Effective Dynamic Properties Research Articles

Effective dynamic properties of 3D composite materials containing rigid penny-shaped inclusions

The propagation of time-harmonic plane elastic waves in infinite elastic composite materials consisting of linear elastic matrix and rigid penny-shaped inclusions is investigated in this paper. The inclusions are allowed to translate and rotate in the matrix. First, the three-dimensional (3D) wave scattering problem by a single inclusion is reduced to a system of boundary integral equations for the stress jumps across the inclusion surfaces. A boundary element method (BEM) is developed for solving the boundary integral equations numerically. Far-field scattering amplitudes and complex wavenumbers are computed by using the stress jumps. Then the solution of the single scattering problem is applied to estimate the effective dynamic parameters of the composite materials containing randomly distributed inclusions of dilute concentration. Numerical results for the attenuation coefficient and the effective velocity of longitudinal and transverse waves in infinite elastic composites containing parallel and randomly oriented rigid penny-shaped inclusions of equal size and equal mass are presented and discussed. The effects of the wave frequency, the inclusion mass, the inclusion density, and the inclusion orientation or the direction of the wave incidence on the attenuation coefficient and the effective wave velocities are analysed. The results presented in this paper are compared with the available analytical results in the low-frequency range.

Thermal properties and glass transition in PMMA + SWCNT composites

The effective thermal and dynamic properties of composites containing polymethyl-metha-acralyte (PMMA) dispersed with single-wall carbon nanotubes (SWCNTs) were studied by modulation/ac calorimetry (ACC) and modulation-differential-scanning (MDSC) calorimetric techniques. The specific heat and effective thermal conductivity were determined by ACC from 300 to 400 K as a function of SWCNT content. A large enhancement of the effective thermal conductivity is observed as the mass fraction (ϕm) of SWCNTs increases from 0.014 to 0.083. These results are in good agreement with a simple geometric model at low SWCNT content but are better described by more sophisticated models above ϕm ∼ 0.039. The dynamics of the glass transition were studied by MDSC as a function of temperature scan rate. The hysteresis of the reversible specific heat between heating and cooling scans decreases with decreasing scan rate for pure PMMA but is essentially zero in the composites, indicating that the SWCNT may be quenching slow glass dynamics. In all samples, the effective glass transition temperature, Tg, increases with increasing scan rate (though less so for higher ϕm) but the MDSC determined Tg does not fall inline with that determined by the ACC method. This discrepancy is attributed to the effect of prolonged heat treatment of the composite sample used in the ACC experiments.

Homogenization Techniques and Micromechanics. A Survey and Perspectives

In this paper, we present a critical survey on homogenization theory and related techniques applied to micromechanics. The validation of homogenization results, the characterization of composite materials and the optimal design of complex structures are issues of great technological importance and are viewed here as a combination of mathematical and mechanical homogenization. The mathematical tools for modeling sequentially layered composites are explained. The influence of initial and boundary conditions on the effective properties in nonlinear problems is clarified and the notion of stability by homogenization is analyzed. Multiscale micromechanics methods are outlined and the classical as well as the emerging analytical and computational techniques are presented. Computation of effective static and dynamical properties of materials with linear or nonlinear constitutive equations is closely related to the development of generalized theories such as the strain-gradient mechanics. Selected applications of these techniques are outlined. Moreover, the extension of kinetic techniques in homogenization and the related inverse imaging problem are presented.

Minimum variational principles for time-harmonic waves in a dissipative medium and associated variational principles of Hashin–Shtrikman type

Minimization variational principles for linear elastodynamic, acoustic or electromagnetic time-harmonic waves in dissipative media were obtained by Milton et al. (Milton et al. 2009 Proc. R. Soc. A 465 , 367–396 ( doi:10.1098/rspa.2008.0195 )), generalizing the quasistatic variational principles of Cherkaev and Gibiansky (Cherkaev & Gibiansky 1994 J. Math. Phys. 35 , 127–145 ( doi:10.1063/1.530782 )). Here, a further generalization is made to allow for a much wider variety of boundary conditions, and in particular Dirichlet and Neumann boundary conditions. In addition minimization or maximization principles of the Hashin–Shtrikman type, incorporating ‘polarization fields’, are developed. The corresponding principles for static problems have found substantial use in bounding the effective static properties of composite materials. The new dynamical principles offer the prospect of developing bounds on the effective dynamic properties of such materials.

