  Ductile damage models and cohesive laws incorporate the material plasticity
entailing the growth of irrecoverable deformations even after complete failure.
This unrealistic growth remains concealed until the unilateral effects arising
from the crack closure emerge. We address this issue by proposing a new
strategy to cope with the entire process of failure, from the very inception in
the form of diffuse damage to the final stage, i.e. the emergence of sharp
cracks. To this end, we introduce a new strain field, termed discontinuity
strain, to the conventional additive strain decomposition to account for
discontinuities in a continuous sense so that the standard principle of virtual
work applies. We treat this strain field similar to a strong discontinuity, yet
without introducing new kinematic variables and nonlinear boundary conditions.
In this paper, we demonstrate the effectiveness of this new strategy at a
simple ductile damage constitutive model. The model uses a scalar damage index
to control the degradation process. The discontinuity strain field is injected
into the strain decomposition if this damage index exceeds a certain threshold.
The threshold corresponds to the limit at which the induced imperfections merge
and form a discrete crack. With three-point bending tests under pure mode I and
mixed-mode conditions, we demonstrate that this augmentation does not show the
early crack closure artifact which is wrongly predicted by plastic damage
formulations at load reversal. We also use the concrete damaged plasticity
model provided in Abaqus commercial finite element program for our comparison.
Lastly, a high-intensity low-cycle fatigue test demonstrates the unilateral
effects resulting from the complete closure of the induced crack.
