Fracture Mechanics of Concrete Structures (Proceedings of FraMCoS-5),
ON MESH BIAS OF LOCAL DAMAGE MODELS FOR CONCRETE
Peter Grassl and Milan
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:
- The isotropic damage model with a realistic biaxial strength envelope
is strongly sensitive to the mesh orientation, even if the mesh is fine.
- The isotropic damage model with a modified von Mises definition of
equivalent strain appears to be less sensitive to the mesh orientation, but
this is to a large extent an artifact caused by the unrealistic increase of
tensile strength under compression parallel to the crack.
- The anisotropic damage model used in this study can reasonably well
capture arbitrary crack trajectories, while the biaxial strength envelope
remains close to typical experimental data for concrete.
- Mesh refinement often reduces sensitivity to the mesh orientation,
but is not a universal remedy.
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 / email@example.com