Viscoelastic Material Properties Research Articles

Flexural wave parameter measurements of viscoelastic panels using a laser doppler correlation vibrometry

Characterizing broadband dynamic properties of viscoelastic panel materials represents a challenging task, particularly when the frequency band of interest needs to be extended toward low frequency range. This work applies a laser Doppler vibrometer in measuring flexural wave properties of the viscoelastic panel materials. The measurement relies on a time-domain broadband correlation technique which experimentally measures impulse responses at two points radially away from a flexural wave exciter. Using reasonable sized panel samples, boundary conditions of the measurements present insignificant obstacles towards high frequency range, since a time-domain windowing facilitates extraction of direct wave components. While boundary reflections will still obscure measurement results towards low frequencies. This work examines a possible mitigation approach by rotating the sample panel, the coherence of direct wave pulses measured equidistant from the exciter and the lack thereof disturbing boundary reflections enables largely removing the undesirable reflections. In this way angular averaging significantly reduces boundary reflections. This paper discusses experimental investigations on the characterization method of flexural wave parameters including wave speed, flexural modules and loss factor.

Improvement of Torque Estimation for Series Viscoelastic Actuator Based on Dual Extended Kalman Filter

Adding damping such as viscoelastic element in series elastic actuators (SEA) can improve the force control bandwidth of the system and suppression of high frequency oscillations induced by the environment. Thanks to such advantages, series viscoelastic actuators (SVA) have recently gained increasing research interests from the community of robotic device design. Due to the inconvenience of mounting torque sensors, employing the viscoelastic elements to directly estimate the output torque is of great significance regarding the real-world applications of SVA. However, the nonlinearity and time-varying properties of viscoelastic materials would degrade the torque estimation accuracy. In such a case, it is paramount to simultaneously estimate the output torque state and viscoelastic model coefficients in order to enhance the torque estimation accuracy. To this end, this paper first completed the design of a rubber-based SVA device and used the Zenner linear viscoelastic model to model the viscoelastic element of the rubber. Subsequently, this paper proposed a dual extended Kalman filter- (DEFK) based torque estimation method to estimate the output torque and viscoelastic model coefficients simultaneously. The noisy observations of two Kalman filters were provided by motor current-based estimated torque. Moreover, the dynamic friction of harmonic drive of the designed SVA was modeled and compensated to enhance the reliability of current-based torque estimation. Finally, a number of experiments were carried out on SVA, and the experimental results confirmed the DEFK effectiveness of improving torque estimation accuracy compared to only-used rubber and only-used motor current torque estimation methods. Thus, the proposed method could be considered as an effective alternative approach of torque estimation for SVA.

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.

A new method for obtaining model-free viscoelastic material properties from atomic force microscopy experiments using discrete integral transform techniques.

Viscoelastic characterization of materials at the micro- and the nanoscale is commonly performed with the aid of force–distance relationships acquired using atomic force microscopy (AFM). The general strategy for existing methods is to fit the observed material behavior to specific viscoelastic models, such as generalized viscoelastic models or power-law rheology models, among others. Here we propose a new method to invert and obtain the viscoelastic properties of a material through the use of the Z-transform, without using a model. We present the rheological viscoelastic relations in their classical derivation and their z-domain correspondence. We illustrate the proposed technique on a model experiment involving a traditional ramp-shaped force–distance AFM curve, demonstrating good agreement between the viscoelastic characteristics extracted from the simulated experiment and the theoretical expectations. We also provide a path for calculating standard viscoelastic responses from the extracted material characteristics. The new technique based on the Z-transform is complementary to previous model-based viscoelastic analyses and can be advantageous with respect to Fourier techniques due to its generality. Additionally, it can handle the unbounded inputs traditionally used to acquire force–distance relationships in AFM, such as ramp functions, in which the cantilever position is displaced linearly with time for a finite period of time.

