Void swelling volume fraction relation ($S=f/(1-f)$)

If a fixed matrix volume $V_0$ acquires cavity volume $V_c$, then $S=V_c/V_0$ and the cavity fraction of the current total volume is $f=V_c/(V_0+V_c)$. Eliminating $V_c$ gives $S=f/(1-f)$; for small cavity fractions, $S\simeq f$.