Dynamic Behavior of Viscoelastic Solids at Low Frequency: Fractional vs Exponential Relaxation (original) (raw)
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Memory decay rates of viscoelastic solids: not too slow, but not too fast either
Rheologica Acta, 2011
Fading memory is a distinguishing characteristic of viscoelastic solids. Its assessment is often achieved by measuring the stress due to harmonic strain histories at different frequencies: from the experimental point of view, the storage and loss moduli are, hence, introduced. On the other side, the mathematical modeling of viscoelastic materials is usually based on the consideration of a kernel function whose decay rate is sufficiently fast. For several different solid materials, we have collated experimental evidence showing an high sensitivity to frequency variations of both the storage and loss moduli. By contrast, we prove that the commonly employed viscoelastic kernels (Prony series, continuous kernel, etc.) cannot reproduce this experimental behavior, as the resulting frequency sensitivity of the storage modulus is always zero when assessed at low frequency. This leads to identification problems of the material parameters which are strongly ill conditioned. However, we identify the specific kernel property which is responsible for this misbehavior: the long-term material memory must not decrease too fast. Some viscoelastic kernels, showing the correct memory's rate of decay, are introduced and their improved ability to match the experimental data analyzed.
Prediction of viscoelastic material functions from constant stress- or strain-rate experiments
Mechanics of Time-Dependent Materials, 2013
To predict durability of polymeric structures an information on polymer's longterm properties in the form of relaxation modulus and/or creep compliance is required. It is well known that determination of relaxation or creep properties from experimental data is an inverse problem, which, due to presence of experimental errors in input data, becomes ill-posed. To find a stable solution using standard integration schemes is practically impossible. In this paper we propose a "hands-on" methodology which bypasses the solution of ill-posed integral equation and allows finding long-term relaxation or creep properties from simple constant strain rate or constant stress-rate experiments performed at different temperatures. The proposed approach can be applied not only for characterization of viscoelastic materials in solid state but can also be used for prediction of time-dependent properties of polymer melts. The paper presents the detailed steps of the proposed method as well as its validation on several simulated and real experimental data. It has been shown that the proposed approach can accurately reconstruct the desired long-term time-dependent properties obtained in traditional way (i.e., from step loading).
Modelling viscoelastic materials whose storage modulus is constant with frequency
International Journal of Solids and Structures
This paper presents a relaxation function characterising viscoelastic materials whose storage modulus is constant with frequency, and whose loss factor shows the representative peak of damping materials. This behaviour is typical of some composite materials, where the elastic constituents give the constant modulus, and the polymeric components provide the variable loss factor. The new model gives a way to provide comparative data for different materials in a form which can easily be incorporated into simulations. The physical meaning of the model parameters is defined from the analysis of the complex modulus in frequency domain. The presented relaxation function is validated by curve fitting to experimental measurements carried out on polymer concrete specimens, made of epoxy resin matrix with mineral aggregates.
Separable finite viscoelasticity: integral-based models vs. experiments
Mechanics of Time-Dependent Materials, 2018
In the present paper, the predictive capabilities of some integral-based finite strain viscoelastic models under the time-strain separability assumption have been investigated through experimental data for monotonic, relaxation and dynamic shear loads, in time and frequency domains. This analysis is instigated by experimental investigation results on two vulcanized carbon black filled rubbers. A unified identification procedure has been deployed to all models to determine the constitutive parameters. The monotonic tests were performed to capture the rate dependent and the long-term response of the materials. For the purely hyperelastic response, we considered the proposed hyperelastic potential proposed in Abaqus for incompressible materials. Relaxation tests were intended to identify the time-dependent material properties, and completed with a dynamic mechanical analysis. Models under consideration are Christensen, Fosdick & Yu, a variant of BKZ model, and the Simo model implemented in Abaqus. In the time domain, for each test case and for each model, the nominal stress is hence compared to experimental data, and the predictive capabilities are then examined with respect to three polynomial hyperelastic potentials forms. The dynamic properties had been investigated in the frequency domain with respect to the frequency and predeformation dependencies, and then comparison conclusions have been drawn.
Polymer Engineering & Science, 2000
The nonlinear dynamic behavior of a vulcanized rubber compound employed in the production of tires was investigated. The values of the dynamic storage modulus, E', and the loss factor, tans, were measured at Merent frequencies, temperatures and strain amplitudes. Data were subsequently analyzed and treated by an empirid method of frequency-temperature-deformation reduction that provided for E' and tans, respectively, a single master curve and the frequency-temperature and frequency-deformation shift factors. The E' trend, extrapolated at higher strain amplitudes on the basis of the master curves, resulted in good agreement with E values obtained from direct experimental measurements. INTELODUCTION frequency-temperature reduction of experimental data he dynamic behaviors of rubber components,
Analytically driven experimental characterisation of damping in viscoelastic materials
Aerospace Science and Technology, 2015
The damping assessment of highly dissipative materials is a challenging task that has been addressed by several researchers; in particular Oberst defined a standard method to address the issue. Experimental tests are often hindered by the poor mechanical properties of most viscoelastic materials; these characteristics make experimental activities using pure viscoelastic specimens prone to nonlinear phenomena. In this paper, a mixed predictive/experimental methodology is developed to determine the frequency behaviour of the complex modulus of such materials. The loss factor of hybrid sandwich specimens, composed of two aluminium layers separated by the damping material, is determined by experimental modal identification. Finite element models and a reversed application of the modal strain energy technique are then used to recover the searched storage modulus and loss factor curves of rubber. In particular, the experimental setup was studied by comparing the solutions adopted with the guidelines given in ASTM-E756-05. An exhaustive validation of the values obtained is then reported.
Mechanics of Materials, 2010
Carbon black-filled rubber and soft biological tissues are only two examples of materials which undergo large deformation processes and exhibit relevant dissipation and hysteresis losses. Nonlinear viscoelasticity encompass a wide class of constitutive models aimed at describing the behavior of such materials. The main goal of the present paper is to draw a comparison between the many viscoelastic constitutive relations recently proposed. To this aim the current stress value is expressed through a single hereditary integral of the deformation history; this choice, although generalizable, yet permits the introduction of an unifying formulation in which hereditary, strain rate and fractional-derivatives models can all be included.
2014
In this paper, dynamic material constants of 2-parameter Mooney-Rivlin model for elastomeric components are identified in broad frequency range. To consider more practical case, an elastomeric engine mount is used as the case study. Finite element model updating technique using Radial Basis Function neural networks is implemented to predict the dynamic material constants. Material constants of 2-parameter Mooney-Rivlin model are obtained by curve fitting on uni-axial stress-strain curve. The initial estimations of the material constants are achieved by using uni-axial tension test data. To ensure of the consistency of dynamic response of a real component, frequency response function of three similar engine mounts are extracted from experimental modal data and average of them used in the procedure. The results showed that this technique can successfully predict dynamic material constants of Mooney-Rivlin model for elastomeric components.