Cohesive Zone Models identification using an inverse homogenization method
Résumé
A major challenge when using cohesive zone models (CZMs) in numerical damage
and fracture simulations (e.g. cohesive-volumetric finite element method with CZMs
embedded between each volumetric elements) lies in the appropriate identification of
their parameters. Such a calibration has to be able to predict the response of the
studied material and also to handle the mesh-dependency issue.
In order to avoid the usual cumbersome numerical-experimental fitting of CZMs, we
propose an original and practical method for the CZMs parameters calibration. The
formulation is based on a micromechanical approach and consists in deriving explicit
relationships between the local cohesive parameters, the bulk properties, the mesh
characteristics and the applied loading triaxiality rate.
The main ingredient of this approach is the introduction of a cohesive ‘matrixinclusion’
composite as an equivalent representation of a continuum medium with
embedded cohesive zones: the matrix has the same behavior as the bulk elements
of the finite element discretization whereas the inclusions follow a surface damage
behavior corresponding to the traction-separation CZM law. The effective behavior of
this medium can be then bounded or estimated using advanced non-linear
homogenization methods.
Since the effective cohesive-volumetric behavior is obtained, practical criteria for the
calibration of the CZMs parameters are obtained through an inverse analysis. The
originality of this calibration lies in its ability to be applied for the case of brittle as
ductile damage and hence to be used whatever the cohesive law shape. Moreover, it
exhibits the dependence of the cohesive parameters on the triaxiality rate of the
applied loading for the case of ductile behaviors and allows to properly avoid the
inherent mesh-sensitivity problem. The proposed micromechanical model provides
accurate predictions of the overall material response.