Computational Physics Group

Karel Matous









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.


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 Hillís 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.


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 Hillís 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.


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.

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© 2009 Notre Dame and Dr. Karel Matous