A transientanisotropic gradientenhanced damage model with displacement smoothing for failure analysis in quasibrittle materials

It is widely recognized in engineering fracture mechanics that integral and differential forms of nonlocal damage models with a constant internal length scale suffer from an incorrect representation of failure mechanisms either by spurious damage growth or by incorrect damage initiation and propagation. In this regard, in this thesis, a displacement-based gradient-enhanced damage model (GEDM) with a transient internal length scale is formulated and used for failure analysis of quasi-brittle materials. Research is focused on mode-I and mode-II failure mechanisms.
In a GEDM, a local field is enhanced into a nonlocal field and the nonlocal field is the output of the enhancement. Displacement-based GEDM enhances local displacement fields into nonlocal displacement fields instead of enhancing local equivalent strain fields into nonlocal equivalent strain fields, as in strain- and stressbased GEDMs. The key ingredient of the proposed extension is a transient internal length scale that tends to zero as the damage parameter tends to one. Various expressions for this transient internal length scale are proposed, formulated, and discussed. Also, the need for correction on the gradient activity operator in mode-II failure is demonstrated. To this end, an anisotropic formulation of the displacementbased GEDM is formulated and used to control the material failure mechanism in mode-II failure. Examples of the new model regularization capabilities are compared to the original/classical displacement-based GEDM with a constant internal length scale.
Despite the existence of spurious damage growth in mode-I failure for two dimensional problems (4-point bending beam example) for both the transient isotropic and the transient anisotropic versions, spurious damage growth is eliminated for mode-I failure in one-dimensional problems. Also, the proposed transient isotropic model eliminates spurious damage growth for mode-II failure in two-dimensional problems. However, the damage migration issue is not solved. This issue is addressed by the implementation of the transient anisotropic model. The transient anisotropic model has no damage spreading and damage migration issues in mode-II failure and realistic damage initiation and propagation are guaranteed. These features enable the representation of failure patterns i.e., thin crack-like shear-band. In practical terms this leads to a non-broadening shear fracture process zone in the wake of the crack tip, addressing one of the main criticisms of existing gradient damage models. Applicability of the proposed models is demonstrated by representative one- and two-dimensional examples.