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| An effective strategy for dealing with the complex features of heterogeneous materials is based on the notion of "effective" or "equivalent" properties. The effective thermoelastic properties of a heterogeneous system are defined as the effective properties of a hypothetical homogeneous material which stores the same amount of energy as the actual composite under the same surface displacements. This approach presumes that a length scale exists over which the variation in properties of the fiber, matrix and the geometry can be appropriately averaged. This length scale must be large enough to capture the important structural fluctuations yet smaller than the dimensions of the macroscopic body. This equivalency hypothesis provides the basis for the utilization of the powerful tools of continuum elasticity theory. Volumetric averaging requires a specification of the distribution of fiber orientations and aspect ratios (or fiber lengths). The current model assumes that the distribution of fiber aspect ratios falls within a narrow band. The effective aspect ratio is the root-mean square of the distribution. The fiber orientation distributions are assumed to be uni-modal and centered about the origin of the principal axes. A specific form of the fiber orientation distribution is assumed in order to reduce the number of independent orientation parameters. Although tedious, the characteristics of the aspect ratio and orientation distributions can be obtained experimentally through microscopic examinations. Additional information and mathematical details are given in the following references. The models used in this program are described in reference 1. REFERENCES (1.)"Elastic Properties of Composites," by R. F. Eduljee and R. L. McCullough, Chapter 9 (pages 381-474), in Volume 13 Structure and properties of Composites (T. W. Chou Ed.), VCH, New York, 1993. |
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