Microinhomogeneous Medium Research Articles

Regularities of Changing the Limiting Values of Stress and Strain Invariants in Microinhomogeneous Media

Regularities of Changing the Limiting Values of Stress and Strain Invariants in Microinhomogeneous Media

Regularities of Changing the Limiting Values of Stress and Strain Invariants in Microinhomogeneous Media

By using nonlinear equations of constraints between macro- and micro-states, the regularities of changes in the limiting values of stress and strain invariants in microinhomogeneous media are studied. It is shown that the extreme relative moduli of stress tensor deviators in polycrystals with a cubic lattice are invariant with respect to external conditions of reversible force and depend only on the crystal anisotropy factor. In the irreversible region of deformation, analytical relations are obtained for bulk and tensile normal stresses. The effect of cyclic change in bulk and tensile stresses in some subelements under external monotonic loading has been established. It is shown that, on the basis of nonlinear equations of constraints, a complex pattern of material failure can be described using the theory of maximum normal stresses at the local level.

ON APPROXIMATE OPTIMAL CONTROL FOR THE REACTION-DIFFUSION PROCESS IN MICROINHOMOGENEOUS MEDIUM

The problem of constructing an approximate optimal control for controlled processes of chemical kinetics in microinhomogeneous medium is considered. Such processes are described by semilinear parabolic equations of the reaction-diffusion type with coefficients of the form . The preference of an approximate control as the optimal control in the problem with averaged coefficients is justified. An example of the construction of such a control is discussed and its efficiency is demonstrated.

To the Construction of the Amplitude Dependence of Internal Friction with Vibrations of Porous Metal Composites

Purpose of research was to plot the amplitude dependence of the decrement of longitudinal and bending vibrations of samples of porous metal composites manufactured using 3D technology.Methods. The main attention is paid to the role of microplasticity in the scattering of the vibration energy, since the decrement value in composite will be greater than in monolithic material. The effect of porosity on the level of energy dissipation is taken into account. We have used a statistical model based on the results of the theory of functionals given on random processes.Results. This made it possible to find the concentration of microplastic zones in the composite during longitudinal and bending vibrations of the sample. The value of the vibration decrement is defined as the ratio of the potential energy of plastic deformations to the total potential energy of the entire sample. To calculate the effective moduli in the composite, the well-known technique of the theory of elasticity of micro-inhomogeneous media is used. The results obtained indicate that porosity significantly affects the concentration of microplastic zones and the scattering of internal friction during longitudinal and bending vibrations. However, it should be noted that at low amplitudes, microplastic regions are not formed in the vicinity of the pores. Therefore, the reasons for the appearance of energy dissipation are not explained only by microplasticity. The source of such losses are dislocation, ferromagnetic and other reasons. However, the level of these losses is much less than that indicated in this work, and depends only on the oscillation frequency.Conclusion. The results obtained can be used to establish the patterns of behavior of various natures of ingot, powder and composite materials with high dispersion in phase and structural components in various conditions and states.

Nonlinear Wave Processes in Polycristalline Solids with Hysteresis-Loss Saturation and Relaxation

Using the perturbation method, we study the processes of nonlinear propagation of the initially harmonic elastic waves in micro-inhomogeneous media, namely, polycrystalline solids with hysteresis-loss saturation and relaxation. The media with the basic hysteresis types, elastic and inelastic, are considered. The efficient nonlinearity parameters of such media are determined for the processes of self-action of a quasiharmonic wave and generation of its higher harmonics.

Porosity, Specific Surface and Permeability in Micro-Inhomogeneous Media

Porosity, Specific Surface and Permeability in Micro-Inhomogeneous Media

Effect of Violation of the Continuity of Materials by Dispersed Microcracks on the Electroelastic Parameters of Piezoceramics

A continual model of deformation of piezoelectric materials weakened by a system of microcracks dispersed over the bulk of the material is constructed with use of the energy method. This method is based on the assumption of equivalence of the strain energy of the cracked electroelastic medium and the strain energy of a continuum modeling the indicated medium. A generalization of the Eshelby principle is used to determine the strain energy of microinhomogeneous media with inclusions.

Effective thermal conductivity of micro-inhomogeneous media containing imperfectly bonded ellipsoidal inclusions

In this paper we consider the problem of thermal polarization of an ellipsoidal inclusion surrounded by a thin conducting layer. To calculate the effective thermal conductivity of a medium containing such inclusions we use the homogenization scheme named the effective field method. The application of this scheme allows one to take into account the texture of micro-inhomogeneous medium. We obtained the solution for a set of parallel and randomly oriented ellipsoidal inclusions with a thin layer with surface conductivity. Our calculations show that the effective thermal conductivity depends on the size of inclusions.

