The purpose of the present survey is to review the analysis of composite materials from the applied mechanics and engineering science point of view. The subjects under consideration will be analysis of the following properties of various kinds of composite materials: elasticity, thermal expansion, moisture swelling, viscoelasticity, conductivity (which includes, by mathematical analogy, dielectrics, magnetics, and diffusion) static strength, and fatigue failure.

Analysis of Composite Materials—A Survey

The purpose of the present article is to review recent advances made in the determination and calculation of improved bounds on the effective properties of random heterogeneous media that depend upon the microstructure via n-point correlation functions. New breakthroughs made in the quantitative characterization of the microstructure of heterogeneous materials are also reviewed. The following four different effective properties shall be studied: (i) effective conductivity tensor (which includes, by mathematical analogy, the dielectric constant, magnetic permeability, and diffusion coefficient); (ii) effective stiffness tensor; (iii) diffusioncontrolled trapping constant; and (iv) fluid permeability tensor. It shall be demonstrated that improved upper and lower bounds can provide a relatively sharp estimate of the effective property even when the bounds diverge from one another. Although this article reviews stateof-the-art advances in the field, an attempt will be made to elucidate methods and principles for the nonexpert.

Random Heterogeneous Media: Microstructure and Improved Bounds on Effective Properties

The most recent developments on the propagation of optical beams in a turbulent medium, such as the clear atmosphere, are reviewed. Among the phenomena considered are beam spreading, beam wander, loss of coherence, scintillations, angle-of-arrival variations, and short-pulse effects.

Electromagnetic beam propagation in turbulent media

Some published computational work has suggested that partially coherent beams may be less susceptible to distortions caused by propagation through random media than fully coherent beams. In this paper this suggestion is studied quantitatively by examining the mean squared width of partially coherent beams in such media as a function of the propagation distance. The analysis indicates under what conditions, and to what extent, partially coherent beams are less affected by the medium.

Spreading of partially coherent beams in random media

In this review, the physical properties of composite materials are discussed; however, discussion of the mechanical properties has been excluded except when necessary for the consideration of properties such as thermal expansion or swelling and shrinkage. One of the main aims in the review has been to show how the theoretical and experimental information that is already available may be used (a) to design and construct composite materials with predetermined physical properties and (b) to ensure that the physical properties of composite materials are properly measured and properly defined.

The physical properties of composite materials

In a previous paper, we considered a perturbation solution for propagation of the fourth-order coherence function in a random medium. In this paper, it is shown how under certain conditions this solution may be extended to treat the propagation problem when the field fluctuations need not be small. A differential equation governing the fourth-order coherence function is derived. A solution is obtained in the geometric-optics limit when the four points of the coherence function are distinct.

Propagation of the Fourth-Order Coherence Function in a Random Medium (a Nonperturbative Formulation)*

In this paper an approximate solution is given for the development of the ensemble-averaged mutual-coherence function {Γ(x1,x2,τ)} as it propagates through statistically homogeneous and isotropic random media. Only small-angle scattering about the principal propagation direction z is considered and it is assumed that {Γ(x1,x2,τ)} is a function of [(x1 − x2)2 + (y1 − y2)2]1/2, z1 − z2, and z1. Under these conditions, it is possible to solve the governing equations using an iteration procedure. The solution is valid for long path lengths. The results are compared to the results given in Chernov, and Tatarski under those conditions where it is appropriate to do so.

Propagation of the Mutual Coherence Function Through Random Media

We present here bounds for the effective conductivity (permittivity, permeability) of a fiber reinforced material in terms of volume fractions and a geometric factor. The results are simple algebraic expressions. Two parameters, G1 and G2 are needed to describe the fiber and matrix geometries, respectively. Both parameters lie between 1 and 1; 1 represents a circle and 1 a parallel lamella. We show 4 2 4 2

Effective Electrical, Thermal and Magnetic Properties of Fiber Reinforced Materials:

We consider here the beam spread of laser light when it propagates in a random medium. The analysis is given in terms of the coherence function. Explicit results are obtained principally for the region of multiple scatter. In this region, it is shown that the irradiance pattern is always gaussian and that the characteristic beam diameter increases at a rate proportional to z32, where z is the propagation distance. The proportionality constant is determined for an arbitrary index-of-refraction spectrum, and the Kolmogorov spectrum is given as a special case. The results obtained are considered in atmospheric and oceanographic applications.

Beam Spread of Laser Light Propagating in a Random Medium

In this paper a determinate equation is derived for the propagation of a finite beam of radiation in a random medium The radiation is described by a mutual coherence function The analysis is restricted to beam diameters that are large compared to the characteristic correlation lengths in the random medium A scalar theory is used and the characteristic wavelength is assumed to be very small compared to the smallest correlation length The method used is an iteration procedure similar to that considered in the propagation of a plane wave The resulting equation is suitable for numerical integration

Mark J. Beran

Papers

Propagation of the Fourth-Order Coherence Function in a Random Medium (a Nonperturbative Formulation)*

Propagation of the Mutual Coherence Function Through Random Media

Effective Electrical, Thermal and Magnetic Properties of Fiber Reinforced Materials:

Beam Spread of Laser Light Propagating in a Random Medium

Propagation of a Finite Beam in a Random Medium