Propagation of waves in a fluid-saturated porous elastic solid

A theory is developed for the propagation of waves in a porous elastic solid containing a compressible viscous fluid using a homogenization process. The matrix is a lattice of periodically distributed gaps of arbitrary shape, the period of the lattice being small compared with the wave length. The present treatment is concerned with materials where fluid and solid are of comparable densities. Two cases are considered: the situation in which the pores are connected and that in which they are not. When pores are closed, the bulk medium behaves like an elastic medium; when they are connected, the fluid filtration and the bulk deformation are coupled. Boundary conditions, for macroscopic variables, at the interface between such a porous medium and the adjacent free flow are given.     

Boundary integral equations for the scattering of elastic waves by elastic inclusions with thin interface layers

Elastic waves are scattered by an elastic inclusion. The interface between the inclusion and the surrounding material is imperfect: the displacement and traction vectors on one side of the interface are assumed to be linearly related to both the displacement vector and the traction vector on the other side of the interface. The literature on such inclusion problems is reviewed, with special emphasis on the development of interface conditions modeling different types of interface layer. Inclusion problems are formulated mathematically, and uniqueness theorems are proved. Finally, various systems of boundary integral equations over the interface are derived.     

Effective elastic properties of solids with irregularly shaped inclusions

A unit rectangular cell is usually cut out from a medium for investigating fracture mechanism and elastic properties of the medium containing an array of irregularly shaped inclusions. It is desirable to clarify the geometrical parameters controlling the elastic properties of heterogeneous materials because they are usually embedded with randomly distributed particulate. The stress and strain relationship of the rectangular cell is obtained by an ad hoc hybrid-stress finite element method. By matching the boundary condition requirements, the effective elastic properties of composite materials are then calculated, and the effect of shape and arrangement of inclusions on the effective elastic properties is subsequently considered by the application of the ad hoc hybrid-stress finite element method through examining three types of rectangular cell models assuming rectangular arrays of rectangular or diamond inclusions. It is found that the area fraction (the ratio of the inclusion area over the rectangular cell area) is one dominant parameter controlling the effective elastic properties.     

Propagation of low-frequency elastic waves in double-porositymedia containing viscoelastic component in the pores

A self-consistent scheme named the effective field method (EFM) is applied for the calculation of the velocities and quality factors of elastic waves propagating in double-porosity media. A double-porosity medium is considered to be a heterogeneous material composed of a matrix with primary pores and inclusions that are represent by flat (crack-like) secondary pores. The prediction of the effective viscoelastic moduli consists of two steps. First, we calculate the effective viscoelastic properties of the matrix with the primary small-scale pores (matrix homogenization). Then, the porous matrix is treated as a homogeneous isotropic host where the large-scale secondary pores are embedded. Spatial distribution of inclusions in the medium is taken into account via a special two-point correlation function. The results of the calculation of the viscoelastic properties of double-porosity media containing isotropic fields of crack-like inclusions and double-porosity media with some non-isotropic spatial distributions of crack-like inclusions are presented.     

Interaction of harmonic plane waves with a mobile elastic phase boundary in anti-plane shear

This paper is concerned with the effect of sustained infinitesimal harmonic plane wave excitation of a phase boundary in a non-linearly elastic material that is subject to anti-plane shear deformation. The phase boundary is capable of motion that is here described by a harmonic travelling waveform. The reflected wave is also a harmonic plane wave, however the transmitted wave may be either in the form of a harmonic plane wave or a harmonic surface wave. The phase boundary motion is determined on the basis of a standard kinetic relation that involves a single mobility parameter. This gives phase boundary motion that is synchronized with the incident wave for the case of a transmitted plane wave, but is not synchronized with the incident plane wave for the case of a transmitted surface wave. A certain fraction of the energy provided by the incident wave is dissipated by phase boundary motion in a fashion that can be explicitly quantified. Special incident angles can suppress the reflected wave, suppress the transmitted wave or cause the dissipation to vanish.     

Interaction of plane harmonic waves with inclusions in the elastic space

We solve the problem of interaction of harmonic elastic waves with a thin elastic inclusion in the form of a strip in an unbounded body (matrix) under the conditions of plane deformation. In view of the small thickness of the inclusion, it is assumed that its bending and shear displacements coincide with the displacements of the corresponding points of its median plane. The displacements of the medium plane are found from the corresponding equations of the theory of plates. The method of solution is based on the representation of displacements in the form of singular solutions of the Lamé equations with subsequent determination of the unknown jumps from singular integral equations. The indicated integral equations are solved numerically (by the collocation method). The relations for the approximate evaluation of the stress intensity factors at the ends of the inclusion are obtained. __________ Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 43, No. 3, pp. 58–64, May–June, 2007.     

