Frequency-dependent Viscoelastic Properties Research Articles

Optimal viscoelastic properties for passive damping treatments

In the context of noise and vibration control, constrained viscoelastic materials can be used to reduce structure-borne noise of vibrating structure. This passive damping treatment finds many applications due to its robustness and low cost. While several approaches are proposed in the literature to optimise the placement of constrained viscoelastic patches, few studies has been dedicated to the optimisation of the viscoelastic material's properties. The difficulty stems from their frequency-dependency. In this work, a fractional derivative model is used to describe the complex frequency-dependent viscoelastic properties. This study illustrates the effectiveness of using surrogate modeling to predict the damping performance of viscoelastic patches. A multi-model reduction method combined with a modal parameter identification method is used to build a surrogate model at a reasonable computational cost. Once trained, this metamodel is explored to optimise the parameters of the fractional derivative model, thus allowing the design optimisation of viscoelastic properties. This approach could be extended to optimise the material properties of viscoelastic foams in the low frequency range.

Dynamic Mechanical Analysis of Cementitious Composites: Test Method Optimization and Materials Characterization

Dynamic mechanical analysis (DMA) applies an oscillating force to a specimen and analyzes the rheological and viscoelastic properties of a material. Since this method is used to characterize the frequency-dependent viscoelastic properties, it is mostly used for polymers, which have high sensitivity to the loading frequency. Cementitious composites are brittle and require more attention to specimen preparation and experimental settings to obtain reliable results. This work develops a DMA test protocol for cementitious composites which includes analyzing the effect of preload test, frequency pretest, and amplitude sweep on properties of cementitious composites. We propose a statistical method to analyze the variation between samples and determine the outliers among the specimens with the same mix to obtain valid test results from a sample group. The dynamic results obtained by using the proposed method are also discussed to serve as the baseline. The experimental setup parameters and statistical analysis presented in this work can be a robust foundation for the DMA analysis of cementitious composites.

Measurements and estimation of frequency-dependent multi-scale viscoelastic damping properties of materials

The state-of-art viscoelastic property measurement and estimation methods at different frequencies/length scales inherently couple structural effects or sometimes lose accuracy for relevant parameters at smaller length scales in the material. We report a unified approach to measuring and estimating the frequency-dependent viscoelastic damping properties across different frequency scales independently of the specimen size effect and boundary conditions. The Dynamic Mechanical Analysis (DMA) method with three-point bending configuration is extended to higher-fidelity modeling in terms of time–frequency scales and material micro-mechanical scales together. The methodology demonstrates ways to identify the possible sources of undesired dynamics in the measurement process and eliminate those effects. It includes exciter tip contact dynamics in three-point bending configuration, anharmonic energy transfer to different frequencies (fractal bifurcation), and unmodelled artifacts or noise. Critically reviewing the standard DMA procedure with normal mode synthesis, this paper proposes a time–frequency Fourier spectral method that resolves a broader frequency range that extends to even acoustic/ultrasonic wave regimes of viscoelastic damping. An algorithm proposed in this paper with the advanced viscoelastic model with multi-parameters (standard linear solid model) estimates the fundamental material parameters at small length scales, which is more insightful to obtain a frequency-dependent correlation of material response to general dynamic loading. Stiffness and damping properties are estimated from measured data and validated for self-consistencies via different controls regarding static preload, specimen resonance, filtered noise, and model fidelity across the frequency range, and certain consistency and convergence properties of a series solution. The unified approach with a single test will be helpful in the design and evaluation of a wide variety of materials and their applications in vibration and acoustic problems. The proposed technique further demonstrates a novel way to extend low-frequency measurement to high-frequency response modeling.

Dynamic concatenation of ring DNA leads to non-equilibrium viscoelasticity tuned by DNA size and concentration.

