Multiscale Cohesive Failure Modeling of
Heterogeneous Adhesives
K. Matous1,2, M.G. Kulkarni2 and P.H.
Geubelle2
1Computational Science and Engineering
2Department of Aerospace Engineering
University of Illinois at Urbana-Champaign
Urbana, IL 61801, USA.
Abstract
A novel multiscale cohesive
approach that enables prediction of the macroscopic properties of
heterogeneous thin layers is presented. The proposed multiscale model
relies on the Hill’s energy equivalence lemma, implemented in the
computational homogenization scheme, to couple the micro- and
macro-scales and allows to relate the homogenized cohesive law used to
model the failure of the adhesive layer at the macroscale to the
complex damage evolution taking place at the microscale. A simple
isotropic damage model is used to describe the failure processes at the
microscale. We establish the upper and lower bounds on the multiscale
model and solve several examples to demonstrate the ability of the
method to extract physically-based macroscopic properties.
Conclusions
A multiscale cohesive model capable of linking the microscale failure
events in heterogeneous thin layers to the macroscopic constitutive
relationship has been developed and implemented. The model relies on
the Hill’s energy equivalence lemma for bridging the micro- and
macro-scales within the computational homogenization scheme. A simple
isotropic damage constitutive relation has been used to model the
failure of heterogeneous adhesives. The classical micromechanics bounds
on the multiscale cohesive solution in the hardening as well as the
softening region have been presented. The robustness of the framework
has been demonstrated by solving several examples, including various
model heterogeneous adhesive layers with stiff and soft particles
subjected to a range of loading conditions. Through these examples, we
have demonstrated how the multiscale cohesive framework can be used to
extract physically-based macroscopic constitutive law from microscale
failure processes. The multiscale cohesive framework is not specific to
the damage model considered in this study and can readily be applied to
a wide range of damage models used to
capture the failure processes taking place at the microscale.
Acknowledgment
This work is supported by the National Science Foundation under Grant
Number CMS 0527965. The authors also gratefully acknowledge support
from the Center for Simulation of Advanced Rockets (CSAR) at the
University of Illinois, Urbana-Champaign. Research at CSAR is funded by
the U.S. Department of Energy as a part of its Advanced Simulation and
Computing (ASC) program under contract number B523819.