Effective Dynamic Modulus Research Articles

Numerical Modeling of the Dynamic Elastic Modulus of Concrete.

This article introduces simulations of theoretical material with controlled properties for the evaluation of the effect of key parameters, as volumetric fractions, elastic properties of each phase and transition zone on the effective dynamic elastic modulus. The accuracy level of classical homogenization models was checked regarding the prediction of dynamic elastic modulus. Numerical simulations were performed with the finite element method for evaluations of the natural frequencies and their correlation with Ed through frequency equations. An acoustic test validated the numerical results and obtained the elastic modulus of concretes and mortars at 0.3, 0.5 and 0.7 water-cement ratios. Hirsch calibrated according to the numerical simulation (x = 0.27) exhibited a realistic behavior for concretes of w/c = 0.3 and 0.5, with a 5% error. However, when the water-to-cement ratio (w/c) was set to 0.7, Young's modulus displayed a resemblance to the Reuss model, akin to the simulated theoretical triphasic materials, considering matrix, coarse aggregate and a transition zone. Hashin-Shtrikman bounds is not perfectly applied to theoretical biphasic materials under dynamic situations.

Brownian motion with radioactive decay to calculate the dynamic bulk modulus of gases saturating porous media according to Biot theory

We present a new stochastic simulation method for determining the long-wavelength effective dynamic bulk modulus of gases, such as ambient air, saturating porous media with relatively arbitrary microgeometries, i.e., simple enough to warrant Biot’s simplification that the fluid and solid motions are quasi-incompressible motions at the pore scale. The simulation method is based on the mathematical isomorphism between two different physical problems. One of them is the actual Fourier heat exchange problem between gas and solid in the context of Biot theory. The other is a diffusion-disintegration-controlled problem that considers Brownian motion of diffusing particles undergoing radioactive-type decay in the pore volume and instant decay at the pore walls. By appropriately choosing the decay time and the diffusion coefficient, the stochastic algorithm we develop to determine the average lifetime of the diffusing particles, directly gives the effective apparent modulus of the saturating fluid. We show how it leads to purely geometric stochastic constructions to determine a number of geometrical parameters. After validating the algorithm for cylindrical circular pores, its power is illustrated for the case of fibrous materials of the type used in noise control. The results agree well with a model of the effective modulus with three purely geometric parameters of the pore space: static thermal permeability divided by porosity, static thermal tortuosity, and thermal characteristic length.

Effect of 3D aggregate shape on thermo-mechanical properties of asphalt concrete using a mesostructure-based homogenisation method

ABSTRACT Morphological characteristics of aggregates have long been recognised as an essential factor influencing the thermo-mechanical behaviour of asphalt concrete. However, studies on accurate quantification of this influence are still very limited. For this reason, the present study developed a mesoscale finite element method to investigate the effects of three-dimensional (3D) aggregate shape on the complex modulus, thermal expansion coefficient, thermal conductivity, and mesoscale responses of asphalt concrete. An upscaling homogenisation method was adopted to predict the effective thermo-mechanical properties of asphalt concrete. The 3D true sphericity (3DTS) was used as an index to characterise the aggregate shape. The computational results showed that the temperature and loading frequency significantly affect the role of aggregate shapes in determining the effective dynamic modulus of asphalt concrete. The high-angularity aggregates can increase the deformation resistance of asphalt concrete under thermal load, and thus reduces the thermal contraction coefficient of asphalt concrete. However, aggregate shape has no significant effect on the thermal conductivity of the asphalt concrete. In addition, the asphalt concretes with less angular aggregates have stronger low-temperature damage resistance, while the aggregates with high angularity can improve the rutting resistance of asphalt pavements.