Sub-wavelength plasmonic crystals: dispersion relations and effective properties

We obtain a convergent power series expansion for the first branch of the dispersion relation for sub-wavelength plasmonic crystals consisting of plasmonic rods with frequency-dependent dielectric permittivity embedded in a host medium with unit permittivity. The expansion parameter is η = kd =2 πd / λ , where k is the norm of a fixed wavevector, d is the period of the crystal and λ is the wavelength, and the plasma frequency scales inversely to d , making the dielectric permittivity in the rods large and negative. The expressions for the series coefficients (also called dynamic correctors) and the radius of convergence in η are explicitly related to the solutions of higher order cell problems and the geometry of the rods. Within the radius of convergence, we are able to compute the dispersion relation and the fields and define dynamic effective properties in a mathematically rigorous manner. Explicit error estimates show that a good approximation to the true dispersion relation is obtained using only a few terms of the expansion. The convergence proof requires the use of properties of the Catalan numbers to show that the series coefficients are exponentially bounded in the H 1 Sobolev norm.

Ab initio volume-dependent elastic and lattice dynamics properties of KTaO3

Ab initio calculations have been performed to investigate the behaviour under hydrostatic pressure of the structural and electronic properties, the optical dielectric constant, the Born effective charges, and elastic and dynamical properties in cubic perovskite KTaO 3 . These physical properties have been calculated within the local density approximation in the frame of density functional theory. The results for the pressure behaviour of these properties of KTaO 3 are in agreement with experimental data when available; in other cases they may be considered as predictions.

Smart-Cue and Smart-Gain Concepts to Alleviate Loss of Control

Unfavorable pilot-vehicle-system interactions including pilot-induced oscillations have long been an aviation safety problem. This was true 100 years ago when the Wright brothers first demonstrated powered flight, and it is still true today even for advanced fly-by-wire flight control systems. Although the effective aircraft dynamic properties involved in these events have been extensively studied and understood, similar scrutiny has not been paid to the many aspects ofthe primary manual control system that converts the pilot control inputs to motions of the control surfaces. It has often been tacitly assumed that the adoption of fly-by-wire systems has eliminated the primary manual control link as an important player in loss of control situations. Consequently, the impact of static and dynamic control system effects that distort ideal pilot-to-surface relationships, the near absence of manipulator tactile cues for some fly-by-wire systems, as well as the total elimination in fly-by-wire systems of some favorable cues present in traditional hydromechanical systems have not received detailed attention. The concept of dynamic has significantly evolved in work conducted by Systems Technology, Inc. during a two-phase program sponsored by NASA Dryden Flight Research Center. In this work the of interest results from control surface rate limiting and is quantified by the surface position error, whereas the distortion metric is the position lag. A force feedback cue (the constraining function) and/or a command path gain reduction are created when the position error exceeds the position lag (the alerting function). The smart-cue and smart-gain concepts, as described in this paper, are remarkable in their simplicity. The overall implementation does, however, require hardware in the form of a programmable, back-driven force feel system.

Size-dependent effective dynamic properties of unidirectional nanocomposites with interface energy effects

This article studies the size effect on wave propagation characteristics of plane longitudinal and transverse elastic waves in a two-phase nanocomposite consisting of transversely isotropic and unidirectionally oriented identical cylindrical nanofibers embedded in a transversely isotropic homogeneous matrix. The surface elasticity theory is employed to incorporate the interfacial stress effects. The effect of random distribution of nanofibers in the composite medium is taken into account via a generalized self-consistent multiple scattering model. The phase velocities and attenuations of longitudinal and shear waves along with the associated dynamic effective elastic constants are calculated for a wide range of frequencies and fiber concentrations. The numerical results reveal that interface elasticity at nanometer length scales can significantly alter the overall dynamic mechanical properties of nanofiber-reinforced composites. Limiting cases are considered and excellent agreements with solutions available in the literature have been obtained.

Coarse-graining in interaction space: a systematic approach for replacing long-range electrostatics with short-range potentials.

