The Multiscale Analysis of Multiple Interacting inclusions Problem: Finite
Number of Interacting Inclusiond
V A Buryachenko1
Nicholas J Pagano2
1 University of Dayton Research Institute, Dayton, OH 045433-0168, USA
2 Air Force Research Laboratory, Materials and Manufacturing Directorate,
AFRL/MLBC, Wright-Petterson AFB, OH 45433-7750, USA
* To whom correspondence should be addressed.
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Abstract |
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A hybrid method based on the combination of the volume integral equation (VIE)
method and the boundary integral (BIE) method is proposed for the micro-macro solution
of electrostatic 2D and 3D multiscale problems in bounded or unbounded solids
contacting interacting multiple inclusions of essentially different scale. The hybrid
micro-macro formulation allows decomposition of the complete problem into two associated
subproblems, one residing entirely at the micro-level and the other at the macro-level
at each interaction. The efficiency of the standard iterative scheme if the BIE and VIE
methods for the singular integral equations involved enhanced by the use of modification
in the spirit of a subtraction technique as well as by the advantageous choice of the
initial analytical approximation for interacting inclusions (micro-level) in an
unbounded medium subjected to inhomogeneous loading. The latter is evaluated by the
macro-scale BIE technique capable of handling complex finite geometries and mixed
boundary conditions. The Interation method proposed converges rapidly in a wide class of
problems considered with high matrix-inclusion elastic contrast, with continuously
varying anistropic and nonlinear elastic properties of inclusions, as well as with sizes
of interacting inclusions differing by a factor varying in the interval from 1 to
107. The accuracy and efficiency of the method are examined through
comparison with results obtained from infinite-element analysis and boundary element
analysis as well as from analytical solution
Key Words:
Muicrostructures, inhomogeneous material, elastic material
