Brittle-elastic bar and waiting links

The force $P$

$$P(z,c)= Y A (1-c) \left( \frac{z}{L} - 1 \right), ... ... 0 & & \mbox{otherwise} \end{array} \right., \quad c(0)=0$$ (1)

$z$ - length, $c$ - damage parameter, $L$ - equilibrium length, $Y$ - Young's modulus, $A$ - cross section area

$\alpha$ - fraction of material put into the shorter rod

Cross-sections $s_1$ and $s_2$ of rods are: $s_1(\alpha)=\frac{\alpha}{L} \quad \mbox{and } s_2(\alpha)=\frac{1-\alpha}{\Delta}$

Figure 1: Waiting Element