A new technique for the characterization of viscoelastic materials: Theory, experiments and comparison with DMA

In this paper we present a theoretical and experimental study aimed at characterizing the hysteretic properties of viscoelastic materials. In the last decades viscoelastic materials have become a reference for new technological applications, which require lightweight, deformable but ultra-tough structures. The need to have a complete and precise knowledge of their mechanical properties, hence, is of utmost importance. The presented study is focused on the dynamics of a viscoelastic beam, which is both experimentally investigated and theoretically characterized by means of an accurate analytical model. In this way it is possible to fit the experimental curves to determine the complex modulus. Our proposed approach enables the optimal fitting of the viscoelastic modulus of the material by using the appropriate number of relaxation times, on the basis of the frequency range considered. Moreover, by varying the length of the beams, the frequency range of interest can be changed/enlarged. Our results are tested against those obtained with a well established and reliable technique as compared with experimental results from the Dynamic Mechanical Analysis (DMA), thus definitively establishing the feasibility, accuracy and reliability of the presented technique.

Scaling theory of rubber sliding friction

Current theoretical descriptions of rubber or elastomer friction are complex—usually due to extensive mathematical detail describing the topography of the solid surface. In addition, the viscoelastic properties of the elastomer material itself, in particular if the rubber is highly filled, further increase the complexity. On the other hand, experimental coefficients of sliding friction plotted versus sliding speed, temperature or other parameters do not contain much structure, which suggests that a less detailed approach is possible. Here we investigate the coefficient of sliding friction on dry surfaces via scaling and dimensional analysis. We propose that adhesion promotes viscoelastic dissipation by increasing the deformation amplitude at relevant length scales. Finally, a comparatively simple expression for the coefficient of friction is obtained, which allows an intuitive understanding of the underlying physics and fits experimental data for various speeds, temperatures, and pressures.

Aspects of modeling and numerical simulation of dry point contacts between viscoelastic solids

The virtual absence of pressure driven flow inside an elastohydrodynamic lubrication (EHL) contact leads to remarkable similarity between lubricated film thickness and separation by a viscoelastic layer as is suggested by experimental and theoretical results, see [1]. This offers interesting opportunities for mixed lubrication modeling without needing the flow continuity-based Reynolds equation. In this paper numerical simulation of viscoelastic concentrated contact modeling is revisited, first considering the problem of a viscoelastic half-space and a rigid sphere, both in static (squeeze) as well as (frictionless) rolling/sliding conditions. In particular modeling aspects are discussed so that the efficiency of computation of the viscoelastic deformation remains close to the efficiency of computation of an elastic deformation. This is achieved by rewriting Hunter’s [2] deformation equation from an integral form into a differential form by applying the Leibnitz integral theorem, even for complex materials with multiple relaxation times to represent complex viscoelastic properties of materials. The approach can be straightforwardly implemented in any (EHL) contact solver regardless of the numerical method. Detailed results are presented, such as the effect of the Deborah number, the relation between the extreme cases of the rolling problem and the static problem, and discussed in detail. In addition to the rigid sphere against a viscoelastic half-space, also the case of two viscoelastic bodies is considered.

Mechanical factors contributing to the Venus flytrap\u2019s rate-dependent response to stimuli

The sensory hairs of the Venus flytrap (Dionaea muscipula Ellis) detect mechanical stimuli imparted by their prey and fire bursts of electrical signals called action potentials (APs). APs are elicited when the hairs are sufficiently stimulated and two consecutive APs can trigger closure of the trap. Earlier experiments have identified thresholds for the relevant stimulus parameters, namely the angular displacement theta and angular velocity omega . However, these experiments could not trace the deformation of the trigger hair’s sensory cells, which are known to transduce the mechanical stimulus. To understand the kinematics at the cellular level, we investigate the role of two relevant mechanical phenomena: viscoelasticity and intercellular fluid transport using a multi-scale numerical model of the sensory hair. We hypothesize that the combined influence of these two phenomena and omega contribute to the flytrap’s rate-dependent response to stimuli. In this study, we firstly perform sustained deflection tests on the hair to estimate the viscoelastic material properties of the tissue. Thereafter, through simulations of hair deflection tests at different loading rates, we were able to establish a multi-scale kinematic link between omega and the cell wall stretch delta . Furthermore, we find that the rate at which delta evolves during a stimulus is also proportional to omega . This suggests that mechanosensitive ion channels, expected to be stretch-activated and localized in the plasma membrane of the sensory cells, could be additionally sensitive to the rate at which stretch is applied.

