No abstract

The present review on inclusion problems emphasizes papers primarily published after 1982. Materials associated with inclusions are composite materials, precipitated or transformed alloys, porous media, and polycrystals. The inclusion problems deal with the following subjects of these materials: (1) stress fields caused by non-elastic strains (eigenstrains) and; (2) stress disturbances due to heterogeneity and inhomogeneities of materials under applied stresses; (3) average elastic moduli and average thermal properties; (4) nonelastic constitutive equations; (5) behavior of inclusions including nucleation, growth, and collapse of voids; (6) cracks and inclusions including the transformation toughening, crack growth through composites and stress intensity factors; (7) sliding and debonding inclusions; and (8) dynamic effects of inclusions. The present review is an update to the review paper, which appeared in Applied Mechanics Reviews, Volume 41 (1988), and includes opinions of some of the experts who made significant contributions to the field of inclusion problems. It is our hope that we cited all the important papers relevant to the subject of inclusion problems. The first author would welcome anyone’s comments and any references which were not included in this review.

Consider a double-inhomogeneity system whose microstructural configuration is composed of an ellipsoidal inhomogeneity of arbitrary elastic constants, size, and orientation encapsulated in another ellipsoidal inhomogeneity, which in turn is surrounded by an infinite medium. Each of these three constituents in general possesses elastic constants different from one another. The double-inhomogeneity system under consideration is subjected to far-field strain (stress). Using the equivalent inclusion method (EIM), the double inhomogeneity is replaced by an equivalent double-inclusion (EDI) problem with proper polynomial eigenstrains. The double inclusion is subsequently broken down to single-inclusion problems by means of superposition. The present theory is the first to obtain the actual distribution rather than the averages of the field quantities over the double inhomogeneity using Eshelby’s EIM. The present method is precise and is valid for thin as well as thick layers of coatings, and accommodates eccentric heterogeneity of arbitrary size and orientation. To establish the accuracy and robustness of the present method and for the sake of comparison, results on some of the previously reported problems, which are special cases encompassed by the present theory, will be re-examined. The formulations are easily extended to treat multi-inhomogeneity cases, where an inhomogeneity is surrounded by many layers of coatings. Employing an averaging scheme to the present theory, the average consistency conditions reported by Hori and Nemat-Nasser for the evaluation of average strains and stresses are recovered.

Often, during fabrication processes of fiber-matrix composites, the pertinent interface may be made imperfectly bonded either deliberately or undesirably. The effect of electric capacitors and mechanical imperfections on the electro-mechanical fields associated with an anisotropic piezoelectric matrix containing a cylindrical inhomogeneity made of a different anisotropic piezoelectric material is of interest. In fact the interface imperfection condition presented in this paper is quite general, in the sense that any combination of mechanical and electrical imperfections may exist. The interface electrical imperfection is mimicked by the electric capacitors. The capacity of the capacitors is a measure of the electrical imperfection. The notion of complete electric barrier realizes when the capacity is equal to zero. For finite values of capacity, different electrical imperfections are modeled. When the capacity is infinitely large, perfect electrical interface reveals.

In addition to enhancement of the resuits near the point of appiication of a concentrated ioad in the vicinity of nano-.size defects, capturing surface effects in smaii structures, in the framework of second strain gradient eiasticity is of particuiar interest. In this framework, .sixteen additionai material constants are reveaied, incorporating the roie of atomic .structures of the eiastic soiid. In this work, the analytical formuiations oftiiese constants corresponding to fee metáis are given in terms of the parameters of Sutton-Chen interatomic potentiai function. The constants for ten fee metáis are computed and tabuiized. Moreover, the exact dosed-form soiution of the bending of a nano-size Bernoulli-Euler beam in second strain gradient eiasticity is provided: the appearance of the additionai constants in the corresponding formuiations, through the governing equation and boundary conditions, can .serve to deiineate tiie true behavior of the materiai in uitra .smaii eiastic structtves. having very iarge swface-to-voiume ratio. Now that the vaiues of the materiai constants are avaiiabie, a nanoscopic study of the Keivin probiem in .second strain gradient theory is performed, and the result is compared quantitativeiy with those of the first strain gradient and traditionai tlwories.