On effective moduli of inhomogeneous media characterized by several small parameters

Composites and porous media of elongated structure, as well as materials with pores or inclusions having the shape of parallelepipeds or channels of rectangular cross-section, are considered under certain conditions on the inclusion-to-matrix modulus ratio and the volume fraction of inclusions (pores). The effective moduli are calculated by the method of mathematical homogenization theory. Numerical results on the dependence of the effective moduli on the prolateness of the structure, the shape of the inclusions (pores), the inclusion-to-matrix modulus ratio, and the volume fraction of inclusions (pores) are given. The effective moduli computed according to the algorithm of mathematical homogenization theory are compared with those given by the explicit approximate formulas earlier developed by the authors.     

Generation of ring-shaped optical vortices in dissipative media by inhomogeneous effective diffusion

Nonlinear Dynamics - By means of systematic simulations, we demonstrate generation of a variety of ring-shaped optical vortices (OVs) from a two-dimensional input with embedded vorticity, in a...     

Path-independent integrals in inhomogeneous media

Summary The concept of path independent integrals introduced previously for homogeneous media is extended to the case of a crack in the interface between dissimilar half planes. Using any of the pathindependent integrals defined in this paper we obtain the stress intensity factor when the lips of the crack are loaded by identical distributions of stresses in both lips, or by concentrated forces or couples. The above integrals are extended in order to include the case of an arbitrary number of collinear cracks in the interface of two half planes. The case of periodic cracks may be derived from the above analysis. Finally, an interesting generalization may be obtained for the case where arbitrary cracks, inclusions or concentrated forces and couples, not necessarily applied at the lips of the crack, interact.

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Wegunabhängige Integrate in inhomogenen Medien

Übersicht Das Konzept wegunabhängiger Integrale, welches für homogene Medien früher eingeführt wurde, wird für den Fall eines Risses in einer Grenzfläche zwischen zwei verschiedenen Halbebenen erweitert. Durch Verwendung eines der in dieser Arbeit definierten wegunabhängigen Integrale erhalten wir den Spannungsintensitätsfaktor, wenn die Eißlippen durch an beiden Lippen identisch verteilter Spannungen oder Einzelkräfte oder Momente belastet werden. Die oben genannten Integrale sind erweitert, um den Fall einer willkürlichen Zahl von kollinearen Bissen in der Grenzfläche der Halbebenen einzuschließen. Der Fall von periodischen Rissen kann aus dieser Analysis erhalten werden. Schließlich kann eine interessante Verallgemeinerung für den Fall erhalten werden, daß willkürliche Risse, Einschlüsse oder nicht unbedingt an den Rißlippen wirkende Einzelkräfte und Momente in Wechselwirkung stehen.

     

Decaying surface waves in inhomogeneous media

Two problems on plane decaying surface waves in an inhomogeneous medium are under consideration: the problem where the waves similar to Rayleigh waves propagate in an isotropic elastic half-space that borders with a layer of an ideal incompressible fluid and the problem where the waves similar to Love waves propagate in a semi-infinite saturated porous medium that borders with a layer of an isotropic elastic medium.     

Thermoelastic wave propagation in inhomogeneous media

Summary A novel approach to the modeling of thermoelastic wave propagation is presented, based on the thermodynamics of discrete systems. The first novelty includes the representation of integral balance laws for thermoelasticity in terms of contact quantities that describe the nonequilibrium state of elements. The next new aspect is a modification of the recently proposed wave-propagation algorithm, which is used as a tool for determining the contact quantities in a finite-volume scheme for the numerical simulation of two-dimensional thermoelastic wave propagation in inhomogeneous media. Such a modification is needed to provide the satisfaction of the thermodynamic consistency conditions between adjacent discrete elements. Results of computations for certain test problems show the efficiency and physical consistency of the algorithm. Received 11 November 1999; accepted for publication 2 May 2000     

Acoustics of stochastically inhomogeneous,deformable media

S. P. Timoshenko Institute of Mechanics, Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 29, No. 10, pp. 109–115, October, 1993.     