A short-range effective potential for long-range electrostatic interactions in homogeneously disordered condensed phase systems has been determined with a novel approach to coarse-graining in interaction space. As opposed to coarse-graining the system resolution, this approach "coarsens" the system's interactions by mapping multiple configurations of an accurate long-range atomistic potential onto a more efficient, short-range effective potential with a force-matching (FM) method. Developing an empirical potential in this manner is fundamentally different from existing strategies because it utilizes condensed-phase (as opposed to gas-phase) atomistic interactions to determine general pair potentials defined on distance meshes (as opposed to fitting predetermined functional forms). The resulting short-range ( approximately 10 A) effective potential reproduces structural, dynamical, and many thermodynamic properties of liquid water, ions in water, and hydrophobes in water, with unprecedented accuracy. The effective potential is also shown to be transferable to a nonaqueous molten salt system. With continued development, such effective potentials may provide an accurate and highly efficient alternative to Ewald-based long-range electrostatics methods.

Dynamic effective thermal properties of functionally graded fibrous composites using non-Fourier heat conduction

A micromechanics-based thermo-dynamical model is proposed to predict the distribution of dynamic effective thermal properties of functionally graded fibrous composites resulting from thermal waves. Generally speaking, in functionally graded materials there exist two microstructurally distinct zones: fiber-matrix zone and a transition zone. In the fiber-matrix zone, based on the non-Fourier heat conduction equation in materials, the dynamic effective thermal properties for any macroscopic material points are determined by employing the effective medium method in the corresponding microstructural representative volume element (RVE). In transition zone, a transition function is introduced to make the wave fields continuous and differentiable. Numerical examples of the dynamic effective thermal properties in the gradation direction under different parameters are graphically presented. Analysis shows that the material properties of each phase, the incident frequency, and the gradation parameter of materials have great effect on the distribution of dynamic effective properties in the gradation direction. In different material zones, the effect displays great difference. In the region of higher frequencies, the relaxation time of the two phases also has great effect the dynamic thermal properties. At last, the results are discussed in detail.

Dynamic effective thermal properties of ceramics–metal functionally graded fibrous composites

This work is dedicated to investigate the dynamic effective thermal properties of ceramics–metal functionally graded fibrous composites resulting from thermal waves. A micromechanics-based thermo-dynamical model is developed to predict the distribution of dynamic effective thermal properties of functionally graded fibrous composites in the gradation direction. Generally speaking, in functionally graded materials there exist two microstructurally distinct zones: fiber–matrix zone and a transition zone. In fiber–matrix zone, based on the heat conduction equation in materials, the dynamic effective thermal properties for any macroscopic material points are determined by employing effective medium method in the corresponding microstructural representative volume element (RVE). In transition zone, a transition function is introduced to make the wave fields continuous and differentiable. Numerical examples of the dynamic effective thermal properties in the gradation direction under different parameters are graphically presented. Obtained results reveal that the material properties of each phase, the incident frequency, and the gradation parameter of materials have great effect on the distribution of dynamic effective properties in the gradation direction. In different material zones, the effect displays great difference. At last, the results are discussed in detail.

Dynamic effective properties of matrix composite materials with high volume concentrations of particles

A new approach is proposed to investigate the propagation of a plane compressional wave in matrix composite materials with high volume concentrations of particles. The theory of quasicrystalline approximation and Waterman’s T matrix formalism are employed to treat the multiple scattering resulting from the particles in composites. The addition theorem for spherical Bessel functions is used to accomplish the translation between different coordinate systems. The Percus–Yevick correlation function widely applied in the molecular theory of liquids is employed to analyze the interaction of the densely distributed particles. The analytical expression for the Percus–Yevick correlation function is also given. The closed form solution for the effective propagation constant is obtained in the low frequency limit. Only numerical solutions are obtained at higher frequencies. Numerical examples show that the phase velocities in the composite materials with low volume concentration are in good agreement with those in previous literatures. The effects of the incident wave number, the volume fraction and the material properties of the particles and matrix on the phase velocity are also examined.