Energy dissipation of CFRP composites coated by wavy CNT with focus on the CNT maximum reachable volume fraction

Dynamic moduli and energy dissipation capability of polymer hybrid nanocomposite reinforced with carbon fiber (CF) coated by carbon nanotube (CNT) which makes a fuzzy fiber nanocomposite (FFNC) are estimated through a micromechanical model. An analytical expression is derived to extract the damping properties in the frequency domain. Then, a separate phase known as interphase whose properties vary gradually is taken into account to model the CNT/polymer interactions. The CNT waviness and random orientation are also included. Acceptable agreements in comparison with the molecular dynamics simulations and experiments prove the accuracy of the proposed model. Moreover, the maximum reachable volume fraction of CNTs is studied considering the radius of gyration of polymer chain, the CNT aspect ratio (CNTAR), radius, and waviness amplitude. The effects of the CNT inter-tube distance (CNTID), waviness, CNTAR, and the loading frequency are examined on the energy dissipation and storage capability, and hysteresis loop of FFNC. It is found that the FFNC effective dynamic moduli enhance by increasing the CNTAR, while the CNTAR becomes less influential as the CNTID increases. Furthermore, as the frequency increases, the area of the hysteresis loop is decreased. Whereas the hysteresis loop is converted to a straight line beyond the frequency of about 1e17 Hz.

Differentiation of thixotropy from damage for accurately characterizing fatigue resistance of asphalt binder

Accurate characterization of the fatigue resistance of asphalt binder is of great significance to the prediction of asphalt pavement performance. Traditionally, apparent changes in viscoelastic parameters, including dynamic shear modulus and phase angle, with the number of loading cycles are used to define the fatigue performance of the asphalt binder. However, thixotropy also leads to changes in these viscoelastic parameters, and its contribution is not yet well understood. This study develops a method to quantify the effects of damage and thixotropy on the changes of viscoelastic parameters under the cyclic stress-controlled loading mode. The new method includes the four key steps: (1) determining the thixotropy influence-dominated phase; (2) establishing a thixotropy model to characterize the influence of thixotropy on the effective dynamic shear modulus; (3) calculating damage density from the apparent and effective dynamic shear moduli; and (4) characterizing thixotropy behavior based on Black space diagram. The effectiveness of the newly developed method is verified by the time sweep test, which is conducted on two types of asphalt binder under varying stress levels.with a loading frequency of 10 Hz and a test temperature of 25 °C. The results show that: (1) the change of dynamic shear modulus is resulted from the damage and thixotropy, while that of phase angle is only caused by the thixotropy; (2) thixotropy leads to the decrease of dynamic shear modulus and increase of phase angle; and its influence on viscoelastic parameters increases with the loading time and stress level increased; (3) under the influence of thixotropy, the dynamic shear modulus is linearly related to the phase angle, which is independent of the stress level applied and the damage accumulated in the asphalt binder.

Suspension of discrete microscopic oscillators as a model of an ultrasonic metafluid

We present a model of ultrasonic metafluids---acoustic metamaterials in the form of suspensions of discrete microscopic oscillators coupled to the embedding fluid. Contrary to a common assumption about metamaterials, and as already established in the field of metafluids, the metafluid concept need not be based on position periodicity or correlation of the suspended micro-oscillators, and in this case not even on ideally designed micro-oscillators. For the speculation that metafluids may one day be produced as solutions of macromolecules, it is essential that the micro-oscillators be allowed to be randomly distributed in the host fluid and generally have irregular (modal) shapes. We formulate the detailed operating principle of such a metafluid model, give explicit formulas for its effective dynamic moduli in terms of the modal structure of the micro-oscillators, and discuss basic practical issues of performance optimization in terms of their mass and size.

Dynamic Effective Properties of Lead-Reinforced Epoxy Resin Composites with Differential Method

In this paper, the quasi-P wave propagation in epoxy/lead composites is studied by the differential method with polarization stress and polarization momentum. The corresponding differential equations are numerically solved by the fourth-order Runge–Kutta method, and the dynamic effective modulus and density are obtained. Correctness of the results obtained by the differential method is verified by comparing with the results obtained by the self-consistent method as well as experiments. Results show that the dynamic effective modulus L 1133 and L 3333 increase with the increase of aspect ratio δ , whereas L 1111 and L 1122 decrease with the increase of δ . The phase velocity ratio of the quasi-P wave propagation in the composites tends to 1 when the dimensionless wave number is large, and the dynamic effective density and modulus obtained are not isotropic when δ ≠ 1 . It is believed that the differential method can be a choice for solving dynamic effective properties of heterogeneous composites.