Dynamic mechanical relaxation and thermal creep of high-entropy La30Ce30Ni10Al20Co10 bulk metallic glass

Dynamic mechanical relaxation is a fundamental tool to understand the mechanical and physical properties of viscoelastic materials like glasses. Mechanical spectroscopy shows that the high-entropy bulk metallic glass (La30Ce30Ni10Al20Co10) exhibits a distinct β-relaxation feature. In the present research, dynamic mechanical analysis and thermal creep were performed using this bulk metallic glass material at a temperature domain around the β relaxation. The components of total strain, including ideal elastic strain, anelastic strain, and viscous-plastic strain, were analyzed based on the model of shear transformation zones (STZs). The stochastic activation of STZ contributes to the anelastic strain. When the temperature or external stress is high enough or the timescale is long enough, the interaction between STZs induces viscous-plastic strain. When all the spectrum of STZs is activated, the quasi-steady-state creep is achieved.

Effect of damping material thickness on vibration analysis in pretension layer damping process

Vibration reduction is a critical necessity in many fields of engineering, technology, and industry. As a result, there is a need for vibration management. To restrict or adjust the system’s vibration response, a variety of techniques are employed. In recent years, there has been a lot of enthusiasm for the easy implementation of these vibration-control structures. The damping properties of viscoelastic materials tend to be excellent. Damping is determined by the material’s ability to dissipate energy. To minimise the vibration of vibrating surfaces, viscoelastic materials are commonly used. In this study, viscoelastic material (Dyad 606) is applied on the AL plate in the form of free layer damping and pretension layer damping. First aluminium structure using free layer damping and another one using pretension layer damping by applying tension load (two layers of damping plates, one on the top surface of the Al alloy and the other on the lower face). Passive vibration damping of the plate is achieved. These layers are influenced by axial uniform distributed load. The damping behaviour of the AL Plate is discussed in relation to the thickness variation of the pre-tension damping material. The results show that the loss factor and the attenuation percentage of the structure with pretension layer damping are increased as compared to free layer damping. It is also found that the most effective thickness of the damping material to increase the damping capacity of the framework is around half the base plate thickness

Viscoelastic Material Characterization: A Realistic Approach to Stress Analysis

This paper presents an advanced method in materials characterization for the mold compound material in semiconductor packages to build models that can technically explain the actual warpage or stress observations under different thermal conditions and time history. In the study, the mold compound material characterization was conducted using Dynamic Mechanical Analyzer (DMA) followed by curve fitting to obtain parameters for the computer modeling input requirement. Thermo-mechanical modeling using viscoelastic material properties was conducted on a bi-material test sample model. Results showed that the new characterized viscoelastic material properties exhibited dependence on time and temperature. Slow cool down from post mold cure (PMC) to room temperature resulted in lower warpage or stress. This observed rate dependent response was explained using viscoelastic material properties in contrast to the usual linear elastic material simplification. Thus, a realistic result from stress or warpage analysis could be achieved using viscoelastic material characterization.

Time-dependent model for unidirectional composite with a viscoelastic matrix

Modelling of time-dependent properties of unidirectional fiber reinforced plastics on the basis of structural mechanics of composite materials and mechanics of hereditary media has been proposed in this research. The constitutive equations of unidirectional fiber reinforced plastics have been obtained using the Volterra correspondence principle and the algebraic properties of resolvent operators. Modelling of viscoelastic properties of a unidirectional composite material on the basis of EDT-10 epoxy resin has been shown.

Viscoelastic damping design – Thermal impact on a constrained layer damping treatment

Constrained layer damping treatments have been commonly used for vibration damping. The included viscoelastic material exhibits high damping potential that is retrieved under shear deformation. However, the impact of temperature on the viscoelastic properties and thus on the vibration damping often remains unconsidered. This paper addresses the design of viscoelastic damping under thermal consideration. For this purpose, the frequency and temperature dependent properties of a bromobutyl rubber compound were characterized in a dynamic mechanic thermal analysis. The viscoelastic material properties are employed in a finite element model of a structure with a constrained layer damping treatment. Subsequently, the modal damping of the structural vibrations is analyzed under varying temperature conditions. The analyses show a significant thermal impact on the modal damping. In this context, an approach is presented for compensating the adverse thermal effect on damping by a modified geometric design of the viscoelastic core layer.

