Complex Elastic Modulus Research Articles

Effects of the magnetic field on the viscoelastic wave propagation and dynamic material properties

In this paper, the longitudinal wave propagation of a thin ferromagnetic (Fe-Cr-Al alloy) rod under the transverse magnetic field is investigated analytically without ignoring the viscoelastic characteristics of this alloy. The analysis is based on the Bernoulli-Euler rod theory and a 4-element viscoelastic model based on the experimental observation. The viscoelastic wave characteristics and the behaviours of dynamic material properties under the magnetic field are investigated. The analytically results show that the longitudinal wave propagation and the dynamic material properties of the rod are affected by the magnetic field existence (for magnetic field magnitude values greater than about 107A/m), except the imaginary part of the complex elasticity modulus. Furthermore, in a large frequency range, depending on the ratio of the group velocity to the phase velocity an abnormal dispersion characteristic is observed.

The Comparison of Fractional Derivative Model and Classical Spring-Dashpot Model in the Identification of Viscoelastic Characteristics of a Rubber Material

In the design of viscoelastic materials used in rubber products, not theoretical approaches but experimental approaches have been usually employed. This is due to the difficulties in mathematical procedures of the dynamic material characteristics such as the dependencies of strain amplitude, frequency and/or environmental temperature in deformation. In mathematical approach there are two kind of analytical models for a complex module of the material, which are a fractional derivative model and a spring-dashpot model. However there are few papers dealing with the study of the identifications of parameters for the experimental modulus actually obtained not only by using the fractional derivative model but also by using the spring-dashpot model and the discussion of the comparisons of the two models. In the present paper, the complex elastic modulus for a rubber material are obtained experimentally for a wide range of excitation frequency, and the modulus-frequency relations are derived analytically by using the two models, respectively. Finally, the applicability of the models are discussed from the numerical results.

Improving Recycled Poly(lactic Acid) Biopolymer Properties by Chain Extension Using Block Copolymers Synthesized by Nitroxide-Mediated Polymerization (NMP).

The aim of this contribution is to assess the use poly(styrene-co-glycidyl methacrylate-b-styrene) copolymers synthesized by nitroxide mediated polymerization (NMP) as chain extenders in the recycling of poly(lactic acid) biopolyester. Concisely, the addition of such block copolymers during the melt processing of recycled poly(lactic acid) (rPLA) leads to important increases in the viscosity average molecular weight of modified polymeric materials. Molar masses increase from 31,000 g/mol for rPLA to 48,000 g mol−1 for the resulting rPLA/copolymer blends (bPLA). Fortuitously, this last value is nearly the same as the one for pristine PLA, which constitutes a first piece of evidence of the molar mass increase of the recycled biopolymer. Thermograms of chain extended rPLA show significant decreases in cold crystallization temperature and higher crystallinity degrees due to the chain extension process using NMP-synthesized copolymers. It was found that increasing epoxide content in the NMP-synthesized copolymers leads to increased degrees of crystallinity and lower cold crystallization temperatures. The rheological appraisal has shown that the addition of NMP synthesized copolymers markedly increases complex viscosity and elastic modulus of rPLA. Our results indicate that P(S-co-GMA)-b-S) copolymers act as efficient chain extenders of rPLA, likely due to the reaction between the epoxy groups present in P(S-co-GMA)-b-PS and the carboxyl acid groups present in rPLA. This reaction positively affects viscometric molar mass of PLA and its performance.

Seismic wave modeling in vertically varying viscoelastic media with general anisotropy

Seismic anisotropy, wave attenuation, and dispersion are critical phenomena of wave propagation in real media. Full-wavefield modeling of wave behavior in such media plays an important role in investigating dynamic features of the earth’s interior and in full-waveform inversion of anisotropic parameters and velocity dispersion. We have developed a numerical scheme to model the full-waveform response from a point source in a vertically varying viscoelastic medium of arbitrary anisotropy. The method is implemented in the frequency domain, so the complexity of anelasticity and anisotropy can be described by a complex elastic stiffness matrix and frequency-dependent moduli can also be readily incorporated. In our scheme, we solve the elastodynamic equations for general anisotropy through finite-element method in the frequency-wavenumber domain and we use the stiffness reduction method to suppress reflections from artificial boundaries along the depth direction. A nonuniform 2D Fourier transform strategy is developed to reconstruct the spatial-domain counterparts from the wavenumber-domain solutions. The time-domain responses are then obtained by taking inverse fast Fourier transform with respect to frequency. We validate the method by comparing the numerical results with the exact solutions for a homogeneous transversely isotropic model and a two-layered model. In the application example, we further proved the feasibility and generality of the scheme using an attenuative, dispersive model with velocity and attenuation anisotropy. Our scheme enjoys significant advantages in incorporating various viscoelastic/dispersive behaviors and general anisotropy, and thus provides a useful tool for numerical simulation of dynamic responses in practical application.