Nondestructive assessment of cross-laminated timber using non-contact transverse vibration and ultrasonic testing

Cross-laminated timber (CLT) is a new generation of engineered wood product developed initially in Europe and has been used in North America for various applications. CLT is composed of at least three layers of lumber boards stacked crosswise in orthogonally alternating orientation to the adjacent layers. CLT has been gaining popularity and increasing application areas in the construction industry, such as building systems, mats for construction and temporary road applications as well as temporary bridges. It is especially identified as the prevailing material in modular construction for the future building industry. However, CLT as a relatively new structural material has limited studies related to their durability and long-term performance. Moreover, nondestructive evaluation methods to understand their mechanical behavior after exposure to harsh environment are lacking. This paper contributes to the development of a rapid nondestructive evaluation method to assess the mechanical properties using transverse vibration method and ultrasonic testing. The free vibration response triggered by the impulse excitation is captured using contact accelerometer and non-contact laser Doppler vibrometer (LDV). The LDV measurement is proven to respond similar to conventional accelerometers but more convenient as a rapid assessment method. While the longitudinal wave speed is measured by ultrasonic testing (UT) in a through-transmission mode, the modulus of elasticity was calculated in terms of measured wave speed. By investigating the different structural states and dimensions of CLT samples, the laboratory and the manufacturing facility, the influences of aging on effective dynamic modulus of elasticity (MOE) and damping are shown. The numerical and experimental results indicate the increase in moisture content decreases the fundamental frequency. Therefore, moisture content should be measured in order to examine the coupled effects of moisture content and aging on the fundamental frequency. The damping ratio extracted using half-power bandwidth method is shown as an additional information related to the moisture content. The non-contact transverse vibration method and UT are shown as an efficient nondestructive evaluation method for assessing the CLT structural state right after the manufacturing as a quality assurance method or after their service in field as a diagnostic tool.

Mesomechanical prediction of viscoelastic behavior of asphalt concrete considering effect of aggregate shape

Accurate prediction of effective (overall) viscoelastic properties and mesoscopic responses of asphalt concrete is crucial to investigating the mechanical behavior and damage mechanisms of asphalt pavement. The present study evaluated the effect of aggregate shape on mesomechanical prediction of viscoelastic behavior of asphalt concrete. Two two-dimensional (2D) computational mesomechanics methods, i.e., a random aggregate generation (RAG)-based method and a digital image processing (DIP)-based method, and a three-dimensional (3D) analytical two-layer built-in (TLB) mesomechanics method were adopted. In the RAG-based approach, four regular aggregate shapes (circle, hexagon, pentagon and square) and irregular aggregate shapes were considered. The results showed that when asphalt concrete was treated as a composite consisting of coarser aggregates larger than 2.36 mm, asphalt mortar and air voids, the volume fraction of coarse aggregates was a more critical factor than their shapes for the effective dynamic modulus prediction. The 3D TLB method performed better in predicting the macroscopic effective dynamic modulus of asphalt concrete than the 2D methods, whereas the 2D methods generated superior effective phase angle predictions. The RAG-based model with irregular aggregates and the DIP-based model exhibited significantly higher maximum principal stresses on the mesoscale than those from the RAG-based models with regular aggregates under the compressive loading condition, indicating the importance of applying the realistic aggregate shapes in the mesoscopic stress and damage analysis of asphalt concrete.

Interface stress effect tuning and enhancing the energy dissipation of staggered nanocomposites

ABSTRACTNatural biological composites and artificial biomimetic staggered composites with nanoscale internal structures can exhibit extraordinary energy dissipation, compared with conventional composites. It is believed that the interface stress effects of the interfaces between hard platelets and a viscous matrix play an important role in the extraordinary damping properties of such nanocomposites. In this study, a viscoelastic model is established to investigate the mechanism of the influence that the interface stress effect has on the damping properties, based on the Gurtin-Murdoch interface model and the tension-shear chain model. An explicit analytical solution of the effective dynamic moduli characterising the damping properties is obtained by using the correspondence principle, which is also validated by comparison with a finite element analysis. From the obtained analytical solution, an interface factor is abstracted to characterise the synergistic effect of the feature size and material parameters on the damping properties. Based on the model established, the optimal size of the platelets and the optimal loading frequency can be designed to achieve superior energy dissipation, when the staggered nanocomposites bear the dynamic load. Therefore, the findings of the present study not only reveal the damping mechanism of biological structures at nanoscale but also provide useful guidelines for the design of biomimetic nanocomposites from the nanoscale to the macroscopic scale.