On attenuation and measurement of Lamb waves in viscoelastic composites

In this work, the influence of viscoelastic material properties, as featured by fibre reinforced plastics, on the measurement of Lamb waves with the aid of surface-applied piezoelectric sensors is examined. The focus points are frequency dependent material dampening and dispersion on the one hand and the impact of sensor size, wave excitation and measurement method on the other hand. The dependence of the measured wave propagation characteristics and the deviation from the actual characteristics is investigated to assess the relevance for Lamb wave based nondestructive testing and structural health monitoring methods. The sensor responses of piezoelectric sensors bonded to the surface of a viscoelastic composite are predicted by a comprehensive model including these influencing factors. The modelling approach is compared with experimentally measured values to evaluate both the methods and the relevance of the influencing factors.     

Propagation of Love waves in an elastic layer with void pores

The paper presents a study of propagation of Love waves in a poroelastic layer resting over a poro-elastic half-space. Pores contain nothing of mechanical or energetic significance. The study reveals that such a medium transmits two types of love waves. The first front depends upon the modulus of rigidity of the elastic matrix of the medium and is the same as the love wave in an elastic layer over an elastic half-space. The second front depends upon the change in volume fraction of the pores. As the first front is well-known, the second front has been investigated numerically for different values of void parameters. It is observed that the second front is many times faster than the shear wave in the void medium due to change in volume fraction of the pores and is significant     

Rigorous bounds on the effective thermal conductivity of composites with ellipsoidal inclusions

A new method is developed to derive the bounds of the effective thermal conductivity of composites with ellipsoidal inclusions. The transition layer for each ellipsoidal inclusion is introduced to make the trial temperature field for the upper bound and the trial heat flux field for the lower bound satisfy the continuous interface conditions which are absolutely necessary for the application of variational principles. According to the principles of minimum potential energy and minimum complementary energy, the bounds of the effective thermal conductivity of composites with ellipsoidal inclusions are rigorously derived. The effects of the distribution and geometric parameters of ellipsoidal inclusions on the bounds of the effective thermal conductivity of composites are analyzed. It should be shown that the present method is simple and needs not calculate the complex integrals of multi-point correlation functions. Meanwhile, the present method provides a powerful way to bound the effective thermal conductivity of composites, which can be developed to obtain a series of bounds by taking different trial temperature and heat flux fields. In addition, the present upper and lower bounds still are finite when the thermal conductivity of ellipsoidal inclusions tends to ∞ and 0, respectively.     

Modulation of nonlinear waves in a viscous fluid contained in a tapered elastic tube

In the present work, treating the arteries as a tapered, thin walled, long and circularly conical prestressed elastic tube and the blood as a Newtonian fluid, we have studied the amplitude modulation of nonlinear waves in such a fluid-filled elastic tube, by use of the reductive perturbation method. The governing evolution equation is obtained as the dissipative nonlinear Schrödinger equation with variable coefficients. It is shown that this type of equations admit solitary wave solutions with variable wave amplitude and speed. It is observed that, the wave speed increases with distance for tubes of descending radius while it decreases for tubes of ascending radius. The dissipative effects cause a decay in wave amplitude and wave speed.     

Evolution equations for nonlinear waves in a tapered elastic tube filled with a viscous fluid

In this work, employing the reductive perturbation method and treating the arteries as a tapered, thin walled, long and circularly conical prestressed elastic tube, the propagation of weakly nonlinear waves is investigated in such a fluid-filled elastic tube. By considering the blood as an incompressible viscous fluid, depending on the viscosity and perturbation parameters we obtained various evolution equations as the extended Korteweg-de Vries (KdV), extended KdV Burgers and extended perturbed KdV equations. Progressive wave solutions to these evolution equations are obtained and it is observed that the wave speeds increase with the distance for negative tapering while they decrease for positive tapering.     

Propagation of electroacoustic axial shear waves in a piezoelectric medium reinforced by continuous fibers

The propagation of electroacoustic axial shear waves in a fiber reinforced piezocomposites is studied in which matrix and fibers consist of piezoelectric transversely isotropic materials with symmetry axes parallel to the fiber axes. The effective medium method self-consistent variant as developed by Sabina and Willis is used to obtain explicit equations for the complex wave vector and it is solved numerically. Its real part determines the effective wave velocity and the imaginary part the attenuation factor. Integral equations expressed via dynamic Green’s function kernels are set up. The central problem of the method is the axial shear electroacoustic wave scattering on one isolated fiber in the medium having the effective piezoelectric properties. It is solved approximately by the Galerkin type method. The obtained expressions for the effective wave velocity and attenuation factor cover not only the long-wave region but the intermediate wave and it is valid for long wavelenghts up to the diameter of the inclusion. Wave velocity and attenuation coefficient coincide with ones obtained earlier in some other way. Some numerical examples are presented for real materials.     

