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The main object of this paper is to give the connection between macro and micromechanics (or continuum mechanics and solid state physics) as far as it can be delineated today. The theory of the residual stress state is rather well-developed. The state is described geometrically by elastic strain and lattice curvature, the latter being equivalent to the dislocation density. The static description uses force and couple stresses, the latter being the reaction of the body against the lattice curvature. The material constant connecting bending-type lattice curvature with the corresponding couple stress is derived by applying elasticity theory on a microscopic scale. The material constant depends on the ordinary elastic constants of the body and on the distance of the glide planes of the dislocations. Beside these positive results, the paper contains an outline of what still has to be done.

Polycrystalline materials are visualized in this paper as a statistical ensemble of microelements whose crystallographic axes are randomly, but not uniform randomly, oriented in the material system. Based on this concept the influence of internal dislocations and grain boundaries on the elastic response of such metals is discussed. The latter influence is taken into consideration by combining the grain boundary coincidence cell models of Bollmann with the relaxation technique of Weins in the case of symmetric tilt boundaries. The micromechanics theory of Axelrad and Provan is also briefly discussed to indicate where these quantitative metallurgical studies are of importance in the further development of this theory. Resume Dans cette etude, les materiaux poly cristallins sont consideres comme un ensemble statistique de micro-elements dont les axes cristallographiques sont orientes au hasard, mais non uniformement, dans le materiau. A partir de ce concept, les auteurs discutent de l'influence de di...

This paper is a survey of the principal analytical and experimental developments in the field of composite material mechanics. Emphasis is placed on filamentary-type composite materials. Topics covered are (1) elastic micromechanics, including a great variety of analytical approaches to the problem, and (2) thermal and other transport phenomena, including a number of useful analogies for such phenomena. The survey concludes with a brief discussion of future trends in the field.

Two-dimensional stress fields in crystals due to edge dislocations, vacancies, precipitations, cracks and their combinations are obtained experimentally by using the slab analogy between an Airy stress function in a slice and a deflection in a slab. The results agree fairly well with those obtained theoretically. It is thus found that some complicated problems in stress analysis in the field of micromechanics can be solved with the method proposed in this paper.

Having noted an important role of image stress in work hardening of dispersion hardened materials, (1,3) the present paper discusses a method of calculating the average internal stress in the matrix of a material containing inclusions with transformation strain. It is shown that the average stress in the matrix is uniform throughout the material and independent of the position of the domain where the average treatment is carried out. It is also shown that the actual stress in the matrix is the average stress plus the locally fluctuating stress, the average of which vanishes in the matrix. Average elastic energy is also considered by taking into account the effects of the interaction among the inclusions and of the presence of the free boundary.

This paper presents an analytical determination of the elastic constants of composite materials with transversely isotropic elastic circular fiber inclusions in terms of the elastic moduli and the geometric parameters of the constituents. Hexagonal array fiber arrangement is assumed. The problem is solved within the framework of linear elasticity theories of isotropic and anisotropic elastic bodies by subjecting the composite to uniform normal and shearing strain fields. Solutions are obtained in series forms and the Fourier method and the least-square method are used. Numerical results are compared with existing analysis and experiments.

Existing micromechanics analyses for the prediction of composite material properties, which are based upon the assumption of various idealized regular filament packings, indicate the significant influence of the assumed geometry on numerical results obtained. To represent the random filament packing of actual composite materials more accurately, a method of analyzing random arrays is presented in this paper. Although certain geometric constraints have necessarily been retained for mathematical reasons, it has been dem onstrated that as the degree of randomness is increased, the agree ment between analytical predictions and available experimental data is improved. Because of the necessary approximations and additional complexities involved in random array analyses, the methods presented here are not intended to replace regular array analyses, but rather to supplement them, indicating the influence of this difficult-to-predict characteristic of real materials.

The point matching numerical method and its generalization, the method of boundary point least squares, have been successfully applied to numerous boundary value and eigenvalue problems. The present paper demonstrates the application of these techniques to problems in the micromechanics of fibrous composite materials, i.e. determination of elastic moduli and stress concentrations for parallel-fibre materials which are loaded transversely with respect to the fibres. The solution technique utilizes exact solutions of the governing equations of plane elasticity for each component fibre and its surrounding matrix material in a typical repeating section of the composite material. The continuity conditions for stresses and displacements between fibre and matrix and the repeatability conditions at the boundary of the repeating section are satisfied approximately in a pointwise manner. Some special numerical techniques which were found to be particularly useful in applying the point matching method to these problems are delineated. The method is demonstrated for composite materials having circular, elliptical and square fibres in regular, staggered arrays. Numerical results are given which show the accuracy of the method as well as stress concentration and composite elastic moduli data.

This paper demonstrates the usefulness of micromechanical analysis in predicting gross properties of a fiber reinforced composite. In particular, the elastic coefficients of a multidirectional composite are calculated as a function of fiber and matrix properties and fiber orientation. The calculations are based on current theory. The connection between micromechanics and macromechanics is demonstrated by an example showing the effects of constituent properties on the buckling of a fiber reinforced composite plate.