Topology optimization of constrained layer damping plates with frequency- and temperature-dependent viscoelastic core via parametric level set method

Frequency- and temperature-dependent properties of viscoelastic materials have a significant effect on vibration characteristics of constrained layer damping (CLD) structures. In this article, parametrized level set method (PLSM) is extended to solve the topology optimization problem of CLD plates, in which the viscoelastic material with frequency- and temperature-dependent characteristics is employed as damping core. The single/weighted modal loss factors, which are solved by an iterative method, are defined as objective functions, and topology optimization problem is formulated based on the finite element model for CLD plates which are described by combining parametric level set (PLS) functions. The sensitivities of objective functions with respect to expansion coefficients in PLS are calculated by the use of adjoint vector method. As the optimized results with complex constant shear modulus for viscoelastic core indicates, the proposed method is effective for topology optimization of CLD structures and insensitive to initial design. Numerical examples with the consideration of frequency- and temperature-dependent characteristics for “soft” and “hard” viscoelastic core are implemented. Through comparing the optimal results with different models for viscoelastic core, the influences of frequency- and temperature-dependent characteristics for viscoelastic core on natural frequencies, modal loss factors and optimized layouts are analyzed. Similarity indices are defined for distinguishing the difference among optimized layouts and initial design induced by modal strain energy contour. The optimal design dependence on layer thicknesses is further discussed with additional mass of CLD materials unchanged.

Vibrations of a viscoelastic isotropic plate under periodic load without considering the tangential forces of inertia

A mathematical model of the problem of viscoelastic isotropic plate vibrations based on the Kirchhoff-Love hypothesis in a geometrically nonlinear formulation was presented. The mathematical model was built without considering the tangential forces of inertia. To describe the viscoelastic properties of the plate material, a weakly singular Koltunov-Rzhanitsyn kernel with three different rheological parameters was chosen. To solve the problem of parametric vibrations of a viscoelastic plate with a weakly singular relaxation kernel, a numerical method based on the use of quadrature formulas was applied. A discrete model of this problem was first constructed using the Bubnov-Galerkin method; i.e., a system of integro-differential equations with variable coefficients was obtained, and then, using a numerical method based on the elimination of a singularity of the kernel, the problem of parametric vibrations of viscoelastic rectangular plates was solved. The influence of the viscoelastic properties of the material and the variability of the plate thickness on the oscillatory process was shown.

Controlling the Vibration Amplitude of a System with a Piezoelectric Element by Applying an Electric Voltage to it

The article is devoted to the study of the mechanical response of an electro-viscoelastic structure if an electric voltage with given characteristics supplied to a piezoelectric element attached to the surface of the structure. A cantilever plate made of a viscoelastic material is considered as a structure under study. The amplitude of displacements of the free end of the plate in resonance modes occurring at forced steady-state vibrations is considered as the mechanical response. Excitation of vibrations is realized by a harmonic movement applied to the clamped end of the plate. The control of the mechanical response within the framework of this work is supposed to be performed by supplying an electric signal to the piezoelectric element. This signal changes harmonically and has the form of a potential difference which changes according to a harmonic law. The magnitude of the vibration amplitude of the structure is determined numerically by the finite element method implemented in the ANSYS software package. The viscoelastic properties of the plate material are described according to the relations of hereditary theory of viscoelasticity in terms of complex dynamic moduli. Within the framework of this work, the relations between the mechanical response of the structure and the magnitude and polarity of the electric voltage applied to the piezoelectric element were obtained. It is shown that by a proper selection of the characteristics of the electric voltage, it is possible to control the magnitude of the amplitude of forced steady-state vibrations.

Viscoelastic characterization of human descending thoracic aortas under cyclic load