Micromechanical analysis of magneto-electro-thermo-elastic composite materials with applications to multilayered structures

The method of asymptotic homogenization was used to analyze a periodic magnetoelectric smart composite structure consisting of piezoelectric and piezomagnetic phases. The asymptotic homogenization model is derived, the governing equations are determined and subsequently general expressions called unit-cell problems that can be used to determine the effective elastic, piezoelectric, piezomagnetic, thermal expansion, dielectric, magnetic permeability, magnetoelectric, pyroelectric and pyromagnetic coefficients are presented. The latter three sets of coefficients are particularly interesting in the sense that they represent product or cross-properties; they are generated in the macroscopic composite via the interaction of the different phases, but may be absent from the constituents themselves. The derived expressions pertaining to the unit-cell problems and the resultant effective coefficients are very general and are valid for any 3-D geometry of the unit cell. The model is illustrated by means of longitudinally-layered smart composites consisting of piezoelectric (Barium Titanate) and piezomagnetic (Cobalt Ferrite) constituents. Closed-form expressions for the effective properties are derived and the results are plotted vs. the volume fraction of the piezoelectric phase. Pertaining to the product properties of this particular magnetoelectric laminate, it is observed that the effective pyroelectric and pyromagnetic coefficients attain a maximum value at a BaTiO₃ volume fraction of 0.5 and maximum values for the magnetoelectric coefficients at a BaTiO₃ volume fraction of 0.4. Likewise, the maximum value of a magnetoelectric figure of merit (characterizing efficiency of energy conversion in longitudinal direction) is also attained at a volume fraction of 0.4.     

液相夹杂复合软材料的设计、制备与力学性能研究进展

液相夹杂复合软材料是一类由功能液体或相变材料作为夹杂物的智能材料,由于其具备优异的变形特性和功能可设计性,近年来在柔性电子器件、可穿戴设备、软体机器人等领域得到广泛研究和应用。本文从以下几个方面回顾液相夹杂复合软材料的最新研究进展:首先,重点介绍非相变夹杂和相变夹杂复合软材料的功能设计及制备方法;然后,详细阐述液相夹杂复合软材料等效力学性能研究及尺寸效应;最后,简要探讨液相夹杂复合软材料研究所面临的挑战及值得关注的研究方向。     

Propagation of plastic waves in a long rod with consideration given to temperature rise

The strain and temperature distributions along a long rod subjected to a longitudinal impact at a high strain level are investigated using Malvern's linear strain-rate dependent theory with consideration being given to the temperature rise caused by the plastic work. The results show that a steeply decreasing part of strain appears near the impacted end and the region is followed by an uniform-strain (strain-plateau) one along the rod, and that the formation and growth of the uniform-strain region depends on the strain-hardening sensitivity of the rod. The computed profile of the temperature distribution is similar to that of the strain distribution. However, the growth of a uniform-temperature region (temperature plateau) is much slower that that of the strain plateau.     

Scattering of elastic waves by spherical inclusions with applications to low frequency wave propagation in composites

Scattering of plane elastic waves by a spherical inclusion is considered. A unified method of solution is presented which treats compressional and shear incidence on a similar basis. Explicit results are given for Rayleigh scattering. We apply the results of the single scattering problem to the propagation of low frequency waves in a composite containing a dilute concentration of spherical inclusions. Explicit formulae are given for the effective wave speeds and attenuations when the inclusions are voids. Both the compressional and shear wave speeds decrease initially as a function of frequency.     

Combining self-consistent and numerical methods for the calculation of elastic fields and effective properties of 3D-matrix composites with periodic and random microstructures

The work is devoted to the calculation of static elastic fields in 3D-composite materials consisting of a homogeneous host medium (matrix) and an array of isolated heterogeneous inclusions. A self-consistent effective field method allows reducing this problem to the problem for a typical cell of the composite that contains a finite number of the inclusions. The volume integral equations for strain and stress fields in a heterogeneous medium are used. Discretization of these equations is performed by the radial Gaussian functions centered at a system of approximating nodes. Such functions allow calculating the elements of the matrix of the discretized problem in explicit analytical form. For a regular grid of approximating nodes, the matrix of the discretized problem has the Toeplitz properties, and matrix-vector products with such matrices may be calculated by the fast fourier transform technique. The latter accelerates significantly the iterative procedure. First, the method is applied to the calculation of elastic fields in a homogeneous medium with a spherical heterogeneous inclusion and then, to composites with periodic and random sets of spherical inclusions. Simple cubic and FCC lattices of the inclusions which material is stiffer or softer than the material of the matrix are considered. The calculations are performed for cells that contain various numbers of the inclusions, and the predicted effective constants of the composites are compared with the numerical solutions of other authors. Finally, a composite material with a random set of spherical inclusions is considered. It is shown that the consideration of a composite cell that contains a dozen of randomly distributed inclusions allows predicting the composite effective elastic constants with sufficient accuracy.     

Two analytical models for the study of periodic fibrous elastic composite with different unit cells

In this work, the effective elastic moduli of two-phase fibrous periodic composites are obtained by means of the Asymptotic Homogenization Method (AHM) and eigenfunction expansion-variational method (EEVM), for different types of parallelogram cells. The constituents exhibit transversely isotropic properties. A doubly periodic parallelogram array of cylindrical inclusions under longitudinal shear is considered. The behavior of the shear elastic coefficient for different geometry arrays of the cell related to the angle of the fibers is studied. Some numerical examples and comparisons with other theoretical results demonstrate that both methods (AHM and EEVM) are efficients for the analysis of composites with presence of rhombic cell. The effect of the configuration of the cells on the shear effective property is observed.