The Wave Processes in Micro-Inhomogeneous Media with Different-Modulus Nonlinearity and Relaxation

We present the results of analytical and numerical studies of propagation of longitudinal acoustic waves in micro-inhomogeneous media with different-modulus nonlinearity and relaxation. The solutions for evolution of the profiles and spectral characteristics of the initially harmonic waves are obtained.

Parametric interaction of acoustic waves in micro-inhomogeneous media with hysteretic nonlinearity and relaxation

A theoretical investigation of parametric processes that arise as a result of the interaction of powerful and weak longitudinal acoustic waves in micro-inhomogeneous media with hysteretic nonlinearity and relaxation was carried out. The case of degenerate interaction between a powerful high-frequency wave and a weak low-frequency one was considered. The nonlinear damping coefficient and the carrier frequency phase delay of the weak wave propagating under the action of the powerful wave were determined.

The spectrum of natural vibrations in a medium composed of layers of elastic material and viscous fluid

In this study, we investigated the spectral properties of two homogenized models corresponding to transverse and longitudinal vibrations in a microinhomogeneous layered combined medium. It is established that investigation of the spectrum of each model is reduced to finding the roots of the corresponding cubic equations, and the qualitative difference between the spectra of these models is also revealed.

Nonlinear elastodynamics in micro-inhomogeneous solids observed by head-wave based dynamic acoustoelastic testing

Dynamic acoustoelastic testing provides a more complete insight into the acoustic nonlinearity exhibited by micro-inhomogeneous media like granular and cracked materials. This method consists of measuring time of flight and energy modulations of pulsed ultrasonic waves induced by a low-frequency standing wave. Here pulsed ultrasonic head waves were employed to assess elastic and dissipative nonlinearities in a region near the surface of a solid. Synchronization of the ultrasound pulse sequence with the low-frequency excitation provided instantaneous variations in the elastic modulus and the attenuation as functions of the instantaneous low-frequency strain. Weak quadratic elastic nonlinearity and no dissipative nonlinearity were detected in duralumin. In limestone, distinction between tensile and compressive behaviors revealed an asymmetry in the acoustic nonlinearity and hysteresis in both the elastic modulus and the attenuation variations. Measured nonlinear acoustical parameters are in good agreement with values obtained by different techniques. Reversible acoustically induced conditioning modified the acoustic nonlinearity both quantitatively and qualitatively. It reduced tension-compression asymmetry, suggesting a nonequilibrium modification of the sources of acoustic nonlinearity. Additionally to the metrology of the acoustic nonlinearity, head wave based dynamic acoustoelastic testing may be a useful tool to monitor changes in the microstructure or the accumulation of damage in solids.

Interaction of acoustic waves in microinhomogeneous media with hysteretic nonlinearity and relaxation

The propagation of a weak high-frequency pulse in the field of an intense standing low-frequency pump wave excited in an acoustic resonator with quadratic hysteretic nonlinearity and relaxation is theoretically investigated. The nonlinear damping coefficient and the carrier phase delay of the weak high-frequency pulse propagating under the action of an intense low-frequency wave are determined.

Dispersion of elastic waves in microinhomogeneous media and structures

The propagation of elastic waves in periodic stratified media with arbitrary local anisotropy and in anisotropic plates and bars inhomogeneous in thickness is considered under the condition that the ratio of the scale characterizing the inhomogeneity of the medium or the thickness of a plate or bar in thickness to the typical wavelength is small. The propagation of long waves is described using the effective averaged equations with high-order accuracy, which are derived by the method of two-scale asymptotic expansions in ɛ. The results of analytic and numerical studies of their principal terms responsible for the dispersion of waves are presented. The form of the dependence of the wave velocity on the wavelength is studied for structures with different types of symmetry.

