Popovics

There are a series of curves based on the work of Popovics.

These have been adjusted and are based on the Thorenfeldt base curve.

In the Canadian offshore code (CAN/CSA S474-04) this is characterised by

$$\frac{f}{f_c}=k_3 \eta \frac{n}{n-1+\eta^{n k}}$$

with (in MPa)

$$\begin{aligned} & \eta=\frac{\varepsilon}{\varepsilon_c} \\ & k_3=0.6+\frac{10}{f_c} \\ & n=0.8+\frac{f_c}{17} \\ & \varepsilon_c=\frac{f_c}{E_c} \frac{n}{n-1} \\ & k= \begin{cases}1 & \eta \leq 1 \\ 0.67+\frac{f_c}{62} & \eta>1\end{cases} \end{aligned}$$

The peak strain is referred to elsewhere as $\varepsilon_{p o p}$.

$$\varepsilon_{pop}=\varepsilon_c$$

All the concrete models require a strength value and a pair of strains: the strain at peak stress or transition strain and the failure strain.