## Multi-scale modeling of heterogeneous adhesives:
Effect of particle decohesion

M.G. Kulkarni^{1}, P.H. Geubelle^{1} and
K. Matous^{1,2}

^{1}Department of Aerospace Engineering

^{2}Computational Science and Engineering

University of Illinois at Urbana-Champaign

Urbana, IL 61801, USA.

#### Abstract

We examine the microscopic toughening mechanisms and their
effect on the macroscopic failure response of
heterogeneous adhesives made of stiff particles embedded
in a more compliant matrix. The analysis relies on a
multi-scale cohesive framework first described in Matouš
et al. [Matouš, K., Kulkarni, M., Geubelle, P., 2008.
Multiscale cohesive failure modeling of heterogeneous
adhesives. Journal of the Mechanics and Physics of Solids
56, 1511–1533]. Two microscopic constitutive failure
models are incorporated: an isotropic damage model to
capture the fracture response of the matrix and a cohesive
law to model the inclusion-matrix interfacial debonding. A
detailed study of the RVE size is presented followed by a
set of examples that illustrate the effect of filler size,
volume fraction and particle–matrix interface properties
on the macroscopic effective traction-separation law of
heterogeneous adhesives.

#### Conclusions

A multi-scale cohesive scheme has been used to study the
failure processes occurring at the micro-scale in
heterogeneous adhesives and their effect on the
macroscopic cohesive response. A study of the RVE size has
shown that the microscopic domain width has to be about 2
or 3 times the layer thickness for the macroscopic
response to be representative for the loading histories
considered. The effect of particle size, volume fraction
and particle–matrix interfacial parameters on the failure
response and effective macroscopic properties has been
analyzed. In contrast to the perfect particle–matrix
interface case, where the failure is of adhesive–cohesive
nature, a weak interface between the constituents
generally results in a cohesive type of failure. The
presented response curves (Figs. 5(b), 10(b), 11(b), and
12(b)) could be used as design diagrams to yield a
potentially new heterogeneous adhesive with desired
macroscopic properties.

#### Acknowledgment

The authors gratefully acknowledge the support from the
National Science Foundation for this work under Grant No.
CMS 0527965. The authors also acknowledge the support from
the Center for Simulation of Advanced Rockets (CSAR) at
the University of Illinois, Urbana-Champaign. Research at
CSAR is funded by the US Department of Energy as a part of
its Advanced Simulation and Computing (ASC) program under
Contract No. B523819.

© 2009 UIUC and Dr. Karel
Matous