Reversed Doppler effect based on hybridized acoustic Mie resonances

The realization of reversed Doppler effects in double-negative acoustic metamaterials remains challenging. This paper demonstrates the reversed Doppler effect associated with sound wave propagation in negative group velocity in hybridized metamaterial (HM) system using a simple Mie-resonator configuration. Double-negative acoustic parameters act simultaneously on the effective dynamic bulk modulus and mass density within overlapped frequency region of multiple Mie resonances. Notably, while ordinary media exhibits higher received frequency during the approach and lower during the recession, we observe that in HM the detected signals show redshift compared to the emitted frequency when approaching to the source while depict blue shift when receding from the source. On this basis, the HM exhibits negative phase velocity with reversed wavefronts and negative refraction effect for certain frequency range. Focusing of sound waves emitted from a point source is further realized with a flat lens composed by such a HM slab.

Effective dynamic properties of random complex media with spherical particles.

The effective dynamic bulk modulus and density are presented for random media consisting of particles in a viscous host fluid, using a core-shell, self-consistent effective medium model, under the large compressional wavelength assumption. These properties are relevant to acoustic or dynamic processes in nano- and micro-particle fluids including particle density determination, resonant acoustic mixing, and acoustic characterisation. Analytical expressions are obtained for the effective bulk modulus and mass density, incorporating the viscous nature of the fluid host into the core-shell model through wave mode conversion phenomena. The effective density is derived in terms of particle concentration, particle and host densities, particle size, and the acoustic and shear wavenumbers of the liquid host. The analytical expressions obtained agree with prior known results in the limit of both static and inviscid cases; the ratio of the effective bulk modulus to that of the fluid is found to be quasi-static. Numerical calculations demonstrate the dependence of the effective mass density on frequency, particle size (from nano- to micro-regime), and concentration. Herein it is demonstrated both theoretically and numerically that the viscosity, often neglected in the literature, indeed plays a significant role in the effective properties of nanofluids.

Prediction of dynamic modulus of asphalt mixture using micromechanical method with radial distribution functions

Inter-particle interaction is one of the major reinforcement mechanisms for aggregates in asphalt mixture, which is a classic example of high-volume fraction particulate composites. This paper introduced the modified Ju-Chen (J-C) micromechanical method based on two types of radial distribution assumptions for inclusions in the matrix, namely the uniform distribution and Percus–Yevick (P–Y) distribution. A two-step approach was proposed and the elastic–viscoelastic correspondence principle was used to predict the effective dynamic modulus of asphalt mixture at different frequencies. The prediction results show that the uniform distribution and P–Y distribution based J-C method could generate the upper and lower bounds of dynamic modulus for asphalt mixture, respectively. As compared to the measured dynamic modulus at different temperatures and loading frequencies, the modified J-C method showed better prediction accuracy as compared to two traditional micromechanical models based on single inclusion configuration, Mori–Tanaka (M–T) and differential scheme effective medium models. The J-C method assuming P–Y distribution provided better accuracy at the low frequencies; while the J-C method assuming the uniform distribution only had good accuracy at the high frequencies. The study findings indicate that dynamic modulus of asphalt mixture can be predicted based on laboratory tests conducted at the fine aggregate mix level and the void ratio and the gradation of coarse aggregate using appropriate micromechanics methods.

Acoustic perfect absorption and broadband insulation achieved by double-zero metamaterials

We report the mechanism for simultaneous realization of acoustic perfect absorption (PA) and broadband insulation (BI) in the acoustic free field by a layered acoustic metamaterial (LAM). The proposed LAM comprises two critically coupled membrane-type acoustic metamaterials sandwiching a porous material layer. Both theoretical and experimental results verify that the proposed LAM sample can achieve nearly PA (98.4% in experiments) at 312 Hz with a thickness of 15 mm (1/73 of wavelength) and BI in the frequency range of 200–1000 Hz with an areal density of 2.2 kg/m2. In addition, the real parts of both the effective dynamic density and bulk modulus reach zero precisely at the critical frequency of 312 Hz, arising from the monopolar eigenmode of LAM. Our work advances the concept of synthetic design of sound absorption and insulation properties of multi-impedance-coupled acoustic systems and promotes membrane-type acoustic metamaterials to more practical engineering applications.