Hopping and clustering of oxygen vacancies in BaTiO3−δ and the influence of the off-centred Ti atoms

The diffusion and aggregation of oxygen vacancies (VO) in perovskites are still poorly understood, even though they are involved in a wide range of applications and phenomena, from solid-state electrolytes for fuel cells to ferroelectric fatigue. In strontium titanate it has been possible, by measuring the complex elastic modulus, to identify peaks in the elastic energy loss versus temperature due to hopping of isolated and paired VO and evaluate all the relevant kinetic and thermodynamic parameters. We present similar experiments in barium titanate, where the ferroelectric transition at TC = 400 K partially hides the anelastic relaxation processes due to VO. The introduction of VO, however, depresses TC, and it has been possible to lower it enough to reveal all the relaxation processes due to free and clustered VO. The resulting anelastic spectra are similar to those of SrTiO3−δ but there are also important differences. In BaTiO3−δ the anisotropy of the elastic dipole of the isolated VO is about three times larger, the anelastic relaxation peaks markedly shift to lower temperature with doping, the activation energy for the diffusion of the isolated VO is 0.72 eV, larger than 0.60 eV in SrTiO3, while that for the pair reorientation is smaller, 0.86 eV compared to 0.97 eV. All these observations are explained by taking into account that, unlike in SrTiO3, Ti is dynamically disordered over eight off-centre positions. A strong indication in this sense comes from the temperature dependence of Young’s modulus, with anharmonic stiffening perfectly linear in temperature down to 200 K in SrTiO3, and with anomalous softening already below 750 K in BaTiO3.

A Novel Wave Propagation Method for Measuring Viscoelastic Properties of Prestrained Materials

Abstract Viscoelastic materials are widely used for vibroacoustic solutions due to their ability to dissipate energy and thus mitigate vibrations and structure-borne sound. Wave propagation methods belong to a growing family of material characterization techniques based on the analysis of waveform patterns in one-dimensional structures. The time evolution of patterns results from material elasticity and damping. Conversely, it is possible to identify these properties once the pattern's time evolution is known. The most frequently used propagation methods, namely, Hopkinson bar methods, assume no dispersion, i.e., the complex elasticity modulus is not frequency dependent. However, this is not relevant for resilient materials such as elastomers. More recent approaches have been developed to measure frequency-dependent properties from a pulse propagating in a slender bar. In the previous works, we showed how to adapt these methods for shorter samples of materials. This represented a real advance, as extrusion is a cumbersome process for many materials. The main concept was to reconstruct the time history of the wave propagating in a composite structure composed of a long incident bar made of a known material and extended by a shorter sample bar. The sample material's viscoelastic properties were then determined in the frequency domain by optimization and wave fitting in the time domain. In industry, most insulation solutions that rely on mounts and bushings have to support structural weights. Consequently, it is particularly useful to measure the tangent viscoelastic properties of the material around the static stressed state and not only in stress-free conditions. Measuring strained materials not only requires modifying the experimental apparatus but also extending the scope of the underlying theory as the waves propagate differently in composite structures made of strained media. Here, we show how to overcome this challenging issue. The theoretical framework and its numerical implementation are described, and the method was validated experimentally by characterizing an elastomer sample under prestrained conditions.

A Hybrid magnetic-ultrasonic technique for spectral viscoelastic characterization of soft solids

We present a hybrid technique that combines magnetic forces and ultrasonic waves (MMUS based) to explicitly characterize the complex elastic modulus of soft-solids in the frequency domain. The results show the dependence of the viscoelastic properties with the frequency content of the applied magnetic impulse.

