# Understanding stress-strain calculations

I'm trying to compute the stress-strain curve for an elastic material with cylindrical geometry subject to an increasing uniaxial load. I understand that this requires:

stress = $F/A_0$ where $A_0$, the initial cross-sectional area of the cylinder, is a constant whereas $F$ is increasing.

strain = $\Delta{L}/L_0$ where $\Delta{L}$ varies but $L_0$, the inital length of the cylinder, is constant.

Is my understanding correct? My confusion stems from the fact that the wikipedia page on Young's modulus says that $A_0$ is the actual cross-sectional area rather than the original cross-sectional area. Subject to an increasing uniaxial load the actual cross-sectional area would be decreasing so $A_0$ wouldn't be a constant.