Voigt Element Research Articles

Analyzing Experimental Data Validity and Error Structure for Second-Harmonic Nonlinear Electrochemical Impedance Spectroscopy

Second harmonic nonlinear electrochemical impedance spectroscopy (2nd-NLEIS) is a powerful and complementary technique to traditional EIS, often resolving model degeneracy issues in electroanalytical half-cell measurements and enabling better parameter assignment in two-electrode systems such as lithium-ion battery (LIB) experiments. Since the initial 2nd-NLEIS data for Li-ion batteries was reported by Murbach et al., [1] methods for testing the validity of 2nd-NLEIS datasets have been lacking. In EIS, the Kramers-Kronig (KK) relation is foundational for evaluating if experimental data meets key metrics for linearity, causality, and stationarity. [2] While the nonlinear nature of the 2nd-NLEIS response does not allow the direct application of KK relation, other approaches for data validation established in the EIS literature can be adapted to data validation and experimental error analysis in 2nd-NLEIS experiments.In this work, we provide a pathway to quantify the quality of 2nd-NLEIS data, providing better confidence in the simultaneous analysis of EIS and 2nd-NLEIS. The Data validation for 2nd-NLEIS relies on the use of a series of nonlinear Voigt elements to describe a 2nd-NLEIS spectrum, enabling a foundational assessment of data quality and stochastic error analogous to the practice in linear EIS data quality assessments. [3,4] Our method builds on prior work showing the 2nd-NLEIS Randles circuit response is directly proportional to the square of the linear EIS response. [5] By feeding the KK-transformable EIS response into the 2nd-NLEIS governing equation, we obtained a KK equivalent nonlinear transformation for the 2nd-NLEIS. That is, the 2nd-NLEIS response can be represented by the sum of M nonlinear Randles in the absence of measurement noise. Similarly, the difference between the data and fit provides a measure of the experimental noise. Overall, this work leverages methods from linear EIS and basic circuit elements we’ve developed for the 2nd-NLEIS response to provide data quality quantification of the 2nd-NLEIS data.

Trajectory-based breakup modelling for dense bubbly flows

A new model to predict the breakup of gaseous bubbles in a continuous liquid phase is developed. In the model each bubble is modelled as a spring–damper system, namely a Kelvin–Voigt element, while the outer force is derived by a Lagrangian analysis determining the largest stretching rate of the flow field below. The developed model is based on physical principles and no further arbitrary parameters have to be adjusted. Each bubble is observed on its way through the bubbly flow individually, taking into account its history along its respective path. With the implemented model numerical simulations in a wide range of scales are conducted, ranging from the laboratory scale of a vessel of 3L to the large industrial scale of 15m3. The simplicity of the model allows for a good cost to benefit ratio. In the present work, the achieved results are compared to experimental data obtained from optical measurements in a replica of a 200L aerated stirred tank reactor for various stirrer frequencies.

On the Correlation of Kramers-Kronig (KK) Analysis and Non-Linear Harmonic Analysis (NHA)

