= Solution
The maximum recoverable <elastic energy> per initial <volume> is the <area> under the linear <stress>–<strain> curve up to failure:
$$
u_f=\int_0^{\varepsilon_f}E\varepsilon\,d\varepsilon=\frac12E\varepsilon_f^2=\boxed{\frac{\sigma_f^2}{2E}}.
$$
Using $\sigma_f=C\sqrt{EG_c}$ gives $u_f=C^2G_c/2$, so \b[maximize $G_c$] for the fixed geometry. $G_c$ has units of energy per crack <area>, while $u_f$ has energy per specimen <volume>; the geometric factor supplies the necessary inverse length. The cancellation of $E$ is why the strain-maximizing index from (a) is not appropriate here.
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