On wave propagation in inhomogeneous elastic media

Wave propagation in an inhomogeneous elastic rod or slab is considered. The governing equations are written in a matrix form and transformations are sought which reduce the system to a form associated with the wave equation. Integration of the system is then immediate. It is shown that such reduction may be achieved subject to a function involving the density and elastic parameters of the material adopting certain multi-parameter forms. These parameters are available for fitting to the behaviour of a variety of inhomogeneous elastic materials. A specific initial boundary value problem is solved by utilising the present method.     

Statistically inhomogeneous media with randomly distributed inclusions

Based on Kunin's microstructure theory, the Random Point Field Theory is proposed to study a statistically inhomogeneous medium with randomly distributed inclusions. By using the theory, several examples are worked out, such as the effective modulus of composites and the micro-field around and in an inclusion.     

Plane SH-waves in harmonically inhomogeneous elastic media

This paper considers the oblique propagation of a plane SH-wave in an inhomogeneous elastic medium whose material properties vary harmonically with a space variable. Assuming a small deviation in the harmonic variation, the method of multiple scales is applied and approximate solutions are obtained for three types of the medium.Effects of oblique propagation of SH-waves on a resonant frequency and on an unstable region of wave propagation are discussed. Effects on the reflection coefficient at a stress-free boundary when the wave propagates in a semi-infinite space are also discussed.     

Foundations of physical mesomechanics of structurally inhomogeneous media

We present the basic principles of physical mesomechanics of structurally inhomogeneous media; the theory is developed on the basis of common approaches of nonequilibrium thermodynamics, gauge theory of defects, and mechanics of structured media. Within a multilevel approach, the plastic deformation evolution is considered in the entire hierarchy of structure-scale levels: at the nano, micro, meso, and macro level. Fracture is treated as the final stage of increasing disequilibrium of a solid, when the nonequilibrium thermodynamical Gibbs potential becomes zero and the structure-phase decay of the crystal occurs.     

A method of interface inversion in inhomogeneous media

First, an approximate solution of time domain interface scattering field is derived by extending the classical Born approximation in the problem of interface scattering. In accordance with the solution form, a projection density compensation (PDC) inversion method is developed according to the projection slice theorem, which is valid for the cases of inhomogeneous media and wave mode transformation. Finally, in the model of layered media, the calculation algorithm and the simulation inversion comparison results of point defect, crack, and crack on an interface, as well as the experiment method and results in the condition of acoustic wave, are given. The project supported by the National Natural Science Foundation of China (No.19232031) and Chinese Education Commission Science Foundation     

水平成层介质中粘弹性波的计算

本文提出了一种水平成层介质中弹性波粘弹性波计算的新方法，分别研究了线源和点源作用情况。该方法适用于各种粘弹性模型，数值计算简单，可模拟任意震源及所产生的各种体波、面波，数值结果表明具有很高的计算精度和计算效率。     

Bounds for effective elastic moduli of inhomogeneous solid bodies

In connection with the extensive use of various kinds of inhomogeneous materials (glass, carbon and boron reinforced plastics, cermets, concrete, reinforced materials, etc.) in technology, there arises a need to calculate the elastic properties of such systems. Here in each case it is necessary to work out specific methods for finding both elastic fields and effective moduli. Since, as a rule, such methods do not take into account the character of distribution of inhomogeneities in space, which is reflected on the form of the central moment functions [1], they can be referred to a single class and, consequently, can be obtained by a common method [2], In the given paper, by means of the method of solution of stochastic problems for microinhomogeneous solid bodies proposed in the work of the author [2], we find elastic fields and effective moduli in an arbitrary approximation. Depending on the choice of parameters, the latter form bounds within which there lie the exact values of the effective moduli. It is shown that the conditions used earlier for finding these parameters [3] are not the best ones. The effective elastic moduli of an inhomogeneous medium are calculated, and bounds, narrower than the bounds formed in [3], are found for them.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhniki, No. 5, pp. 144–150, September–October, 1973.