Damageability of a material reinforced with unidirectional orthotropic fibers for an exponential function of long-term microstrength

UDC 539.3 The theory of long-term damageability of a homogeneous material is generalized to the case of an orthotropic fibrous composite material with a stochastic structure. Equations of mechanics of microinhomogeneous media of this structure form the base of the theory. The process of damage of components of a composite is modeled by the formation of stochastically located micropores. The criterion of fracture of a unit microvolume is characterized by its long-term strength determined by the dependence of the time of brittle fracture on the degree of closeness of the equivalent stress to its limit value, which characterizes the short-term strength on the basis of the Huber–von Mises criterion accepted as an arbitrary function of coordinates. Efficient deformation properties and the stress-strain state of an orthotropic fibrous composite with microdamages in components are determined on the base of stochastic equations of elasticity of orthotropic media. For given macrostresses and macrostrains and an arbitrary moment of time, balance equations of damage (porosity) of components are formulated. On the basis of the iteration method, we construct algorithms for calculating dependences of microdamage of components of an orthotropic fibrous material on time and dependences of macrostresses or macrostrains on time and obtain the corresponding curves for the case of a bounded function of the long-term microstrength, which is approximated by an exponential law.

Scattering of sound in a moving viscous microinhomogeneous medium at large Reynolds numbers

A generalization of the Rayleigh law of a low-frequency sound attenuation in a microinhomogeneous medium to the case of scattering particles moving in a viscous liquid at a large Reynolds numbers is proposed. It is shown that, under these conditions, the attenuation may be independent of the scattering by the moving particles themselves but be only determined by the flow caused by these particles, the maximum attenuation being observed in the direction across the particle motion. The corresponding corrections proportional to the first power of the hydrodynamic Mach number are compared with the corrections lying at the basis of the modified Rayleigh law, which was proposed earlier for the potential flow of an ideal liquid around inhomogeneities, and also with the laws of scattering in a moving viscous microinhomogeneous medium at a small Reynolds numbers. As an example of the operation of the generalized law, characteristics of the sound scattering by rain are refined.

On the low-frequency sound scattering in a moving microinhomogeneous medium

The Rayleigh law that governs low-frequency sound attenuation due to the scattering by inhomogeneities in a microinhomogeneous medium is generalized to the case of particles moving in a flow or falling under gravity. Corrections to the scattering’s cross section that adjust the Rayleigh law to the case of a potential flow around inhomogeneities are calculated. It is shown that, when microinhomogeneities are moving in a viscous medium, the characteristics of discrete scatterers may considerably deviate from the Rayleigh law. Based on the data on the velocity and size distribution of falling drops of water in air, refinements are proposed for the laws of low-frequency sound scattering by rain.

Local Spin Configurations of Fe Atoms in Microinhomogeneous PdMn<sub>x</sub>Fe<sub>1-x</sub> Alloys

The Mössbauer spectra of PdMnxFe1-x alloys obtained at 80 K and at 300 K were studied in the 0.2 < x < 0.8 concentration range, in which there realizes a microinhomogeneous multiphase medium formed by isostructure phases of the constituent compositions: ferromagnetic PdFe (ТС=730 К) alloy undergoing atomic ordering and antiferromagnetic PdMn (TN=815 К) intermetallic compound. Magnetic properties studies evidence the presence of a third presumably noncollinear phase with its own ordering temperature lying below the Curie temperature of the ferromagnetic phase in the 0.2 < x < 0.8 concentration range. The Mössbauer spectra at 300 K exhibit a doublet for antiferromagnetic alloys (x > 0.8) and a sextet at Hhf ~350 kOe for ferromagnetic alloys (x < 0.2). In the intermediate concentration range several peaks 0 < Hhf < 350 kOe have been observed in the P(Hhf) curves, which result from microinhomogeneous multiphase state.

Relation between the tidal modulation of seismic noise and the amplitude-dependent loss in rock

Geological materials and many other microinhomogeneous media exhibit pronounced nonlinear properties under very small strains, when one may expect an almost linear behavior of the material. These properties are conventionally described on the basis of elastically nonlinear or hysteretic models. The present paper discusses the amplitude-dependent dissipation that is unrelated to hysteretic nonlinearity but is also a universal property of microinhomogeneous media. This property allows the explanation of the effect of correlation between the tidal strains of the Earth’s crust (on the order of 10−8) and the unexpectedly strong (on the order of 10−2–10−1) variations of seismic noise intensity, which has been observed for more than 25 years without being given any adequate interpretation.

Evolution of acoustic waves in microinhomogeneous media with quadratic elastic nonlinearity and relaxation

A nonlinear wave equation for the velocity “relaxator” is derived in the framework of the rheological model and the corresponding equation of state of a microinhomogeneous medium containing viscoelastic defects with quadratic nonlinear elasticity. The equation is qualitatively analyzed, and numerical solutions to it are presented for a stationary symmetric shock wave and the evolution of initially harmonic waves.