Primary lithium batteries are known for their elevated volumetric and gravimetric energy densities and production cost efficiency. Within this category, lithium thionyl chloride (Li/SOCl2) batteries exhibit a constant discharge voltage (~3.6 V) and a broad operational temperature range (-50ᵒC to 80ᵒC). Moreover, forming a LiCl passivation layer on the metallic Li anode can extend its shelf-life up to 20 years at optimal storage temperature. These characteristics render lithium thionyl chloride batteries applicable in military and security applications, microcomputers, measurement devices, and medical instruments. Therefore, the characterization of lithium thionyl chloride batteries accurately has the utmost importance. Understanding the critical electrochemical processes that occur inside the battery without damaging or disassembling the cell requires delicate techniques.EIS has emerged as a non-destructive and in-situ measurement technique with increasing popularity. Essential battery properties can be derived from EIS data. The credibility of EIS data, considering linearity, causality, and stability, can be verified through Kramers-Kronig relations. The obtained spectrum is fitted with an optimal number of Voigt elements (RC components in parallel)[1]. Given the linearity and stability of these individual Voigt elements, the entire spectrum should exhibit linearity if it is Kramers-Kronig compatible[2].Non-linear harmonic analysis (NHA) is a complementary technique to EIS, wherein the response signal undergoes conversion from the time domain to the frequency domain through Fast Fourier Transformation (FFT). While EIS employs a single-phased pure sinusoidal signal as the input, the response includes a fundamental frequency and harmonics at integer frequencies of this fundamental response signal. NHA can be utilized in the diagnosis of non-linear, non-stationary situations alongside the identification of drift and initial transients.This study first explains a new EIS measurement method for Li/SOCl2 batteries and Li/SOCl2/SO2Cl2 mixture batteries. The new method describes the solid electrolyte interface (SEI) stability of the batteries and the modifications needed to get KK-compatible results. After that, the equivalent circuit fits applied to the acquired spectra. Essential battery parameters such as solution resistance, charge transfer resistance, and double-layer capacitance were calculated. Kramers-Kronig analysis of the batteries was conducted, and the residuals of the fits were investigated. Subsequently, the NHA of the batteries was examined and compared to the Kramers-Kronig residuals. A correlation between the residuals and NHA of the batteries was extended based on the terms "KK-compatible" and "non-KK-compatible" in comparing KK-residuals and NHA results.[1] Boukamp, B. A. , Journal of the Electrochemical Society 142.6 (1995): 1885.[2] Agarwal, et al., Journal of the Electrochemical Society 142.12 (1995): 4159. Figure 1

A study of valve-induced water hammer in a woven-jacket fire hose

ABSTRACT The dynamic response of a woven fire hose during valve-induced water hammer events is investigated through a combination of experimental and numerical studies. Unlike conventional polymeric pipes, fire hoses made of synthetic fibres exhibit unique characteristics, transitioning from pliancy to increased rigidity as the pressure within the hose rises. This study explores the transient behaviour of woven fire hoses under variable initial conditions. Experimental studies reveal a direct correlation between the initial piezometric head and the fire hose’s transient response. Numerical simulations employ the viscoelastic Kelvin–Voigt model, proving its suitability for accurately simulating valve-induced hydraulic transients in woven fire hoses. Notably, even a single Kelvin–Voigt element exhibits a relatively good fit with experimental data, accurately reproducing pressure peaks, while the inclusion of two elements enhances the model’s capability, achieving the near-perfect reproduction of pressure oscillations.

Sensitivity of creep parameters to pressure fluctuation of transient flow in viscoelastic pipes

ABSTRACT A stepwise method is one of the efficient approaches in the calibration of transient flow in viscoelastic pipes. However, there is the lack of comprehensive research on the calibration method for retarded time and creep compliance. Therefore, the sensitivity of the order of magnitude of the creep parameters in the presence of interactions to transient flow pressure damping and phase in the case of the two-element Kelvin–Voigt model is investigated. Also, the calibration methods of retarded time and creep compliance in the stepwise method of transient flow parameter calibration for viscoelastic pipes are proposed. The results indicate that the creep compliances do not affect the phase of the pressure fluctuations when the selected retarded times are greater than the order of magnitude 10−1. For the first Kelvin–Voigt element, when the order of magnitude of the retarded time exceeds 10−2, an increase in creep compliance results in an increase in the degree of damping of pressure fluctuations. When the order of magnitude of the retarded time is less than 10−2, the rule is reversed. For the second Kelvin–Voigt element, an increase in creep compliance results in an increase in the degree of damping of transient flow pressure fluctuations independent of the retarded time.