Effective material properties for shear-horizontal acoustic waves in fiber composites

The effective dynamic properties of composites made of elastic cylindrical fibers randomly distributed in another elastic solid can be evaluated with plane shear-horizontal acoustic waves. In this paper, it is shown that the effective mass density and the effective shear stiffness are complex valued and frequency dependent. Simple formulas are derived for these effective quantities. The low-frequency limit of these formulas is found to be in agreement with physical expectations. The derivation is based on the multiple-scattering approach of Waterman and Truell, where each cylinder of finite cross section is replaced with an equivalent line scatterer. Numerical results are presented for the effective mass density and effective shear stiffness for various values of frequency, cylinder concentration, and elastic properties of the cylinders and matrix.

Dynamic effective properties of semi-infinite random unidirectional fiber-reinforced composites subjected to anti-plane shear waves

Based on the theory of elastodynamics, and employing the effective medium method and the image method, the propagation of shear waves in semi-infinite random unidirectional fiber-reinforced composites is investigated. The dispersion relation for the effective wave number in the random composites is derived. The numerical solutions of the dynamic effective properties are obtained by using an iterative scheme. The image method is applied to satisfy the traction free boundary condition of the semi-infinite composite. The effective wave fields are expressed by using the wave function expansion method, and the expanded modal coefficients are determined by satisfying the continuous boundary conditions around the fibers. Analyses show that the variation of the dynamic effective properties in the semi-infinite composite is significantly different from that in the infinite composite. The maximum dynamic effective properties near the surface increase with the increase of the incident wave number, the volume fraction of fibers, and the properties ratio of the two phases.

Determination of dynamic effective properties in functionally graded materials

This work is dedicated to the investigation of the dynamic effective properties in functionally graded materials resulting from an anti-plane shear wave. A micromechanics-based elastodynamic model is developed to predict the dynamic behavior of two-phase functionally graded materials, and the distribution of dynamic effective properties in the gradation direction is presented. Generally speaking, in functionally graded materials there exist two microstructurally distinct zones: a fiber-matrix zone and a transition zone. In the fiber-matrix zone, the dispersion relation for the effective wave number is derived using the effective medium method, and the dynamic effective properties for any macroscopic material points are determined in the corresponding microstructural representative volume element (RVE). In the transition zone, a transition function is introduced to make the wave fields continuous and differentiable. Numerical examples of the dynamic effective properties in the gradation direction under different parameters are presented graphically. The obtained results reveal that the distribution of dynamic effective properties in the gradation direction is dependent on the material properties of each phase, the incident frequency, and the gradation parameter of the materials. Comparisons between numerical solutions and experimental data are also made. At last, the results are discussed in detail.

A self-consistent approach to dynamic effective properties of a composite reinforced by distributed spherical particles

A self-consistent approach to dynamic effective properties of a composite reinforced by randomly distributed spherical inclusions is studied. The coherent plane waves propagating through the particle-reinforced composite are of attenuation nature. It implies that there is an analogy between the particle-reinforced composite and the effective medium with complex-valued elastic constants from the viewpoints of wave propagation. A composite sphere consisting of the inclusion, the matrix and the interphase between them is assumed embedded in the effective medium. The effective wavenumbers of the coherent plane waves propagating through the particle-reinforced composite are obtained by the dynamic self-consistent conditions which require that the forward scattering amplitudes of such a composite sphere embedded in the effective medium are equal to zero. The dynamic effective properties (effective phase velocity, effective attenuation and effective elastic constants) obtained by the present dynamic self-consistent approach for SiC-Al composites are compared numerically with that obtained by the effective field approach at various volume concentrations. It is found that there is a good agreement between the two approaches at a relatively low frequency and low volume concentration but the numerical results deviate from each other at a relatively high frequency and high volume concentration.

Influences of interphase on dynamic effective properties of composites reinforced by dispersed spherical particles

The influences of interphase on dynamic effective properties of composites reinforced by randomly dispersed spherical particles were studied. A thin homogeneous elastic interphase with different shear and bulk moduli, located between the reinforced particle and the host matrix, was introduced to model the interfacial bonding state. The effects of such an interphase on the coherent plane waves were studied numerically. Numerical simulations were carried out for SiC-Al composites with four typical cases of interphase. It was found that the property of interphase has significant influences on the effective propagation constants of coherent waves and the dynamic effective elastic moduli of the composites. The influences on the coherent longitudinal wave and the coherent shear waves were different and dependent upon the frequency range. Moreover, several imperfect interface models, i.e., the spring model, mass model, and spring-mass model, were studied numerically and compared with the interphase model. It was found that the spring model is a more suitable model than the mass model for the light and weak interphase whereas the mass model is a more suitable model than the spring model for the heavy and strong interphase.