Topoisomerases can cleave, twist, untwist and reconnect ring DNA to enable diverse biological processes including DNA replication and repair, as well as the formation of concatenated structures such as kinetoplasts. At the same time, dense solutions of topologically-varying DNA have been shown to exhibit unique viscoelastic properties that can be tuned by DNA concentration, size and topology. Here, we use dynamic light scattering and particle-tracking microrheology to characterize the non-equilibrium viscoelastic properties of dense solutions of ring DNA undergoing dynamic concatenation via the linking and unlinking action of Topoisomerase II. We show that the frequency-dependent viscoelastic properties of these active Olympic ring hydrogels can be precisely tuned by varying the size and concentration of the DNA rings as well as the rate at which Topoisomerase II links and unlinks the DNA. Our work sheds new light on the oft overlooked role of varying viscoelasticity on biological processes that alter DNA topology, including the formation and restructuring of kinetoplasts, and the unwinding of DNA for replication and repair. Future work will build on this bio-inspired platform by incorporating additional enzymes that fragment and ligate DNA for in situ alteration of DNA length.

Effect of Noise on Determining Ultrathin-Film Parameters from QCM-D Data with the Viscoelastic Model.

Quartz crystal microbalance with dissipation monitoring (QCM-D) is a well-established technique for studying soft films. It can provide gravimetric as well as nongravimetric information about a film, such as its thickness and mechanical properties. The interpretation of sets of overtone-normalized frequency shifts, ∆f/n, and overtone-normalized shifts in half-bandwidth, ΔΓ/n, provided by QCM-D relies on a model that, in general, contains five independent parameters that are needed to describe film thickness and frequency-dependent viscoelastic properties. Here, we examine how noise inherent in experimental data affects the determination of these parameters. There are certain conditions where noise prevents the reliable determination of film thickness and the loss tangent. On the other hand, we show that there are conditions where it is possible to determine all five parameters. We relate these conditions to the mathematical properties of the model in terms of simple conceptual diagrams that can help users understand the model's behavior. Finally, we present new open source software for QCM-D data analysis written in Python, PyQTM.

Two dominant timescales of cytoskeletal crosslinking in the viscoelastic response of the cytoplasm

Cells precisely regulate their frequency-dependent viscoelastic properties in response to chemical and mechanical cues. We use optical trap-based active microrheology using intracellular probes to measure the cytoplasmic mechanical response of fibroblast and macrophage cells over a broad frequency range ($\ensuremath{\sim}0.02--350$ Hz). Both cell types show similar frequency-dependent behavior, suggesting that the mechanisms that control the cell's mechanical response are general to many cell types. At frequencies above 1 Hz, the cytoplasmic mechanical behavior shows a broad distribution of relaxation timescales consistent with power-law mechanics. At low frequencies ($<1$ Hz), cells exhibit fluidlike behavior with distinct relaxation timescales, similar to that observed in reconstituted networks of transiently crosslinked actin filaments. The response across all frequencies can be captured by a mathematical model combining a power-law term with two crosslinker-unbinding terms. The two unbinding rates required to describe the low-frequency response suggest that the viscoelastic relaxation of the cytoplasm is governed either by multiple dominant crosslinkers or by a single crosslinker with multiple states.

Synthetic mucus for an ex vivo phonation setup: Creation, application, and effect on excised porcine larynges.

Laryngeal mucus hydrates and lubricates the deformable tissue of the vocal folds and acts as a boundary layer with the airflow from the lungs. However, the effects of the mucus' viscoelasticity on phonation remain widely unknown and mucus has not yet been established in experimental procedures of voice research. In this study, four synthetic mucus samples were created on the basis of xanthan with focus on physiological frequency-dependent viscoelastic properties, which cover viscosities and elasticities over 2 orders of magnitude. An established ex vivo experimental setup was expanded by a reproducible and controllable application method of synthetic mucus. The application method and the suitability of the synthetic mucus samples were successfully verified by fluorescence evidence on the vocal folds even after oscillation experiments. Subsequently, the impact of mucus viscoelasticity on the oscillatory dynamics of the vocal folds, the subglottal pressure, and acoustic signal was investigated with 24 porcine larynges (2304 datasets). Despite the large differences of viscoelasticity, the phonatory characteristics remained stable with only minor statistically significant differences. Overall, this study increased the level of realism in the experimental setup for replication of the phonatory process enabling further research on pathological mucus and exploration of therapeutic options.

Viscoelastic properties of suspended cells measured with shear flow deformation cytometry.