Mechanical insights into jawbone characteristics under chronic kidney disease: A comprehensive nanoindentation approach

The mechanical properties of the jawbone play a critical role in determining the successful integration of dental prostheses. Chronic kidney disease (CKD) has been identified to abnormally accelerate bone turnover rates. However, the impact of CKD on the mechanical characteristics of the jawbone has not been extensively studied. This study sought to evaluate the time-dependent viscoelastic behaviors of rat jawbones, particularly in the scenarios both with and without CKD. We hypothesized that CKD might compromise the bone's innate toughening mechanisms, potentially owing to the time-dependent viscoelasticity of the bone matrix proteins. The maxillary and mandibular bones of Wistar rats were subjected to nanoindentation and Raman micro-spectroscopy. Load-hold-displacement curves from the cortical regions were obtained via nanoindentation and were mathematically characterized using a suitable viscoelastic constitutive model. Raman micro-spectroscopy was employed to identify nuanced vibrational changes in local molecular structures induced by CKD. The time course of indenter penetration onto cortical bones during the holding stage (creep behavior) can be mathematically represented by a series arrangement of the Kelvin–Voigt bodies. This configuration dictates the overall viscoelastic response observed during nanoindentation tests. The CKD model exhibited a reduced extent of viscoelastic contributions, especially during the initial ramp loading phase in both the maxillary and mandibular cortical bones. The generalized Kelvin–Voigt model comprises 2 K–Voigt elements that signify an immediate short retardation time (τ1) and a subsequent prolonged retardation time (τ2), respectively. Notably, the mandibular CKD model led to an increase in the delayed τ2 alongside an increase in non-enzymatic collagen cross-linking. These suggest that, over time, CKD diminishes the bone's capability for supplementary energy absorption and dimensional recovery, thus heightening their susceptibility to fractures.

Experimental and Modelling of Shape Memory Effect of Shape Memory Natural Rubber

Shape memory natural rubber (SMNR) is a form of smart material that can memorise its permanent shape in response to temperature. In this article, a phenomenological constitutive model was adopted to predict the stress-strain evolution during the shape memory process of SMNR to understand the behavior of SMNR. A standard linear solid (SLS) model with Kelvin Voigt element was extended with two Mooney Rivlin models to account for the mechanical response, while a thermal strain model represented the change of length during the programming process and recovery process. An external temperature law was constructed to govern the volume fraction change between the soft active and frozen phase. The proposed constitutive model is capable of capturing the stress-strain behaviour of each shape memory step.

On the Characterization of Viscoelastic Parameters of Polymeric Pipes for Transient Flow Analysis

The behaviour of polymeric pipes in transient flows has been proved to be viscoelastic. Generalized Kelvin–Voigt (GKV) models perform very well when simulating the experimental pressure. However, in the literature, no general indications on the evaluation of the model parameters are given. In the present study, the calibration of GKV model parameters is carried out using a micro-genetic algorithm for experimental tests of transient flows in polymeric pipes taken from the literature. The results confirm that the higher the number of Kelvin–Voigt elements, the better the reproduction of experimental tests, but it is difficult to search for general rules for parameter characterization. Assuming a Kelvin–Voigt (KV) model with a single element, it is shown that the retardation time is related to the oscillation period that can be obtained from the elastic modulus and from easily evaluable pipe characteristics. A simple procedure is then proposed for the characterization of the viscoelastic parameters that can be used by manufacturers and technicians. Considering the limits of such a model, the procedure has to be considered as a first step for the characterization of the viscoelastic parameters of more complex models.

Influence of bushing flexibility and its constitutive behavior on the performance of suspension system

We study the effect of strut top mount bushing flexibility and its constitutive law on the ride comfort performance of a quarter car suspension model. A fractional Kelvin–Voigt model has been employed to capture the viscoelastic behavior of the top mount bushings. To study the effectiveness of the suspension system, we have considered sinusoidal and standard (motion over bumps) road inputs. For the sinusoidal input, the frequency response function for both the traditional and fractional Kelvin–Voigt models has been obtained using the harmonic balance method. However, we have resorted to numerical simulations for the standard base inputs for which a reduced-order system of ODEs has approximated the fractional derivative term. Convergence of the reduced system of ODEs is established by comparing the numerical results for sinusoidal forcing with those obtained analytically. We find that the bushing modeled as a traditional Kelvin–Voigt element increases the response amplitude in the resonance zone, while for higher frequencies, the response reduces. Hence, the inclusion of bushing flexibility is equivalent to decreasing the damping in the suspension. These observations also remain valid for the fractional Kelvin–Voigt model, but the effect is less pronounced than in the traditional model. Ride comfort for standard road profile is studied in terms of performance indices which suggests that a fractional Kelvin–Voigt bushing improves the ride comfort. Accordingly, bushing flexibility with an appropriate constitutive law should be accounted in the design of a suspension system for ride comfort. • Effect of strut top mount bushing (STMB) flexibility on ride comfort is studied. • Fractional Kelvin–Voigt model is employed for the viscoelastic behavior of the STMB. • Studied the suspension system response on sinusoidal and standard road inputs. • Ride comfort has been studied in terms of transmissibility and performance indices. • We find that STMB flexibility improves ride comfort especially during transient loads.

