  In this expository Note, it is shown that the Griffith phase-field theory of
fracture accounting for material strength originally introduced by Kumar,
Francfort, and Lopez-Pamies (J Mech Phys Solids 112, 523--551, 2018) in the
form of PDEs can be recast as a variational theory. In particular, the solution
pair $(\textbf{u},v)$ defined by the PDEs for the displacement field
$\textbf{u}$ and the phase field $v$ is shown to correspond to the fields that
minimize separately two different functionals, much like the solution pair
$(\textbf{u},v)$ defined by the original phase-field theory of fracture without
material strength implemented in terms of alternating minimization. The merits
of formulating a complete theory of fracture nucleation and propagation via
such a variational approach -- in terms of the minimization of two different
functionals -- are discussed.