Numerous cell functions are accompanied by phenotypic changes in viscoelastic properties, and measuring them can help elucidate higher level cellular functions in health and disease. We present a high-throughput, simple and low-cost microfluidic method for quantitatively measuring the elastic (storage) and viscous (loss) modulus of individual cells. Cells are suspended in a high-viscosity fluid and are pumped with high pressure through a 5.8 cm long and 200 µm wide microfluidic channel. The fluid shear stress induces large, ear ellipsoidal cell deformations. In addition, the flow profile in the channel causes the cells to rotate in a tank-treading manner. From the cell deformation and tank treading frequency, we extract the frequency-dependent viscoelastic cell properties based on a theoretical framework developed by R. Roscoe [1] that describes the deformation of a viscoelastic sphere in a viscous fluid under steady laminar flow. We confirm the accuracy of the method using atomic force microscopy-calibrated polyacrylamide beads and cells. Our measurements demonstrate that suspended cells exhibit power-law, soft glassy rheological behavior that is cell-cycle-dependent and mediated by the physical interplay between the actin filament and intermediate filament networks.

Time-, Temperature- and Frequency-Dependent Viscoelastic Properties of a Curing Epoxy Adhesive

Thermoset adhesives convert from liquid to solid due to chemical reactions. Once cured, these adhesives carry the potential to create strong load-bearing joints, resisting even severe detrimental service conditions. In the progress of curing of a thermoset adhesive the viscoelastic properties of the resin and hardener formulation change as the chemical reaction proceeds. Gelation occurs once a continuous 3-dimensional network of polymer chains has been created. After gelation, the microstructure of the resin is fixed and further cure is affected by diffusion limitations [1]. Mastering of the curing kinetics and the physicochemical changes in the transition from the liquid to the solid-state is essential to reliably process adhesives in industrial applications. Rheological experiments in parallel plate configuration have become a well-established practice in investigating viscoelastic properties in the progress of curing. In practice, it has shown to be challenging to access the full range of viscoelastic parameters of thermoset resins with a low initial viscosity from the very beginning of the curing reaction to the post-cure consolidation of the vitrified polymer. This paper will discuss experimental methods and criteria for the viscoelastic analysis of curing thermoset adhesives and present experimental data of the time-, temperature-, and frequency-dependent viscoelastic properties of a curing thermoset epoxy in relation to the features of its time-temperature-transformation-diagram.

Solutions to ramp-hold dynamic oscillation indentation tests for assessing the viscoelasticity of hydrogel by Kelvin-Voigt fractional derivative modeling

Indentation type dynamic mechanical analysis (IT-DMA) is an attractive approach to characterizing viscoelastic properties of soft matter under both quasi-static and dynamic loadings. Frequency-dependent viscoelastic properties are usually characterized by storage and loss moduli whereas extracting inherent viscoelastic model parameters from dynamic loadings remains unsolved. In this study, closed-form solutions to dynamic oscillation loadings were first derived and adapted to a variety of excitations for arbitrary shape indenters. A uniform theoretical framework for ramp-hold-oscillation-relaxation/creep indentation tests are established and Kelvin-Voigt fractional derivative (KVFD) solutions are presented to predict the viscoelastic behavior for both quasi-static loadings (creep, relaxation) and dynamic loadings (sinusoidal displacement/force cycles at 5,10,15,20,30 Hz). Four gelatin-cream hydrogel samples were investigated under ramp-hold-oscillation-relaxation and ramp-hold-oscillation-creep testing conditions. Viscoelastic quantities of elasticity E0, fluidity α, and viscosity τ were extracted by fitting the experimental curves to KVFD predictions. The results show that KVFD models can accurately depict the viscoelastic behavior under both dynamic and quasi-static loadings with high goodness of fit (R2>0.936). To assess the proposed method, comparison of the viscoelastic quantities from different experimental protocols were conducted. Statistical results revealed viscoelastic parameters from different loading are in close agreement. For dynamic loadings, significant differences were found for [E0, α] estimates at different frequencies. For different experimental protocols, estimations were consistent in that E0 showed maximum value on Gel5Cream15 sample, and α was increased with increasing cream percentage. Moreover, viscoelastic quantities extracted from dynamic relaxation were correlated with those of the dynamic creep (r = 0.977, p < 0.001 for E0, and r = 0.969, p < 0.001 for α). Viscoelastic quantities from quasi-static relaxation were highly correlated with those from quasi-static creep (r = 0. 910, p < 0.001 for E0, and r = 0.979, p < 0.001 for α). The complex modulus from KVFD estimations was found to be correlated with that of the DMA measurement (for dynamic relaxation, r = 0.603, p < 0.001 for E′ and r = 0.818, p < 0.001 for E″; for dynamic creep, r = 0.756, p < 0.001 for E′ and r = 0.762, p < 0.001 for E″). Cross validation and assessment by alternative DMA method confirmed that KVFD solutions provided a method for relating viscoelastic measurements at load frequencies from quasi-static to dynamic for soft viscoelastic tissue-like materials.

