Complex Modulus Of Materials Research Articles

A novel approach for the fractional SLS material model experimental identification

A multi-step, iterative technique for the local non-parametric identification of the standard linear solid (SLS) material model employing fractional order time differential operators is presented. Test input data consists of a set of identified material complex modulus values estimated at different frequency values, obtained from input–output experimental measurements made on a material specimen by means of forced harmonic excitation and from experimental measurements made on the same specimen in quasi-static relaxation conditions. The proposed technique is mainly based on an algebraic procedure leading to the solution of an overdetermined system of linear equations, in order to get the optimal value of the model unknown parameters. The procedure is non-parametric, since the SLS model order is initially unknown. The optimal model size can be found by evaluating the stability properties of the solution associated to any model size and by automatically discarding computational, non-physical contributions. The identification procedure is first validated by means of numerically simulated test data from within known model examples, and then it is applied to some experimentally obtained test data associated to different materials.

Parameter determination for the Mini-Oscillator Model of the Viscoelastic Material

The viscoelastic composite structure is widely used in the vibration and noise suppression of thin-walled components. The vibration analysis of viscoelastic composite structures must involve the constitutive equation of viscoelastic materials. The form of the constitutive equation of viscoelastic material has a decisive influence on the dynamic analysis process of viscoelastic composite structures. Since the constitutive relation of the viscoelastic material changes with time, frequency and temperature, the analysis of the dynamic characteristics of the viscoelastic composite structure is greatly complicated. The mini-oscillator model considers the frequency-dependent properties of viscoelastic materials. Therefore, it is widely used in the dynamic analysis of composite structures. Aims at the need of viscoelastic material passive vibration control for viscoelastic composite structures, a method for determining the parameters of mini-oscillator model is proposed. The method obtains the viscoelastic material mini-oscillator model parameters by parameter fitting by the measured viscoelastic material complex modulus data in the frequency domain or other viscoelastic material damping model expressions obtained from experimental data. The results are compared with fractional derivative model. The results show that the mini-oscillator model can correctly describe stress-strain relationship of viscoelastic material and the parameter fitting method proposed in this paper is accurate and effective.

A flexible rheometer design to measure the visco-elastic response of soft solids over a wide range of frequency.

We present a flexible setup for determining the rheology of visco-elastic materials which is based on the mechanical response of a magnet deposited at the surface of a slab of material and excited electromagnetically. An interferometric measurement of the magnet displacement allows one to reach an excellent accuracy over a wide range of frequency. Except for the magnet, there is no contact between the material under investigation and the apparatus. At low frequency, inertial effects are negligible so that the mechanical response, obtained through a lock-in amplifier, directly gives the material complex modulus. At high frequency, damped waves are emitted and the rheology must be extracted numerically from a theoretical model. To validate the design, the instrument was used to measure the rheology of a test polydimethylsiloxane gel which presents an almost perfect scale free response at high frequency.

On merging DMA and microindentation to determine local mechanical properties of polymers

Micro- and nanoindentation and Dynamic Mechanical Analysis (DMA) are different methods to determine mechanical and viscoelastic material properties. The aim of this study was to broaden the capabilities of their utilization by merging these methods. Three standard diamond indenters and a tungsten needle were implemented in a conventional DMA. Four types of standard polymers were investigated. Quasi-static microindentation was performed to determine local material static stiffness, and dynamic microindentation was performed to evaluate local material complex modulus. The results of the quasi-static microindentation showed that different static stiffnesses of the polymers can be distinguished. Even the smallest differences in local mechanical properties due to processing and annealing were distinguished. The complex moduli determined by dynamic microindentation were in good agreement with literature values and three-point bending results. It was shown that a conventional DMA is suitable to determine local and bulk mechanical viscoelastic material properties within one instrument.

An efficient finite element method for computing modal damping of laminated composites: Theory and experiment

This paper presents an efficient finite element method (FEM) for computing the modal damping of laminated composites using the general purpose finite element software. The method is based on an extended elastic-viscoelastic correspondence principle, which accounts for the frequency dependence of viscoelastic complex stiffness matrices. The implementation of the proposed model is described as a UMAT subroutine for ABAQUS/Standard. The experimentally determined material complex modulus values for the carbon/epoxy laminated composites combined with the results of cantilever percussion free-decay testing are used as the input parameters for the model. Subsequently, the analyses of modal damping and frequency response for laminated composites are implemented by using the complex eigenvalue method. The computed results from this model are in good agreement with the test data. Thus, the proposed numerical method is quite efficient and accurate, and capable of providing an effective way to determine the modal damping of anisotropic materials by using ABAQUS code.

