  We derive the variational formulation of a gradient damage model by applying
the energetic formulation of rate-independent processes and obtain a
regularized formulation of fracture. The model exhibits different behavior at
traction and compression and has a state-dependent dissipation potential which
induces a path-independent work. We will show how such formulation provides the
natural framework for setting up a consistent numerical scheme with the
underlying variational structure and for the derivation of additional necessary
conditions of global optimality in the form of a two-sided energetic
inequality. These conditions will form our criteria for making a better choice
of the starting guess in the application of the alternating minimization scheme
to describe crack propagation as quasistatic evolution of global minimizers of
the underlying incremental functional. We will apply the procedure for two- and
three-dimensional benchmark problems and we will compare the results with the
solution of the weak form of the Euler-Lagrange equations. We will observe that
by including the two-sided energetic inequality in our solution method, we
describe, for some of the benchmark problems, an equilibrium path when the
damage starts to manifest, which is different from the one obtained by solving
simply the stationarity conditions of the underlying functional.