Evaluation and Control of the Molar Mass Bimodality and Properties of Polyethylene from Novel Chromocene‐Based Dual Sites Catalysts

AbstractPolyethylene (PE) with bimodal molecular weight distribution (MWD) has drawn attention from researchers because of its great processability and outstanding mechanical properties. Bimodal PE is successfully prepared by novel SiO2‐supported chromocene (S‐9)/chromium (CrOX) and chromocene (S‐9)/vanadium (V) dual sites catalysts in a single reactor. The molar mass bimodality, crystalline properties, and mechanical properties of the bimodal PE prepared by S‐9/CrOX catalysts are controllable through adjusting the loading of active centers. Those are also adjustable by using S‐9/V catalysts under the condition of adding 0.1 MPa hydrogen. Compared with CrOX/SiO2, 4CrOX4S9 shows an increase in tensile strength and Young's modulus by 38% and 17%, respectively. With the increase in high MW fraction, tensile strength, and Young's modulus both increase. S‐9/CrOX catalysts combining the advantages of two active centers show better tensile properties. S‐9/V catalysts have a similar trend in tensile properties. The complex viscosity, elastic modulus, and loss modulus increase with the growth in MW and the thickness of lamellae. Furthermore, the high and low MW fraction has good compatibility for both dual sites catalysts, and their resistance to slow crack growth is most likely to reach the standards for PE100 and PE100RC and even exceed.

The optimal design of the mounting rubber system for reducing vibration of the air compressor focusing on complex dynamic stiffness

Urban rapid railway is one of the most popular transportation methods these days. It is equipped with large-capacity air compressors since it uses pneumatic pressure to supply power for braking and for opening and closing doors. Passengers tend to complain about vibration and noise from the air compressor. In this study, vibration reduction of air compressor was achieved by acquiring exact complex dynamic stiffness of the mounting rubber and optimizing the shape of it. Target stiffness values of the rubber was obtained from multi-body dynamics simulation of the air compressor-mounting system. Complex elastic modulus of the rubber mount was derived through EMA and Gent’s method and verified by finite element method. Through parametric study of mounting rubber, an optimal shape of mounting rubber was derived and produced. Lastly, the proposed value was verified by experiments comparing with baseline value.

Rheology of Polymethylmethacrylate-Collagen Gel Filler: Physiochemical Properties and Clinical Applications.

Soft tissue fillers are comprised of a range of materials with differing physiochemical and rheologic (ie, flow) properties. These properties can inform treatment selection for specific anatomic areas, planes of injection, and clinical applications. The aim of this study was to characterize the rheologic properties of polymethylmethacrylate (PMMA)-collagen gel for comparison with other available fillers. Commercially available PMMA-collagen gel, hyaluronic acid (HA), and calcium hydroxylapatite (CaHA) fillers were obtained from their respective manufacturers. Measures of complex viscosity (η*) and elastic modulus (G') for each filler were collected at 0.7 Hz in triplicate according to standard procedures on a rotational rheometer fitted with a 40-mm steel plate at 25°C on a Peltier plate (500-μm gap). The measured η* and G' values for HA and CaHA fillers were in agreement with previously published data. The difference in η* between CaHA (mean [standard deviation], 358.9 [21.56] Pa-s) and PMMA-collagen gel (656.41 [68.03] Pa-s) was statistically significant (P < 0.0001), as was the difference between the G' of CaHA (1424.8 [83.3] Pa) and the G' of PMMA-collagen gel (2815.27 [304.07] Pa; P < 0.0001). PMMA-collagen gel exhibited the highest η* and G' of all tested fillers. These properties likely underpin an increased capacity for lifting and support in areas where long-lasting revolumization is appropriate. In practice, PMMA-collagen gel is well suited for treatment of acne scars, as well as injection into the supraperiosteal plane in the temple, chin, mandible, and piriform by a retrograde linear threading technique. Additional clinical considerations are discussed.

Sustained-release hydrogels of ivermectin as alternative systems to improve the treatment of cutaneous leishmaniasis.

Background: Leishmaniasis is a neglected tropical disease and its cutaneous form manifests as ulcers or nodules, generally in exposed parts of the body. This work aimed to develop ivermectin (IVM) thermosensitive hydrogels as topical formulations to improve cutaneous leishmaniasis treatment. Materials & methods: Hydrogels based on poloxamers 407 and 188 with different concentrations of IVM were prepared and rheologically characterized. The IVM release profiles were obtained and mathematically analyzed using the Lumped model. Results: The formulation containing 1.5% w/w of IVM presented an adequate gelling temperature, an optimal complex viscosity and elastic modulus. Hydrogels allowed to modulate the release of IVM. Conclusion: IVM thermosensitive hydrogels can be considered a valuable alternative to improve the treatment of cutaneous leishmaniasis.

