Fracture Mechanics of Concrete Structures (Proceedings of FraMCoS-5), 255-262.


Peter Grassl and Milan Jirįsek
LSC, ENAC, Swiss Federal Institute of Technology at Lausanne (EPFL), Switzerland


In the present comparative study, we investigate the influence of mesh bias on failure simulations performed with isotropic and anisotropic damage models. Several fracture tests with curved crack trajectories are simulated on different meshes. The isotropic damage model with a realistic biaxial strength envelope is highly sensitive to the mesh orientation, even for fine meshes. The sensitivity is reduced if the definition of equivalent strain is replaced by the modified von Mises definition, but the corresponding biaxial strength envelope is not realistic for concrete. The anisotropic damage model used in this study captures reasonably well arbitrary crack trajectories, while the  biaxial strength  envelope remains close to typical experimental data for concrete. Finally, a crack tracking technique is combined with the isotropic damage model, and the mesh bias is demonstrated to be substantially reduced.


The evaluation of mesh-induced directional bias of two isotropic and one anisotropic damage model on different types of meshes for a number of concrete fracture tests has lead to the following preliminary conclusions:

These conclusions need to be confirmed by further investigations. In particular, alternative anisotropic models such as the rotating crack model should be included in the comparative study, to see whether anisotropy is indeed the key to mesh bias reduction.

The isotropic damage model is attractive for its simplicity but, with a definition of equivalent strain that provides a realistic biaxial strength  envelope, it is strongly sensitive to the mesh orientation. Modification of the equivalent strain definition is not a physically sound remedy, as discussed before. As an alternative technique aiming at the reduction of mesh bias,  the crack tracking method has been proposed in the present paper. This method is based on the tracking of the crack centerline and can be combined with any standard constitutive model and two-dimensional finite element.  The crack tracking method is able to simulate the crack patterns of complex mixed-mode fracture tests using a simple isotropic damage model with a Rankine loading function. A substantial improvement has been observed in the Nooru-Mohamed DEN test, but  a more extensive evaluation of the true potential of this method is needed.

EPFL / 3 December 2003 /