Dynamic viscoelastic characterisation of human osteochondral tissue: understanding the effect of the cartilage-bone interface

BackgroundDespite it being known that subchondral bone affects the viscoelasticity of cartilage, there has been little research into the mechanical properties of osteochondral tissue as a whole system. This study aims to unearth new knowledge concerning the dynamic behaviour of human subchondral bone and how energy is transferred through the cartilage-bone interface.MethodsDynamic mechanical analysis was used to determine the frequency-dependent (1–90 Hz) viscoelastic properties of the osteochondral unit (cartilage-bone system) as well as isolated cartilage and bone specimens extracted from human femoral heads obtained from patients undergoing total hip replacement surgery, with a mean age of 78 years (N = 5, n = 22). Bone mineral density (BMD) was also determined for samples using micro-computed tomography as a marker of tissue health.ResultsCartilage storage and loss moduli along with bone storage modulus were found to increase logarithmically (p < 0.05) with frequency. The mean cartilage storage modulus was 34.4 ± 3.35 MPa and loss modulus was 6.17 ± 0.48 MPa (mean ± standard deviation). In contrast, bone loss modulus decreased logarithmically between 1 and 90 Hz (p < 0.05). The storage stiffness of the cartilage-bone-core was found to be frequency-dependent with a mean value of 1016 ± 54.0 N.mm− 1, while the loss stiffness was determined to be frequency-independent at 78.84 ± 2.48 N.mm− 1. Notably, a statistically significant (p < 0.05) linear correlation was found between the total energy dissipated from the isolated cartilage specimens, and the BMD of the isolated bone specimens at all frequencies except at 90 Hz (p = 0.09).ConclusionsThe viscoelastic properties of the cartilage-bone core were significantly different to the tissues in isolation (p < 0.05). Results from this study demonstrate that the functionality of these tissues arises because they operate as a unit. This is evidenced through the link between cartilage energy dissipated and bone BMD. The results may provide insights into the functionality of the osteochondral unit, which may offer further understanding of disease progression, such as osteoarthritis (OA). Furthermore, the results emphasise the importance of studying human tissue, as bovine models do not always display the same trends.

Frequency dependent viscoelastic properties of porcine brain tissue

Brain tissue is vulnerable and sensitive, predisposed to potential damage under complicated loading conditions. Its material properties have been investigated, but the characterization of its viscoelastic properties is currently limited. The aim of this study was to investigate the viscoelastic properties of brain tissue. Porcine brain samples, dissected ex vivo in the coronal plane, were tested under compression using dynamic mechanical analysis over a range of frequencies between 0.1 and 35 Hz. Indenters with varying diameters of 8, 12 and 16 mm were used to study the effect on viscoelastic properties under a sinusoidally varying displacement with varying mean displacements (10%, 15% and 20% of a specimen height). As the indenter size increased, the storage and loss stiffness significantly increased (p < 0.05). The storage stiffness decreased significantly as the mean displacement decreased (p < 0.05). The average storage modulus was found to be 8.09 kPa and the average loss modulus was found being 4.85 kPa. Frequency dependent viscoelastic properties of brain are important to improve the accuracy in the computational modelling of the head to develop the prediction of brain injuries.

