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Algorithm for Computing the Effective Linear Elastic Properties of Heterogeneous Materials: Three-Dimensional Results for Composites With Equal Phase Poisson Ratios.

Algorithm for Computing the Effective Linear Elastic
Properties of Heterogeneous Materials:
Three-Dimensional Results for Composites With Equal
Phase Poisson Ratios.
(646 K)

Garboczi, E. J.; Day, A. R.

Journal of the Mechanics and Physics of Solids, Vol.
43, No. 9, 1349-1362, 1995.

### Keywords:

building technology; algorithms; composite materials;
digital images; elasticity; finite elements; poisson
ratio

### Abstract:

*
An algorithm based on finite elements applied to digital
images is described for computing the linear elastic
properties of heterogeneous materials. As an example of
the algorithm, and for their own intrinsic interest, the
effective Poisson's ratios of two-phase random isotropic
composites are investigated numerically and via
effective medium theory, in two and three dimensions.
For the specific case where both phases have the same
Poisson's ratio (v1 = v2), it is found that there exists
a critical value v*, such that when v1 = v2 > v*, the
composite Poisson's ratio v always decreases and is
bounded below by v* when the two phases are mixed. If
v1 = v2 < v*, the value of v always increases and is
bound above by v* when the two phases are mixed. In d
dimensions, the value of v* is predicted to be 1/(2d-1)
using effective medium theory and scaling arguments.
Numerical results are presented in two and three
dimensions that support this picture, which is believed
to be largely independent of microstructural details.
*