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.