Experiments were carried out on 15 human descending thoracic aortas from heart-beating healthy donors who donated organs for transplant. The aortas were kept refrigerated in organ preservation solution and tested were completed within 48 hours from explant. Donors’ age was comprised between 25 and 70 years, with an average of 51.7 ± 12.8 years. Quasi-static and dynamic uniaxial tensile test were carried out in thermally controlled physiological saline solution in order to characterize the viscoelastic behavior. Strips were tested under harmonic deformation of different frequency, between 1 and 11 Hz, at three initial pre-stretches. Cyclic deformations of two different amplitudes were used: a physiological one and a small one, the latter one for comparison purposes to understand the accuracy limits of viscoelastic models. Aortic strips in circumferential and longitudinal directions were cut from each aorta. Some strips were dissected to separate the three layers: intima, media and adventitia. They were tested individually in order to obtain layer-specific data. However, strips of the intact wall were also tested. Therefore, 8 strips per donors were tested. Viscoelastic parameters are accurately evaluated from the hysteresis loops. Results show that small-amplitude cyclic strain over-estimate the storage modulus and under-estimate the loss-factor. Therefore, cyclic deformation of physiological amplitude is necessary to obtain correct viscoelastic data of aortic tissue. The value of the applied pre-stretch is significant on the dynamic stiffness ratio (storage modulus divided by the corresponding quasi-static stiffness), while it is less significant for the loss factor. The median of the dynamic stiffness ratios, in physiological conditions, varies between 1.14 and 1.33 for the different layers and the intact wall; the corresponding median of the loss factors varies between 0.050 and 0.066. The lowest dynamic stiffness ratios and loss factors were obtained from donors of the youngest age group. Statement of significanceThere is an increasing interest in replacing traditional Dacron grafts used to repair thoracic aortas after acute dissection and aneurysm, with grafts in innovative biomaterials that mimic the mechanical properties and the dynamic behavior of the aorta. The human aorta is a complex laminated structure with hyperelastic and viscoelastic material properties and residual stresses. This study aims to characterize the nonlinear viscoelastic properties of ex-vivo human descending thoracic aortas by measuring hysteresis loops of physiological amplitude under harmonic strain. Results show the necessity to characterize the viscoelastic material properties of the aorta under physiological conditions, as well as the necessity to introduce improved models that take better into account the influence of the initial pre-stretch and amplitude of the cyclic load.

Effects of Loading and Boundary Conditions on the Performance of Ultrasound Compressional Viscoelastography: A Computational Simulation Study to Guide Experimental Design.

Most biomaterials and tissues are viscoelastic; thus, evaluating viscoelastic properties is important for numerous biomedical applications. Compressional viscoelastography is an ultrasound imaging technique used for measuring the viscoelastic properties of biomaterials and tissues. It analyzes the creep behavior of a material under an external mechanical compression. The aim of this study is to use finite element analysis to investigate how loading conditions (the distribution of the applied compressional pressure on the surface of the sample) and boundary conditions (the fixation method used to stabilize the sample) can affect the measurement accuracy of compressional viscoelastography. The results show that loading and boundary conditions in computational simulations of compressional viscoelastography can severely affect the measurement accuracy of the viscoelastic properties of materials. The measurement can only be accurate if the compressional pressure is exerted on the entire top surface of the sample, as well as if the bottom of the sample is fixed only along the vertical direction. These findings imply that, in an experimental validation study, the phantom design should take into account that the surface area of the pressure plate must be equal to or larger than that of the top surface of the sample, and the sample should be placed directly on the testing platform without any fixation (such as a sample container). The findings indicate that when applying compressional viscoelastography to real tissues in vivo, consideration should be given to the representative loading and boundary conditions. The findings of the present simulation study will provide a reference for experimental phantom designs regarding loading and boundary conditions, as well as guidance towards validating the experimental results of compressional viscoelastography.

A New Tactile Transfer Cell Using Magnetorheological Materials for Robot-Assisted Minimally Invasive Surgery.

This paper proposes a new type of tactile transfer cell which can be effectively applied to robot-assisted minimally invasive surgery (RMIS). The proposed tactile device is manufactured from two smart materials, a magnetorheological fluid (MRF) and a magnetorheological elastomer (MRE), whose viscoelastic properties are controllable by an external magnetic field. Thus, it can produce field-dependent repulsive forces which are equivalent to several human organs (or tissues) such as a heart. As a first step, an appropriate tactile sample is made using both MRF and MRE associated with porous foam. Then, the microstructures of these materials taken from Scanning Electron Microscope (SEM) images are presented, showing the particle distribution with and without the magnetic field. Subsequently, the field-dependent repulsive force of the sample, which is equivalent to the stress relaxation property of viscoelastic materials, are measured at several compressive deformation depths. Then, the measured values are compared with the calculated values obtained from Young’s modulus of human tissue data via the finite element method. It is identified from this comparison that the proposed tactile transfer cell can mimic the repulsive force (or hardness) of several human organs. This directly indicates that the proposed MR materials-based tactile transfer cell (MRTTC in short) can be effectively applied to RMIS in which the surgeon can feel the strength or softness of the human organ by just changing the magnetic field intensity. In this work, to reflect a more practical feasibility, a psychophysical test is also carried out using 20 volunteers, and the results are analyzed, presenting the standard deviation.

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.