Ricerc@Sapienza

Local damage models with softening needs localization limiters to preserve the mathematical
and physical consistency. In this paper we compare the properties of strain-gradient and
damage-gradient regularizations. Gradient-damage models introduce a quadratic dependency
of the dissipated energy on the gradient of the damage field and are nowadays extensively used
as phase-field approximation of brittle fracture. Their key feature is to provide a smeared
approximation of a crack as a band of localised damage with a finite energy dissipation per
unit of surface, that can be identified with the fracture toughness of the Griffith model. Strain
gradient models introduce a quadratic dependence of the elastic energy on the gradient of the
strain field. A similar term can be physically interpreted as the presence in the material of
linear, but nonlocal, stiffnesses, that can be eventually be affected by damage. Despite this
attractive interpretation, we have found that strain-gradient regularized models can hardly
be used to approximate brittle fracture, because smeared cracks with non-vanishing and finite
dissipated energies are hardly obtained. Our analysis is based on variational models and focuses
on the one-dimensional traction problem.