In this study a micromechanical model is proposed for a collection
of cohesive zone models embedded between two each elements of a standard
cohesive-volumetric finite element method. An equivalent ’matrixinclusions’
composite is proposed as a representation of the cohesive-volumetric
discretization. The overall behaviour is obtained using homogenization
approaches (Hashin Shtrikman scheme and the P. Ponte Casta˜neda approach). The
derived model deals with elastic, brittle and ductile materials. It is available
whatever the triaxiality loading rate and the shape of the cohesive law, and
leads to direct relationships between the overall material properties and the
local cohesive parameters and the mesh density.
First, rigorous bounds on the normal and tangential cohesive
stiffnesses are obtained leading to a suitable control of the inherent
artificial elastic loss induced by intrinsic cohesive models. Second,
theoretical criteria on damageable and ductile cohesive parameters are
established (cohesive peak stress, critical separation, cohesive failure energy,
. . . ). These criteria allow a practical calibration of the cohesive zone
parameters as function of the overall material properties and the mesh length.
The main interest of such calibration is its promising capacity to lead to a
mesh-insensitive overall response in surface damage.