Determination of effective properties and effective thickness of resonant acoustic metamaterial

Multiple scattering in periodic structures with strong modulation of elastic constants leads to phononic band structures. According to the Bragg’s theory, the spatial modulation of the periodic structure must be of the same order as the wavelength of considered elastic waves. A resonant acoustic metamaterial’s respective wavelength is about two orders of magnitude larger than the lattice constant. Each unit cell consists of a locally resonant structural unit in contrast to simple acoustic scatterers in phononic crystals. In this report, we will address the design of locally resonant sonic materials. These materials may offer dynamic effective negative material properties around resonance frequency. Locally resonant sonic crystals, such as an array of Helmholtz resonators and cylinders or spheres coated with acoustically soft material, were analyzed in the literature. However, existing literature lacks a systematic study of the dependence of effective properties for a finite slab of these metamaterials both on the geometry and the properties of its constituent materials. In this report, we present a method for obtaining effective properties and effective thickness of a slab of acoustic metamaterial. The dependence of effective acoustic properties of a metamaterial on the geometrical and acoustic properties of constituent materials will be discussed.

Dynamic Characteristics and Effective Stiffness Properties of Honeycomb Composite Sandwich Structures for Highway Bridge Applications

In this paper, a combined analytical and experimental study of dynamic characteristics of honeycomb composite sandwich structures in bridge systems is presented, and a relatively simple and reliable dynamic experimental procedure to estimate the beam bending and transverse shear stiffness is proposed. This procedure is especially practicable for estimating the beam transverse shear stiffness, which is primarily contributed by the core and is usually difficult to measure. The composite sandwich beams are made of E-glass fiber and polyester resins, and the core consists of the corrugated cells in a sinusoidal configuration. Based on the modeling of equivalent properties for the face laminates and core elements, analytical predictions of effective flexural and transverse shear stiffness properties of sandwich beams along the longitudinal and transverse to the sinusoidal core wave directions are first obtained. Using piezoelectric sensors, the dynamic response data are collected, and the dynamic characteristics of the sandwich structures are analyzed, from which the flexural and transverse shear stiffness properties are reduced. The experimental stiffness results are then compared to the analytical stiffness properties, and relatively good correlations are obtained. The proposed dynamic tests using piezoelectric sensors can be used effectively to evaluate the dynamic characteristics and stiffness properties of large sandwich structures suitable for highway bridge applications.

Structure-property relationships in polymer composites with micrometer and submicrometer graphite platelets

The objectives of this work were (a) to investigate the influence of micrometer and submicrometer scale graphite platelets of different aspect ratios and volume fractions on the effective and local quasi-static and dynamic properties of composites with micrometer and submicrometer scale reinforcement, and (b) to compare and evaluate mechanical property measurements of inhomogeneous materials via local (microscale) and bulk (macroscale) experimental methods. Small platelet volume fractions (0.5%) provided proportionally larger increase of the elastic and storage moduli compared to large volume fractions (3.0%). Randomly distributed 15 μm platelets provided marginally higher composite stiffness compared to 1 μm platelets while small volume fractions (0.5%) of 15 μm platelets had a pronounced effect on the effective Poisson's ratio. It was found that local property measurements of inhomogeneous materials conducted by nanoindentation are not representative of the bulk behavior even when the characteristic length of the inhomogeneity is an order of magnitude smaller than the indentation contact area. In this case, statistical averaging of data from a large number of indentations does not result in agreement with bulk measurements. On the other hand, for small aspect ratio platelets with dimensions two orders of magnitude smaller than the nanoindentation contact area, the nanoindenter-obtained properties agreed well with the effective material behavior. It was found that platelets residing at the specimen surface contribute the most to nanoindentation data, which implies that this technique is only valid for well-distributed nanoparticulate and microparticulate systems, and that nanoindentation cannot be used for depth profiling of microstructured composites.