MODEL OF BLOCK MEDIA TAKING INTO ACCOUNT INTERNAL FRICTION

The block medium is modeled by a discrete-periodic spatial lattice of masses connected by elastic springs and viscous dampers. To describe the viscoelastic behavior of the interblock layers, a rheological model of internal friction with two Maxwell elements and one Voigt element with the quality factor of the material as the determining parameter is proposed. Numerical experiments show that, within the framework of this interlayer model, it is possible to select the viscosity and stiffness of the Maxwell and Voigt elements so that the quality factor of the material differs from the given constant value by no more than 5%. In the one-dimensional case, within the framework of the proposed model, the influence of the quality factor on the dispersion properties of a block medium is studied and it is shown that the greatest effect of the quality factor on the dispersion is observed in the low-frequency part of the spectrum. In the three-dimensional case, within the framework of the proposed model, some geomechanical problems are numerically studied for a block half-space under the action of a surface concentrated vertical load. Namely, the attenuation of the velocity amplitudes of surface blocks was studied depending on the Q-factor under step action and under the action of a Gaussian pulse. In addition, we study a layer on the surface of a half-space under the action of a concentrated vertical impulse load in the case when both the layer and the half-space are block media but have different properties.

Experimental Evaluation and Modeling of Physical Hardening in Asphalt Binders.

The research described in this paper deals with the experimental evaluation and modeling of physical hardening in asphalt binders. The term physical hardening refers to a reversible phenomenon occurring at low temperatures that causes time-dependent changes in viscoelastic properties. The experimental approach, followed to quantitatively assess physical hardening, was based on flexural creep tests carried out by means of the Bending Beam Rheometer at various temperatures and conditioning times. The results obtained confirmed that hardening phenomena have a significant influence on the creep response of asphalt binders, to an extent that can be quantitatively assessed by referring to the appropriate rheological parameters and by applying the loading time–conditioning time superposition principle. The experimental data were fitted to a mechanical model proposed in the literature (composed of a single Kelvin–Voigt element) and thereafter to an improved model (with two Kelvin–Voigt elements in series). Both models were assessed in terms of their prediction accuracy. The improved model was found to better describe physical hardening effects in the case of both short- and long-term conditioning. Practical implications of the study were finally highlighted by referring to possible ranking criteria to be introduced in acceptance procedures for the comparative evaluation of asphalt binders.

The Effects of Altering the Center of Pressure in Standing Subjects Exposed to Foot-Transmitted Vibration on an Optimized Lumped-Parameter Model of the Foot

Many workers are exposed to foot-transmitted vibration, which can lead to the development of vibration-induced white foot: a debilitating condition with neurological, vascular and osteoarticular symptoms. To design effective prevention mechanisms (i.e., boots and insoles) for isolating workers from vibration exposure, continued model development of the foot’s biodynamic response in different positions is necessary. This study uses a previously developed model of the foot–ankle system (FAS) to investigates how altering the center of pressure (COP) location can change the biodynamic response of the FAS to standing vibration exposure. Formerly published experimental responses for apparent mass and transmissibility at five anatomical locations in three COP positions were used to optimize the model. Differences occurred with the Kelvin–Voigt elements used to represent the soft tissues of the foot sole: at the heel, the distal head of the metatarsals and distal phalanges. The stiffness increased wherever the COP was concentrated (i.e., forward over the toes or backward over the heel). The variability of the model parameters was always greatest when the COP was concentrated in the heel. This suggests future FAS models need to more clearly address how the soft tissue of the plantar fat pad is modelled.