Temperature-humidity-time equivalence and relaxation in dynamic viscoelastic response of Chinese fir wood

Design, application and service life of modern engineered wood and its products are closely related to environmental temperature and relative humidity (RH). In this study, the frequency-dependent viscoelastic properties of Chinese fir wood were investigated under different hygrothermal conditions (temperature: 30–80 °C, RH: 0–85%), to verify the applicability of humidity-time and temperature-humidity-time equivalence principles to wood viscoelasticity (i.e., the equal effects of elevating temperature, increasing RH, or prolonging testing time on the changes of stiffness and damping). The relaxation of wood cell wall was compared under moisture equilibrium and non-equilibrium states. It was demonstrated that both the humidity-time equivalence and temperature-humidity-time equivalence principles were applicable for describing the evolution of wood stiffness. Master curves constructed by humidity-time equivalence and temperature-time equivalence principles were basically overlapped at a short-time region (frequency >0.01 Hz) when reference condition was 30 °C/0% RH. However, the humidity-time equivalence principle failed to predict wood damping properties, regardless of hygrothermal condition. The testing frequency (fc, assigned to the transition of different relaxation processes) corresponded to the local minimum value of tan δ was ranged from 8 to 30 Hz and moved to the high frequency direction with increasing RH level. The fc value at moisture equilibrium state was lower than non-equilibrium state (no matter moisture adsorption or desorption). It was attributed the higher fc value at moisture non-equilibrium state to the unstable configuration structure of wood cell wall. These findings not only help understanding the wood-water relations, but also be relevant for the utilization and production processes of engineered wood and its products in the construction and building fields.

Towards viscoelastic characterisation of the human ulnar nerve: An early assessment using embalmed cadavers

Cubital tunnel syndrome is the most prevalent neuropathy of the ulnar nerve and its aetiology is controversial. Potential replacement materials should display similar viscoelastic properties. The purpose of this study was to assess the feasibility and merit of quantifying the frequency-dependent viscoelastic properties of proximal and distal sections of the human ulnar nerve. Four ulnar nerves (n = 4) were dissected from the elbows of human cadavers and sectioned at the level of the cubital tunnel into proximal and distal sections. These eight sections of the ulnar nerve were sinusoidally loaded to induce stresses between 0.05 and 0.27 MPa and the viscoelastic properties were measured between 0.5 and 24 Hz using dynamic mechanical analysis. The nerves were found to exhibit frequency-dependent viscoelastic behaviour throughout this frequency range. The median storage moduli of the proximal nerves ranged between 7.03 and 8.18 MPa, and 8.85–10.19 MPa for distal nerves, over the frequency-sweep tested. The median loss moduli of the proximal nerves ranged between 0.46 and 0.81 MPa and between 0.51 and 0.80 MPa for distal nerves. Ulnar nerves display frequency dependency viscoelasticity. Such characterisation is feasible with potential applications to suitable nerve grafts.

ROSE bitumen: Mesoscopic model of bitumen and bituminous mixtures.

We present a mesoscopic model for bitumen and bituminous mixtures. The model, which is based on dissipative particle dynamics, consists of different dynamical entities that represent the different characteristic time scales. Through the stress relaxation function, the mechanical properties of the model are investigated. For pure bitumen, the viscosity features super-Arrhenius behavior in the low-temperature regime in agreement with experimental data. The frequency-dependent viscoelastic properties show purely viscous behavior at low frequencies with increasing elasticity and hardening at higher frequencies, as expected. The model dynamics are analyzed in the framework of longitudinal hydrodynamics. The thermal process is two orders of magnitude slower than the attenuation of the density-wave propagation; hence the dynamic structure factor is dominated by a sharp Rayleigh peak and a relatively broad Brillouin peak. The model is applied to study triblock-copolymer-modified bitumen mixtures. Effects of the polymer concentration and end-block interactions with the bitumen are investigated. While the polymer concentration has an effect on the mechanical properties, the effect of increasing repulsive interactions between the bitumen and the polymer end-blocks is much more dramatic; it increases the viscosity of the mixture and shifts the onset of the elastic behavior to lower frequencies. For increased repulsion, the polymer end-blocks form small clusters that can be connected by a dynamic polymer backbone network. A simple Flory-Huggins analysis reveals the onset of segregation of the end-blocks in the bitumen mixture in agreement with the simulation data. Hence the changed mechanical properties are due to the emergence of large-scale structures as the repulsion is increased, which conforms to known mechanisms of microphase separation in polymer-modified bitumens.