Active Damping of Nonstationary Vibrations of a Three-Layer Electro-Viscoelastic Composite Plate

A method for constructing nonstationary vibration equations for electro-viscoelastic composite plates with their active damping is described. The problem is solved in an integral Fourier transform frequency space. To construct a multilayer plate model, a discrete structural approach was used, i.e., the plate is divided through the thickness into computational layers, within which the displacements and electric potentials are approximated by means of quadratic Lagrange polynomials. At the edges of the plate, the Navier conditions are met. The semi-analytical nonstationary vibration equations are derived by means of the variational convolutional Lagrange equation. To represent them in a frequency space, a direct integral Fourier transform is used, which makes it possible to use experimentally determined frequency-dependent complex characteristics directly in calculations of nonstationary vibrations of plates without additional transformations of integral physical relations. Solutions of the problem of active damping of nonstationary vibrations for the frequency images of displacements and electric potentials have been found, their convergence is analyzed. The procedure has been evaluated by analyzing the active damping of nonstationary vibrations of a three-layer edge-hinged square plate under the action of a blast wave impulse. The middle layer is made of a composite material, and the outer electro-viscoelastic layers act as a sensor and an actuator. The active damping of vibrations is provided by connecting these layers of the plate into a negative feedback circuit with the proportional-differential control law. The viscoelastic and electro-viscoelastic characteristics of the materials are taken into account by means of complex elastic, dielectric and piezoelectric moduli. The results of analyzing the active damping of nonstationary vibrations of a plate are presented. The values of the proportional and differential components of the controller as characteristics of this damping were chosen taking into account the permissible electric field strength of the actuator. The research results for the case of passive damping of vibrations are also given for comparison. The dependences of the decrement of plate vibrations on the differential component of the controller and of the maximum plate deflection on the reinforcement angle of the middle layer material have been established. The optimum reinforcement angle according to the minimum plate deflection criterion has been determined, which provides an increase in the efficiency of active damping of nonstationary vibrations of the plate owing to an increase in the differential component of the controller.

Đánh giá ảnh hưởng của phụ gia nylon phế thải đến mô đun đàn hồi của bê tông nhựa

Recently, plastic wastes including nylon bag have been becoming a critical issue in many countries worldwide as well as Vietnam. Towards a substainable development, the trend of recycling types of plastic waste is a target of many nations. In transportation field, the use of nylon waste as a binder for asphalt concrete (AC) has been sucessfully applied in some countries. In Vietnam, there have been some studies regarding this topic. Aiming to use nylon waste for AC, this study evaluates the effects of nylon waste on AC elastic moduli including static elastic modulus, dynamic elastic modulus and complex elastic modulus. The results showed that the nylon waste helps to increase the elastic modulus of AC.

General Relations between Elastic Losses and Dispersion in Dissipative Media

An experimental study is performed of the frequency dependences of complex elastic moduli of ceramic matrix piezocomposites with strong elastic dispersion and losses. The experimental data are compared to theoretical results obtained using general Kramers–Kronig relations.

Acoustic Spectroscopy of Ceramic–Matrix Piezocompozites

A new way of determining the dielectric and electromechanical characteristics of piezoelectric materials with high elastic losses is proposed. The complex electrophysical parameters of a ceramic matrix piezocomposite (a PZT-type porous ferro-piezoceramic with randomly distributed pores) are measured. The frequency dependences of the complex parameters are measured via piezoresonance spectra analysis. Anomalies of the frequency dependences of the complex elastic moduli of ceramic-matrix piezocomposites are revealed and interpreted.

