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Elastic Moduli of a Material Containing Composite Inclusions: Effective Medium Theory and Finite Element Computations.

Elastic Moduli of a Material Containing Composite
Inclusions: Effective Medium Theory and Finite Element
Computations.
(2790 K)

Garboczi, E. J.; Berryman, J. G.

Mechanics of Materials, Vol. 33, No. 8, 455-470, 2001.

### Keywords:

concretes; differential effective medium; elastic
moduli; finite elements; random materials;
microstructures

### Abstract:

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Concrete is a good example of a composite material in
which the inclusions (rocks and sand) are surrounded by
a thin shell of altered matrix material and embedded in
a normal matrix. Concrete therefore may be viewed as
consisting of a matrix material containing composite
inclusions. Assigning each of these phases different
linear elastic moduli results in a complicated effective
elastic moduli problem. A new kind of differential
effective medium theory (D-EMT) is presented in this
paper that is intended to address this problem. The key
new idea is that each inclusion particle, surrounded by
a shell of another phase, is mapped onto an effective
particle of uniform elastic moduli. The resulting
simpler composite, with a normal matrix, is then treated
in usual D-EMT. Before use, however, the accuracy of
this method must be determined, as effective medium
theory of any kind is an uncertain approximation. One
good way to assess the accuracy of effective medium
theory is to compare to exact results for known
microstructures and phase moduli. Exact results,
however, only exist for certain microstructures (e.g.,
dilute limit of inclusions) or special choices of the
moduli (e.g., equal shear moduli). Recently, a special
finite element method has been described that can
compute the linear elastic moduli of an arbitrary
digital image in 2-D or 3-D. If a random microstructure
can be represented with enough resolution by a digital
image, then the elastic moduli of the random
microstructure can be readily computed. This method is
used, after proper error analysis, to provide stringent
tests of the new D-EMT equations, which are found to
compare favorably to numerically exact finite element
simulations, in both 2-D and 3-D, with varying composite
inclusion particle size distributions.
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