Boundary condition effects on multiscale analysis of
damage localization
H.M. Inglis1, P.H. Geubelle2 and
K. Matous2,3
1Department of Mechanical Science and
Engineering
2Department of Aerospace Engineering
3Computational Science and Engineering
University of Illinois at Urbana-Champaign
Urbana, IL 61801, USA.
Abstract
The choice of boundary conditions used in multiscale
analysis of heterogeneous materials affects the numerical
results, including the macroscopic constitutive response,
the type and extent of damage taking place at the
microscale and the required size of the Representative
Volume Element (RVE). We compare the performance of
periodic boundary conditions and minimal kinematic
boundary conditions [1] applied to the unit cell of a
particulate composite material, both in the absence and
presence of damage at the particle-matrix interfaces. In
particular, we investigate the response of the RVE under
inherently non-periodic loading conditions, and the
ability of both boundary conditions to capture
localization events that are not aligned with the RVE
boundaries. We observe that, although there are some
variations in the evolution of the microscale damage
between the two methods, there is no significant
difference in homogenized responses even when localization
is not aligned with the cell boundaries.
Conclusions
We have compared the behavior of a particulate composite
system under periodic boundary conditions and under the
minimal kinematic boundary conditions introduced by
Mesarovic and Padbidri [1]. For an undamaged material
system, the computed shear stiffness is 6-7% higher with
periodic boundary conditions
than with minimal kinematic boundary conditions,
consistent with the results obtained by Mesarovic and
Padbidri. In a system where interfacial damage is modeled,
periodic boundary conditions successfully capture weak
localization associated with the particle debonding
process even when that weak localization is not aligned
with the domain axes. For some pack geometries and some
loading cases, the additional constraint of periodicity is
satisfied by the formation of more than one band of
partial localization. Characteristic features of the
homogenized solution, including the initial slope, the
initial peak, and evolution of damage and failure, are
similar for the two boundary conditions across multiple
packs.
The results suggest that the multiscale
scheme based on periodic boundary conditions, which is
supported by a wealth of theoretical development and is
attractive because of its mathematical tractability, can
be used even in the case of off-axis damage localization.
The multiscale scheme based on MKBC presents the key
advantage of not requiring periodic RVE’s, and can
therefore be applied to a wider range of microstructures,
especially those extracted directly from actual
micrographs.
The multiscale scheme based on minimal
kinematic boundary conditions does not perform well when
particles are too close to the boundaries. The integral
constraint is then satisfied by excessive straining of a
narrow ligament, rather than by deformation of the entire
domain. The introduction of a penalty term in the integral
boundary condition may improve the performance of this
method.
Acknowledgment
This work was supported by the Center for Simulation of
Advanced Rockets (CSAR) under contract number B523819 by
the U.S. Department of Energy. Karel Matous would also
like to acknowledge support from ATK/Thiokol (ATK-21316),
with J. Thompson and Dr. I. L. Davis serving as program
monitors.
Download paper here
© 2009 Notre Dame and Dr.
Karel Matous