An iterative method for identification of temperature and amplitude dependent material parameters of fiber-reinforced polymer composites

Temperature and amplitude dependent material properties have been observed for fiber-reinforced polymer composites (FRPCs) in previous studies. Accurate identification of the nonlinear material parameters is the basis of evaluation and optimization design of FRPCs. This paper proposes an iterative method based on differential evolution algorithm (DEA) for identifying the amplitude and temperature dependent material parameters of FRPCs. Initially, the expressions of complex elastic and shear moduli of FRPCs involving temperature and amplitude dependent fitting coefficients are proposed, upon which the iterative identification principle for nonlinear elastic and shear moduli and loss factors of FRPCs are clarified. Then, a series of dynamic experiments are conducted on FRPC plate specimens in thermal vibration environment from 20°C to 160°C with the excitation amplitude varied from 0.1g to 1.2g. The experimental data are adopted to identify the unknown fitting coefficients. Finally, the nonlinear elastic and shear moduli as well as loss factors of another specimen are determined via the proposed method, upon which the natural frequencies and damping ratios are achieved and compared to the measured results to validate the proposed identification approach. The effects of DEA key parameters on the iterative accuracy and efficiency are also discussed. From comparisons of identification results and experimental data, it can be seen the calculation errors of natural frequencies and damping ratios associated with the first four modes of FRPC plate are no more than 6.98 % and 13.34 %, respectively, which is acceptable for engineering applications.

Bioactive amorphous magnesium phosphate-polyetheretherketone composite filaments for 3D printing

ObjectiveThe aim of this study was to develop bioactive and osseointegrable polyetheretherketone (PEEK)-based composite filaments melt-blended with novel amorphous magnesium phosphate (AMP) particles for 3D printing of dental and orthopedic implants. Materials and methodsA series of materials and biological analyses of AMP-PEEK were performed. Thermal stability, thermogravimetric and differential scanning calorimetry curves of as-synthesized AMP were measured. Complex viscosity, elastic modulus and viscous modulus were determined using a rotational rheometer. In vitro bioactivity was analyzed using SBF immersion method. SEM, EDS and XRD were used to study the apatite-forming ability of the AMP-PEEK filaments. Mouse pre-osteoblasts (MC3T3-E1) were cultured and analyzed for cell viability, proliferation and gene expression. For in vivo analyses, bare PEEK was used as the control and 15AMP-PEEK was chosen based on its in vitro cell-related results. After 4 or 12 weeks, animals were euthanized, and the femurs were collected for micro-computed tomography (μ-CT) and histology. ResultsThe collected findings confirmed the homogeneous dispersion of AMP particles within the PEEK matrix with no phase degradation. Rheological studies demonstrated that AMP-PEEK composites are good candidates for 3D printing by exhibiting high zero-shear and low infinite-shear viscosities. In vitro results revealed enhanced bioactivity and superior pre-osteoblast cell function in the case of AMP-PEEK composites as compared to bare PEEK. In vivo analyses further corroborated the enhanced osseointegration capacity for AMP-PEEK implants. SignificanceCollectively, the present investigation demonstrated that AMP-PEEK composite filaments can serve as feedstock for 3D printing of orthopedic and dental implants due to enhanced bioactivity and osseointegration capacity.

Adsorption properties of N-tetradecyl-N,N-dimethyl-N-(2,3-epoxy propyl) ammonium chloride with inorganic salts at air/water

A series of N-alkyl-N,N-dimethyl-N-(2,3-epoxy propyl) ammonium chloride (C n EAC, n = 10, 12, 14, 16) with alkyl of decyl, dodecyl, tetradecyl, and hexadecyl were synthesized. The adsorption properties of C n EAC under the different temperatures, concentrations, interfacial oscillation frequencies as well as the inorganic salts (NaCl and Na2CO3) at air/water interface were investigated by interfacial dilatational rheology. The dilatational properties of C n EAC solutions including complex moduli, elastic moduli and viscosity moduli increased with oscillation frequency. The elastic moduli were higher than those of viscosity ones. With different hydrogen carbon length, the complex moduli of C n EAC showed different changing role with their concentration and temperature. Inorganic salts compressed the oppositely charges on C n EAC micelle surface and induced the decrease of both complex and viscosity moduli.