Modeling of transient flows in viscoelastic pipe network with partial blockage

Abstract In this study, transient flow and partial blockage in polyethylene (PE) pipe network are investigated experimentally and numerically using the method of characteristics in the time domain considering pipe-wall viscoelasticity. The experiments were conducted on a PE pipe network with and without partial blockage. The experimental pressure signals were damped during a short period of time in the blockage-free case. The numerical model was calibrated by the inverse transient analysis (ITA). The hydraulic transient solver calibrated with one Kelvin–Voigt element showed good consistency with the experimental results. Partial blockages with different lengths and sizes were examined at different locations of the pipe network. Results reveal an increase in head loss, pressure signal damping, and phase shift with increase in blockage. In addition, the location and characteristics of blockages with different sizes were determined using the ITA in the pipe network.

Experimental study on the effects of hygrothermal aging on the indentation creep behaviors of PMMA

The effects of aging time on indentation creep behaviors of Polymethyl methacrylate (PMMA) have been investigated and the creep displacement was found to increase with aging time. However, the rate of change weakens as aging time increases. The generalized Calvin model consists of three Voigt elements that provide a good description of the indentation creep behavior of PMMA during the holding stage. Each Voigt element represents the motions with different levels i.e. molecular chain, molecular chain segments, molecular chain linkage, and branched-chain. The motions of molecular chain with different levels always have different delay times. The mechanism on the effects of aging time on the indentation creep responses is analyzed by comparing the contributions of different deformation types to total deformation. The contribution of elastic deformation to the total deformation Rhe decreases initially and then increases as aging time increases, which indicates the weakening of elastic modulus results from hygrothermal aging. With the aging time increasing, the contribution of time-dependent deformation to the total deformation i.e. Rhev+Rhvfirst increases and then decreases, which can be attributed to the different aging mechanisms at different stages. Further studies on the effects of aging time on creep compliance and time delay spectrum of PMMA during the holding stage indicates different deformation levels of PMMA characterized by different Voigt elements.

Washing Machine Dynamic Model to Prevent Tub Collision during Transient State.

In horizontal-axis washing machines, the front gasket as well as the damping system are crucial owing to the possible collision of the tub with the housing during the transient period. However, most dynamic models for predicting tub motion focus on the steady state and consider only the suspension system without including the gasket. We conducted an experimental study to analyze the effect of the gasket on the transient motion of the tub. The results obtained indicate the necessity of implementing the gasket in the multibody model of a washing machine to accurately predict the tub behavior during this period. The gasket model is formed by a combination of Voigt elements. Stiffness parameters are determined using a load cell, and damping factors are estimated using a process that integrates Adams/View, Matlab optimization algorithms, and displacement measurements that are taken using accelerometers. A D-optimal design used to predict the effect of the gasket parameters reveals that the tub displacement is most sensitive to the changes in linear stiffness in the transversal direction. Finally, the model of the gasket provides a better approach for predicting the tub movement during resonance that can be used in the design phase to avoid tub collision.

General fractional models for linear viscoelastic characterization of asphalt cements

Rheological models based on fractional order derivatives have been applied to characterize the linear viscoelasticity of asphalt cements for a long time. Such models provide continuous spectra which are fundamentally related to the molecular characteristics and facilitate analytical investigations as compared to discrete representations. With the increasing complexity in asphalt composition to satisfy various purposes, however, the inadequacy of existing fractional models has been noted. This paper proposed a generalized fractional Maxwell-dashpot (GFMD) model as a general framework for describing the modulus behaviors of asphalt cements. The generalized fractional Voigt (GFV) model was considered the counterpart for the compliances. The material functions given by each model are primarily the superposition of its constituent fractional Maxwell-dashpot or fractional Voigt (FV) elements. Geometric features of these elements were investigated such that a proper initial guess of model parameters can be obtained graphically with relative ease. For computational efficiency, the continuous spectra were discretized to provide the Prony representations of the material functions. To demonstrate the model capability, the dynamic mechanical data of a neat asphalt showing the typical behavior and a heavily polymer-modified asphalt exhibiting strong cross-linking were utilized. For the typical behavior, the GFMD and GFV models containing two fractional elements yielded excellent descriptions. A third fractional unit was necessitated in both models to account for the cross-linking mechanism for the modified asphalt. A relaxation/retardation mode density of two points equidistantly per decade produced material functions with negligible waviness and almost the same accuracy as compared to the use of the continuous spectra.

