering stress

Engineering (nominal) stress is the applied load divided by the original cross-sectional area:

$$\sigma_e = \frac{P}{A_0}$$

Engineering strain is $\varepsilon_e = (L-L_0)/L_0$. It is used in design because $A_0$ is known.

True stress

True stress is the load divided by the instantaneous cross-sectional area at that moment:

$$\sigma_t = \frac{P}{A_i} = \sigma_e\,(1+\varepsilon_e)$$

True strain is $\varepsilon_t = \ln(1+\varepsilon_e)$. These conversions assume constant volume and hold up to the start of necking.