Micro-Structure of Hot Mix Asphalt Containing the 35/50 Bitumen Viewed in Terms of Excess Moisture in the Underlying Course of Pavement

Compaction of Hot Mix Asphalt (HMA) is a process aimed at obtaining the desired performance properties. Attainment of the required compaction can be hampered by external factors, which includes the presence of water. Water is known to cause quick lowering of the HMA temperature. The bottom face of the asphalt layers of a pavement is a sensitive point from the fatigue life point of view. In the site conditions, it is often difficult to obtain the required air void content at the bottom of an asphalt layer and excessive moisture content in the base course lying beneath the asphalt layer can be one of the causes. This article presents the results of tests carried out on a test section on which HMA was placed on an unbound aggregate base layer of varying moisture content. The material used for the binder course was asphalt concrete mixture composed of aggregate of minus 16 mm grading and 35/50 bitumen. Being relatively hard it is the most often specified bitumen for binder courses and also base courses. One of its characteristics is a considerable increase of viscosity with decreasing temperature, which hampers the process of compaction. The bulk specific gravity was measured to determine the variations in the air void content through the specimens. The complex modulus of elasticity and fatigue life were the other parameters which were determined on the specimens with different air void contents. The test results show worsening of the properties which have a decisive bearing on the service life of pavement.

Study of the frecuency dependence of Young’s modulus in synthetic and biological ducts.

The study of frequency dependence of Young’s modulus allows to describe mechanically arterial ducts. This modulus is complex, whose real component represents the purely elastic properties of the material, while its imaginary component represents purely viscous properties. In this work, the complex elastic modulus in two types of ducts was experimentally determined: synthetic type and biological type, (bovine artery). For this purpose, a continuous circulation biodynamic simulator (Bose® Corporation ElectroForce Systems Group) was used where the ducts were subjected to sinusoidal variations of internal pressure, frequency between 1 and 5 Hz. It was observed that the ratio between the measured pressure (Statham P23 DB transducer, Statham‐Gould, Valley View) and the acquired diameter (Laser transducer, Mitutoyo Corporation) constituted a Lissajous figure, with a representative slope of elastic behavior and a hysteresis indicative of viscosity parietal. Given the increase in frequency, the loop experienced an increase in hysteresis. For the calibrated tube, the elasticity (given by the storage modulus) resulted in the order of 14.1 mmHg/mm, while for the other it was 62.3 mmHg/mm. In the case of the bovine duct, the value was 4.88 mmHg/mm. On the other hand, the evaluation of the storage modulus showed differentiated results. While the elastic ducts manifested a linear increase with frequency, the arterial showed a logarithmic dependence. By virtue of them, the synthetic duct could be represented modelling viscosity as a linear function of frequency, but it is not the case of the arterial duct, whose viscoelastic behavior is nonlinear.Support or Funding Information [1]RICARDO L. ARMENTANO y E.I. CABRERA FISCHER, Biomecánica Arterial: Fundamentos para su abordaje en la clínica médica, primera edición, Librería AKADIA, Buenos Aires, 1994. [2]RICARDO L. ARMENTANO, DANIELA VALDEZ JASSO, LEANDO J. CYMBERKNOP, FLORENCIA MONTINI BALLARIN, DANIELA VELEZ, PABLO C. CARACCIOLO y GUSTAVO ABRAHAM, High Pressure Assenssment of Bilayered Electrospun Vascular Grafts by Means of an Electroforce Biodynamic System®, IEEE, 978‐1‐4244‐9270‐1, 3533‐3536, 2015. [3]D. A. MCDONALD, Blood Flow in Arteries, segunda edición, Edward Arnols, London, 1974. [4]W. K. MILNOR, Hemodynamics,Baltimore, MD, USA: WILLIAMS Y WILKINS, 1982. [5]B. S. GOW, M. G. TAYLOR, Measurements of viscoelastic properties of arteries in the living dog, Circ Res 23 (1): 111‐122, 1968. [6]P.B. DOBRIN, Mechanical properties of arteries., Physiol Rev 58 (2): 397‐460, 1978. [7]Y. C. FUNG, Biomechanics. Mechanical Properties of living tissues, Springer‐Verlag, New York, 1981. [8]DANIEL BIA, ISMAEL AGUIRRE, YANINA ZÓCALO, LUCÍA DEVERA, EDMUNDO CABRERA FISCHERC, Y RICARDO ARMENTANO. Diferencias regionales en viscosidad, elasticidad y amortiguamiento parietal de arterias sistémicas: análisis isopulsátil de la relación presión‐diámetro arterial. [9]BERGEL DH. The dynamic elastic properties of the arterial wall. J Physiol 156: 458‐ 469, 1961b.