Circular arc rules of complex plane plot for model parameters determination of viscoelastic material

We present a new approach to determine the rheological parameters of a mechanical model of viscoelastic materials. The fractional derivative solid model composed of a spring in series with a fractional derivative Kelvin–Voigt element has been employed to characterize the dynamic mechanical response of a real viscoelastic material. In dynamic mechanical analysis (DMA) measurements, the frequency-dependent loss modulus is plotted against the storage modulus in the form of complex plane plot. We find that the complex plane plot of the fractional derivative solid model is a depressed or distorted semicircle with its center below the real axis. The model parameters could be identified graphically via its complex plane curve, from which the spring constants can be obtained through the two intercepts of the extrapolated circular arc with the real axis, whereas the order of fractional dashpot can be estimated by the displacement of the semicircle center. The graphical method allows us to easily find rheological parameters, without using complicated calculation and special algorithms.

Semiempirical identification of nonlinear dynamics of a two-degree-of-freedom real torsion pendulum with a nonuniform planar stick\u2013slip friction and elastic barriers

The purpose of this study is to identify the nonlinear dynamics of the double torsion pendulum with planar friction and elastic barriers. The original experimental stand consists of a disk-shaped body that rotates freely on top of a forced column with a system of barriers limiting the torsional vibrations of the pendulum bodies that create an nonuniform planar rotational friction contact. Two beam springs form soft barriers modeled by Voigt elements that limit the angular displacement of one of the pendulum bodies—the disk, while the second limiting system, made of a much more rigid barrier, limits the movement of the pendulum’s second body. The dynamic behavior of the asymmetrical system of two degrees of freedom with discontinuities is identified with the use of the described strategy, numerical solutions of the derived mathematical model and the Nelder–Mead simplex algorithm. The actual measurement series and numerical solutions show a good similarity of the dynamical reaction of the mechanical system and its virtual analog.

Shifted-Chebyshev-polynomial-based numerical algorithm for fractional order polymer visco-elastic rotating beam

Abstract In this paper, an effective numerical algorithm is proposed for the first time to solve the fractional visco-elastic rotating beam in the time domain. On the basis of fractional derivative Kelvin–Voigt and fractional derivative element constitutive models, the two governing equations of fractional visco-elastic rotating beams are established. According to the approximation technique of shifted Chebyshev polynomials, the integer and fractional differential operator matrices of polynomials are derived. By means of the collocation method and matrix technique, the operator matrices of governing equations can be transformed into the algebraic equations. In addition, the convergence analysis is performed. In particular, unlike the existing results, we can get the displacement and the stress numerical solution of the governing equation directly in the time domain. Finally, the sensitivity of the algorithm is verified by numerical examples.

Soil–Structure Interaction of Plates on Extensible Geosynthetic-Stone Column Reinforced Earth Beds

A mechanical model has been presented for analysis of plates resting on extensible geosynthetic reinforced granular fill lying on soft soil improved by stone columns. Foundation has been idealised as a plate and geosynthetic layer as rough elastic membrane. Granular fill, soft soil and stone columns has been idealised respectively as Pasternak shear layer, Kelvin–Voigt elements and Winkler springs and their nonlinear behaviour has been considered. Deformation compatibility condition at interface of geosynthetic and granular fill has been considered. An iterative finite difference scheme with proper boundary conditions has been used to solve governing differential equations and the system of simultaneous equations so obtained, have been solved using LU decomposition method. Response of plate in terms of deflection and bending moment and tension mobilized in geosynthetic has been presented in non-dimensional form. Influence of type of geosynthetic (extensible and inextensible) in reducing the settlements in conjunction with stone columns has been presented and the significance of each parameter influencing the plate response has been studied by means of detailed parametric study.