Abraham I. Beltzer

Reexamination of dynamic problems of elasticity for negative Poisson’s ratio

Recently, isotropic elastic materials with a negative Poisson’s ratio have been manufactured. Since most of the theoretical results of linear elasticity focus on a positive Poisson’s ratio, the need arises for their extension and reexamination. The above materials may have a variety of technological applications so the motivation for this study is not purely academic. The article deals first with some of the limit cases arising when Poisson’s ratio takes on an extreme value. For models represented by these limit cases, the material and structure responses may not be treated independently from each other. Then such basic dynamic elasticity problems as reflection from a free surface, propagation of Rayleigh waves, and lateral vibrations of beams and plates are reconsidered for the case of a negative Poisson’s ratio. It is shown, in particular, that the static definition of the shear factor in Timoshenko beam theory may not be satisfactory in all cases. Extensive numerical results are also given.

The effective dynamic response of random composites and polycrystals - a survey of the causal approach

Abstract Investigations of the effective dynamic response of random multiphase media are reviewed, which are based on the analysis of scattering and other losses and the subsequent application of the Kramers-Kronig relations.

The dynamic response of random composites by a causal differential method

Abstract An extension of the method of causal differential media is given. The present approach makes use of the concept of the generalized extinction cross section of inclusion in a lossy medium to evaluate the total effect of losses, and then resorts to the Kramers—Kronig relations to find the phase velocity. Numerical results and comparison with alternative theories are given.

On wave propagation in random particulate composites

Abstract A new method is presented for analysis of wave propagation in random particulate viscoelastic composites. The method incorporates both the scattering effect and viscoclastic losses as well as the Kramers-Kronig relationships valid for any casual linear system. Explicit expressions for the attenuation and dispersion are given and compared with available experimental data

SH waves of an arbitrary frequency in random fibrous composites via the K-K relations

The Kramers-Kronig relations method is shown to provide the dynamic response of a random fibrous composite for the full frequency interval, 0 < ω < ∞. The method yields a conceptually simple way of deriving the dynamic response of random composites if the approximation of an effective homogeneous medium is adopted. It is shown that some of the widely accepted theories may violate the causality and/or linearity of the effective medium. Extensive numerical data are given as well as comparison with other theories and experiments.

Shear waves in polycrystalline media and modifications of the Keller approximation

Abstract A simple closed-form solution is derived for shear waves of an arbitrary frequency in polycrystalline media by invoking the Kramers-Kronig relations. Then modifications of the Keller approximation are considered from the viewpoint of causality of the coherent wave.

The causal effective field approximation— Application to elastic waves in fibrous composites

Abstract A new version of the effective field approach is presented with application to random fibrous composites. The approach incorporates the causality of the response and the static results, which comply with the best bounds available. Extensive comparison with other methods is given.

The Kramers-Kronig relations method and wave propagation in porous elastic media

Abstract Waves of an arbitrary frequency in a porous elastic medium are investigated via the Kramers-Kronig relations method. It is shown that some of the widely accepted theories of wave propagation in random composites may violate the causality and/or linearity of the effective medium. Experimentally observed dynamic effects in random media, such as stop bands and complicated behavior of the dispersion curve, are shown to follow from the K-K relations.

Causality and the Keller approximation for acoustic waves

A method is presented for specifying the physically meaningful high‐frequency wave velocity (the geometric limit) in the context of the Keller approximation, which describes wave propagation in a weakly inhomogeneous medium. The root regularly chosen is shown to violate causality of the coherent wave.

Neural computing of effective properties of random composite materials

Abstract The effective response of disordered heterogeneous materials, in general, is not amenable to the exact analysis because the phase geometry may not be completely specified. The present paper deals with the problem of effective properties such as thermal conductivity, electrical conductivity, dielectric constant, magnetic permeability, and diffusivity in the realm of disordered composites. Even though all these properties are analogous, their numerical treatment in the same unified frameworks may be difficult. In fact, depending on the physical quantity involved, there may be a large discrepancy in the order of magnitude of relevant material parameters. This paper reports a methodology for investigating the effective scalar parameter of disordered composites with the help of the same neural network, regardless of the above physical context. Particular results are obtained for effectively isotropic and macroscopically homogeneous two-phase materials.