Nonlinear vibration analysis of the resonant column test of granular materials

This paper theoretically analyzes the nonlinear torsional vibration of a granular material specimen in the resonant column test (RCT). The RCT is a material testing method that has been well established in geotechnical engineering. The test provides some important dynamic properties of granular materials including the shear wave speed, effective dynamic shear modulus and damping capacity. Both the elastic modulus and damping capacity show a strong dependence on the amplitude of excitation, which is the essential behavior of materials with hysteretic nonlinearity. The analysis, starting with a constitutive relationship that describes the hysteretic nonlinear behavior of granular materials, is performed specifically on the forced torsional vibration of a circular bar with a fixed and inertia-loaded boundary condition as a model for the specimen in the RCT. Self-interaction of a single resonance mode is assumed in the perturbation analysis to obtain an approximate solution for near-resonance response. The theoretical results predict linear dependences of the resonance frequency and damping ratio on the shear strain; these are in agreement with the existing experimental observations. Notable is that the present model describes the hysteretic nonlinear behaviors with a single parameter, i.e., the hysteresis nonlinearity parameter in the constitutive relationship. The derived equations are applied to a jointed gneiss specimen where how the hysteresis nonlinearity parameter is determined from RCT data is demonstrated.

Integrating the Dynamic Modulus of Asphalt Mixes in the 1993 AASHTO Design Method

The AASHTO Guide for Design of Pavement Structures 1993 (1993 Design Guide) remains the most widely used pavement design manual by highway agencies and design consultants around the world. As defined in the 1993 Design Guide, the structural coefficient of a pavement layer ( ai) is an abstract measure of the relative ability of a unit thickness of a given material to function as a structural component of the pavement. Nevertheless, the assumed ai values of the asphalt layers and a proposed relationship between ai and the resilient modulus do not account for the mechanical and physical properties of asphalt materials, traffic volume and speed, layer thicknesses (thin versus thick pavements), climate, and unbound layer properties. The purpose of this research was to enhance the design methodology incorporated in the 1993 Design Guide by integrating asphalt mixture properties in the design process. The objective was to devise a relationship between the structural coefficient ( ai) of the asphalt layer and the effective dynamic modulus (|E*|eff.) of the corresponding asphalt mix to yield a more realistic estimate of the structural capacity of the asphalt layer. The paper illustrates the development of a multilinear relationship between ai, (|E*|eff.), and the resilient modulus of the aggregate base layer. Pavement structural designs for various asphalt mixes and design inputs using the developed ai–(|E*|eff.) relationship yielded asphalt layer thicknesses that were generally smaller than those obtained using the typical ai value of 0.44 for the asphalt layer and closer to thicknesses obtained with the AASHTO mechanistic–empirical design method using the Pavement ME software.

The implications of increasing temperature due to climate change for asphalt concrete performance and pavement design

The dynamic moduli have been recently introduced and effectively used to express the intrinsic behaviour of the viscoelasticity of an asphalt concrete material across a given range of temperatures and frequencies. Those can generally be represented in a form of the master curve. This study investigated the dynamic moduli of Western Australian (WA) asphalt mixes. In addition, the study modified the dynamic modulus predictive equation of the national cooperative highway research program (NCHRP) project 1-37A to suit WA conditions. Furthermore, in this study, the effect of increased temperatures due to climate change upon flexible road pavement was investigated through the pavement design exercise using WA as the study area. To determine the effective dynamic modulus (|E*|eff), temperature and historical climate data were sourced from a Perth Airport Station to conduct a pavement design exercise. This data covered a 20-year period, a typical asphalt pavement design life. The allowable number of cycles (of traffic) to failure (Nf) under four different pavement design scenarios was then calculated based on this |E*|eff to examine of an increase in temperature potentially resulting from climate change effects. The results of the examination showed that once an increase in temperature due to climate change was taken into account, Nf could be decreased by approximately six million repetitions. This equals a shorter pavement life or design period of around four years compared to a result of the original design, which does not consider the increase in temperature resulting from climate change.