Application of Cork Compounds in Sandwich Structures for Vibration Damping

The remarkable damping over a broad temperature range and thermal insulation properties of cork make it a suitable material to be applied on integrated and surface damping treatments in sandwich structures, improving its dynamic behavior. Experimental analysis and numerical modeling of sandwich structures with cork compound layers is therefore essential for a better understanding of the cork compound influence on the dynamic properties of a layered structure. In this article, an evaluation study on the dynamic properties of a set of sandwich plates with cork compound cores inside two aluminium faces is performed. For this purpose, three test samples were assembled following the described configuration, using cork compounds with different properties (density, granulometry and thickness). To numerically simulate these layered plates, a partial layerwise plate finite element (FE), with a multilayer configuration, was developed and integrated in a MATLAB FE code. The constitutive relation of the cork compounds is included in the FE model by using the material complex modulus in a direct frequency analysis procedure. For the different cork compounds hereby considered, the extensional complex modulus was previously identified by using a specific experimental methodology which simulates a semidefinite two degrees of freedom system, where the cork compound test sample represents the complex stiffness. From the complex modulus data, both extensional storage modulus and loss factor of the cork compound were obtained. The experimental evaluation of the dynamic properties of the sandwich plates was performed carrying out an experimental modal analysis on each test specimen, being measured a set of frequency response functions (FRFs). Additionally, the developed layerwise plate element was validated through the comparison between the measured driving point FRFs and the FE method predicted ones.

Dependence of the contact area on the velocity of a rolling tire

It is known that the eigenfrequencies of a rolling tire depend on the velocity of rotation. We distinguish two causes for the stiffness increase: the frequency dependence of the complex modulus of the materials and the geometrical stiffness. The real part of the Young's modulus is monotonic according to the frequency. It contributes for an important part to the stiffening. The geometrical stiffness also increases with the rotational velocity. A consequence of these effects is the modification of the size of the contact area for different velocities of a rolling tire. Here we first present experimental results estimating the size of the contact area for a tire in statics and for different rolling velocities. Differences of 20% can be observed. Then the viscoelastic behaviours of the tire materials are presented and experimental results showing the frequency dependence of the complex modulus of the tire constitutive materials are given. Then finite element computations are presented with a real distribution of materials in the tire section and the size of the contact area is estimated and compared to experimental measurements. These results could improve the modelling of tire road interaction for tire noise predictions.

Characterization and Modeling of the Low Strain Amplitude and Frequency Dependent Behavior of Elastomeric Damper Materials

The low-strain (0.1 to 20%) amplitude behavior of elastomeric materials in simple shear was investigated both experimentally and analytically. Amplitudes, temperatures (-40° to 150°F), and frequencies (0.01 to lOHz) were chosen to represent the working range of typical helicopter damper applications. A nonlinear model was developed to capture the combined amplitude and frequency dependence. The model extends the nonlinear Anelastic Displacement Fields (ADF) approach to include friction-type elements. These elements operate in parallel with the original ADF model. This configuration is shown to improve the performance of the ADF model over the amplitude and frequency range of interest. Experimental tests (single frequency harmonic) were conducted at several frequencies and amplitudes to support model characterization. The current model and a baseline nonlinear model (which does not include friction-type elements) were characterized using linearized material complex modulus data. The current model captures observed material behavior more accurately than the baseline model. Additional single- and dual-frequency harmonic data (nonlinear stress time-histories) was then used to validate the current model. The model accurately represents the material behavior for these loading conditions. Experimental investigations were further expanded to examine the influence of temperature and static precompression.

Frequency‐temperature superposition in polymer damping behavior

The problem of determining optimum shift factors for frequency‐temperature dependence of polymeric material complex modulus properties has not been fully resolved even half a century after the pioneering work of Williams, Landel, and Ferry. The question of what form, such as the WLF (Williams, Landel, Ferry) equation or the Arrhenius equation, best depends on both the material and th& quality of the test data. In most cases, the data scatter is sufficient to prevent a definitive choice. These issues will be discussed with reference to available test data for several polymeric materials, obtained by various measurement techniques. It will be shown that the least ambiguous shift factor estimates are obtained when data scatter is as low as possible, and the frequency range of data at each temperature is as wide as possible, as would be expected. It will also be shown that differences arising from the use of different shift factor equations are not sufficient for most engineering applications.

Resonance Effects in the Measurement of the Complex Modulus

Various mechanisms by which resonances may be introduced into systems for the measurement of the complex modulus of materials are discussed from the physical viewpoint and are formulated mathematically. The mechanisms under consideration arise primarily from second-order elasticity effects that may be a consequence of the testing technique or of the microstructure behavior of the material. Some comparisons are made between experimental results and mathematical predictions.