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The article is devoted to the study of the possibility of using the principles of circuit design when modeling internal processes occurring in a heterogeneous medium. Modern complex objects in mechanical engineering (elements, processes, components, mixtures, alloys, etc.) can be represented in the form of circuit diagrams, which are understood as a set of elements and relationships between them. Such schemes make it possible to create an unambiguous model of this object. In addition, circuit diagrams allow you to optimize them (and hence objects) in the process of construction: change the number of elements; change the characteristics of the elements. The main advantage of this approach stems from the fact that at present there are special programs, including computer programs, that make it possible to build such models based on the purpose of the functioning of the designed object and the possibilities of its creation. Circuit design in mechanics is the creation of a concept diagram of a future object (method, device, substance), which, when completed (manufactured), will allow the object to achieve its goals. The process of transformation and transfer of an intensive parameter in heterogeneous media is considered, using the example of the propagation of elastic oscillations and thermal processes in them, which is interesting from the point of view of modeling the processes that take place in these media during their flaw detection by the acoustic infrared thermometric method, which is based on the interaction of structural defects with acoustic waves. At the same time, thermal energy is generated at their boundaries, which is an indicator not only of the presence of cracks, but also of their direction and development. When modeling damage such as cracks and fractures in products made of non-metallic heterogeneous materials, special additional elements are introduced that simulate structural integrity violations – relay elements. [ABSTRACT FROM AUTHOR]

A heterogeneous material obtained by means of cold gas dynamic spraying with subsequent laser processing is studied. The reasons for reduction of the particle size of boron carbide B4C under the action of a laser beam and the chemical composition of the material containing the "lost" material of B4C particles are examined. A mathematical model, which takes into account the dissolution of B4C particles and the presence of a chemical reaction, is developed. The elastic properties of the deposited heterogeneous material are analyzed with the use of continuum approaches that describe heterogeneous media and are based on averaging of the original stochastic equations. [ABSTRACT FROM AUTHOR]

The propagation of a short compression pulse in heterogeneous targets containing ceramic inclusions of different sizes is studied numerically. The case of a heterogeneous material with inclusions of macroscopic size is considered. It is shown that during propagation in all targets, the initial shape of the shock pulse evolves to a shape corresponding to an elastic stress-strain state in which its amplitude and length do not depend on the distance traveled. It is found that for heterogeneous materials with large inclusions, the rate of decrease in pulse amplitude is greater than for heterogeneous materials with small inclusions. [ABSTRACT FROM AUTHOR]

A non-local state-based peridynamic method (PD) is employed to simulate the initiation and propagation of the hydraulic fracturing. This study presents a novel 3D simulation of the hydraulic fracturing initiation and propagation in a heterogeneous geological medium by a linear-viscoelastic PD model. The interaction between induced fractures and a pre-existing fracture, as well as the influence of the angle of approach and differential horizontal stress on the fracture propagation behavior was investigated through the simulation. In the lower approach angles and differential horizontal stress, the pre-exiting fracture was dilated by the hydraulic fracture; in higher approach angles with higher differential horizontal stress, the hydraulic fracture crossed the pre-existing fracture. The accuracy of the 3D model was validated by experimental hydraulic fracturing data published based on the laboratory tests. Finally, the influences of the three different injection rates on fracture initiation and propagation, induced fracture surface and shear dilation were investigated. The simulation showed that the maximum dilatation and fractured zone occurred at the injection rate of 0.61 m 3 /min. The 0.61 m 3 /min injection rate caused the highest complete damage (0.9–1) with 5.24% of the total number of atoms. As a result, the peridynamic approach presents promising results in predicting fracture propagation and damage area. [ABSTRACT FROM AUTHOR]

The present paper deals with the effect of point source on the propagation of Love wave in a heterogeneous layer and inhomogeneous half-space. The upper heterogeneous layer is caused by consideration of exponential variation in rigidity and density. Also in half-space inhomogeneity parameters associated to rigidity, internal friction and density are assumed to be functions of depth. The dispersion equation of Love wave has been obtained by using Green’s function technique. As a special case when the upper layer and lower half-space are homogeneous, our computed equation coincides with the general equation of Love wave. The propagation of Love waves are influenced by inhomogeneity parameters. The dimensionless phase velocity has been plotted against the dimensionless wave number for different values of inhomogeneity parameters. We have observed that the velocity of wave increases with the increase of inhomogeneity parameters. [ABSTRACT FROM AUTHOR]

The reflection of a plane sound wave incident normally on the flat boundary of a layered heterogeneous medium is considered. The heterogeneous medium consists of periodically alternating layers of elastic and viscoelastic isotropic materials. All the layers are assumed to be parallel or perpendicular to the wavefront and each layer is much thinner than the sound wavelength. The problem is studied using a homogenized model of the layered heterogeneous medium. Specifically, the complex amplitudes of the reflected and transmitted waves are determined as functions of frequency. [ABSTRACT FROM AUTHOR]

An isothermal transient-state non-Fickian diffusion model is developed and analytically solved for description of gas dissolution in locally heterogeneous media suddenly exposed to a high pressure gas. The full-, short-, and long-time analytical solutions are used to establish the significance of the non-Fickian gas dissolution in heterogeneous media compared to the Fickian diffusion assumption. Parametric studies are carried out by means of the special analytical-solutions obtained for gas transport in the semi-infinite and finite-thickness heterogeneous media involving a delay time. The profiles of concentration and diffusion flux obtained for the non-Fickian wave-diffusion case are compared with the Fickian pure-diffusion case. The initial propagation of a right-running wave and its reflection from the wall are illustrated for the concentrations and diffusion fluxes. The small-time behavior is shown to be inherently wave-like and the discontinuity wave front propagates into the medium with the speed decreasing with time. For small times, the differences between the wave- and pure-diffusion cases are found to be significant depending on the magnitude of the delay time. For sufficiently large times, the wave behavior dies out and the wave solutions approach the equilibrium pure-diffusion solutions, except very near the decaying wave front. The formulations presented in this paper are of practical importance because they can be instrumental in determination of the diffusivity, interface surface mass-transfer coefficient, and rate of dissolution of gases in heterogeneous medium. A parameter estimation method is also proposed and elaborated for estimation of the diffusion and interface surface mass-transfer coefficients from measured pressure decay data. [ABSTRACT FROM AUTHOR]

A heterogenous medium consisting of an isotropic elastic material and a viscous compressible fluid is considered. One half of this medium is a continuous elastic material, while the other consists of alternating layers of an elastic material and a fluid. Using an averaged model of the heterogeneous medium the problem of the reflection of a plane acoustic wave from the plane interface between the continuous elastic material and the layered medium is solved. The reflected and transmitted wave amplitudes are determined for a medium, whose layers are parallel or perpendicular to the wave front. [ABSTRACT FROM AUTHOR]

In order to study the influence of velocity model on the deviation of shock bump earthquake location, three dimensional propagation model of mine quake waves in the layered inhomogeneous media was built based on Huygens principle. Through blasting vibration tests, monitoring was made by microseismic system of mine. The three-dimensional wave equation was built for seismic waves forward, and propagation velocity's calculation formula on the dielectric interface was also given, on which the classical linear positioning method was reasonably improved so that the linear positioning method based on uniform medium suits for inhomogeneous medium. The actual calculation for shock bump can be made through the application of deduction results to mine microseismic monitoring and positioning system. The results show that velocity model greatly affects positioning. By using 3D propagation model in the shock bump positioning, location accuracy is effectively improve. [ABSTRACT FROM AUTHOR]