Validation of low frequency noise attenuation using locally resonant patches.

Since conventional silencers in acoustic ducts have problems of size limitations at low frequencies and being prone to high backpressure, locally resonant aluminum patches are introduced in acoustic duct walls aiming at creating frequency stop bands in the low frequency region (below 1 KHz). With these flush mounted patches, promising noise reductions, with no such drawbacks, can be obtained, building on local resonance phenomenon implemented in acoustic metamaterials techniques. The objective of the current paper is to experimentally validate the performance of an array of flexible side-wall-mounted patches inside ducts. The experimental results are compared with Analytical Green's function method as well as Numerical Finite Element Method and a close agreement was found. The results show that the presence of the patches singly or periodically can play a prominent role in designing any acoustic bandgap materials. The effect of the arrays of patches on the effective dynamic density and bulk modulus has also been investigated.

Sound attenuation in ducts using locally resonant periodic aluminum patches

In recent years, the control of low frequency noise has received a lot of attention for several applications. Traditional passive noise control techniques using Helmholtz resonators have size limitations in the low frequency range because of the long wavelength. Promising noise reductions, with flush mounted aluminum patches with no size problems can be obtained using local resonance phenomenon implemented in acoustic metamaterial techniques. The objective of this work is to introduce locally resonant thin aluminum patches flush mounted to a duct walls aiming at creating frequency stop bands in a specific frequency range. Green's function is used within the framework of interface response theory to predict the amount of attenuation of the local resonant patches. The two-port theory and finite elements are also used to predict the acoustic performance of these patches. No flow measurements were conducted and show good agreement with the models. The effect of varying the damping and the masses of the patches are used to expand the stop bandwidth and the effect of both Bragg scattering and the locally resonant mechanisms was demonstrated using mathematical models. The effect of the arrays of patches on the effective dynamic density and bulk modulus has also been investigated.

Shear properties of heterogeneous fluid-filled porous media with spherical inclusions

An exact analytical solution is presented for the effective dynamic shear modulus in a heterogeneous fluid-filled poroelastic medium containing spherical inclusions. The complex and frequency-dependent properties of the derived shear modulus are solely caused by the physical mechanism of mesoscopic-scale wave-induced fluid flow whose scale is assumed to be smaller than wavelength but larger than the size of pores. Our model consists of three phases: a spherical inclusion, a shell of matrix material with different mechanical and/or hydraulic properties and an outer region of effective homogeneous medium of infinite extent. This three-phase model represents a self-consistent model or an approximate model of composite having periodically distributed inclusions. The behaviors of both the inclusion and the matrix are described by Biot's equations (1941) with standard conditions of Deresiewicz and Skalak (1963) at the inclusion-matrix interface. The effective medium is regarded as an equivalent elastic or viscoelastic material with complex and frequency-dependent moduli to be determined. The derived effective shear modulus is used to quantify the shear-wave attenuation and velocity dispersion. For the problem of fluid patchy saturation (inclusions with the same solid frame as the matrix but with a different pore fluid from that in the matrix), the gas pocket does not affect the shear attenuation and dispersion characteristic of the water-filled matrix medium at all. For the problem of double porosity structure (inclusions having a different solid frame than the matrix but the same pore fluid as the matrix), with the increase of frequency the heterogeneous medium transitions from a low-frequency state having drained inclusions and drained matrix with no pore pressure difference to a higher-frequency state having undrained inclusions and undrained matrix with no fluid communication at the inclusion's surface. The relaxation frequency at which the maximum value of inverse quality factor occurs moves to frequencies by two orders of magnitude lower if the size of a unit cell increases by one order of magnitude. Stiff inclusions imbedded in a relatively soft matrix can cause significant and observable attenuation at seismic frequency bands, but softer inclusions imbedded in a relatively stiff matrix cause very weak attenuation. The mixed heterogeneity in both the solid frame and pore fluid also has important influences on the frequency-dependent shear wave attenuation.