Modelling nonlinear viscoelastic behaviours of loudspeaker suspensions-like structures

Mechanical properties of an electrodynamic loudspeaker are mainly determined by its suspensions (surround and spider) that behave nonlinearly and typically exhibit frequency dependent viscoelastic properties such as creep effect. The paper aims at characterizing the mechanical behaviour of electrodynamic loudspeaker suspensions at low frequencies using nonlinear identification techniques developed in recent years. A Generalized Hammerstein based model can take into account both frequency dependency and nonlinear properties. As shown in the paper, the model generalizes existing nonlinear or viscoelastic models commonly used for loudspeaker modelling. It is further experimentally shown that a possible input-dependent law may play a key role in suspension characterization.

Viscoelasticity of articular cartilage: Analysing the effect of induced stress and the restraint of bone in a dynamic environment.

The aim of this study was to determine the effect of the induced stress and restraint provided by the underlying bone on the frequency-dependent storage and loss stiffness (for bone restraint) or modulus (for induced stress) of articular cartilage, which characterise its viscoelasticity. Dynamic mechanical analysis has been used to determine the frequency-dependent viscoelastic properties of bovine femoral and humeral head articular cartilage. A sinusoidal load was applied to the specimens and out-of-phase displacement response was measured to determine the phase angle, the storage and loss stiffness or modulus. As induced stress increased, the storage modulus significantly increased (p < 0.05). The phase angle decreased significantly (p < 0.05) as the induced stress increased; reducing from 13.1° to 3.5°. The median storage stiffness ranged from 548 N/mm to 707 N/mm for cartilage tested on-bone and 544 N/mm to 732 N/mm for cartilage tested off-bone. On-bone articular cartilage loss stiffness was frequency independent (p > 0.05); however, off-bone, articular cartilage loss stiffness demonstrated a logarithmic frequency-dependency (p < 0.05). In conclusion, the frequency-dependent trends of storage and loss moduli of articular cartilage are dependent on the induced stress, while the restraint provided by the underlying bone removes the frequency-dependency of the loss stiffness.

Viscoelastic properties of mitral valve leaflets: An analysis of regional variation and frequency-dependency.

The aim of this study was to determine the regional variation in viscoelastic properties of mitral valve leaflets over a range of physiological and patho-physiological frequencies. This included comparisons to be made between anterior and posterior leaflets, anterior leaflet clear and rough zones, and radial and circumferential leaflet orientation. Dynamic mechanical analysis was used to determine frequency-dependent viscoelastic properties. The valve leaflets were dissected from eight porcine hearts. The leaflets were loaded under a sinusoidal tensile displacement, with a mean dynamic peak to trough strain of 11%, applied to all leaflet samples at nine different frequencies, ranging from 0.5 to 10 Hz. The anterior leaflet has higher storage and loss stiffness than the posterior leaflet. The storage stiffness of circumferential tissue is greater than that of radially oriented valve tissue (2.0 ± 1.6 N/mm cf. 1.7 ± 0.9 N/mm; p < 0.05); however, the loss stiffness is greater for radial tissue (0.15 ± 0.07 cf. 0.14 ± 0.09 N/mm; p < 0.05). Likewise, the storage stiffness of the anterior leaflet clear zone is greater than that of the rough zone (2.4 ± 1.6 cf. 2.1 ± 1.2; p < 0.05), but the loss stiffness is greater for the rough zone (0.17 ± 0.09 N/mm cf. 0.14 ± 0.08 N/mm; p < 0.05). In conclusion, the viscoelastic properties of porcine mitral valve leaflets have regional variations, with dynamic stiffness being dependent on circumferential or radial orientation and on location at a clear or rough zones.

Laser Speckle Rheology for evaluating the viscoelastic properties of hydrogel scaffolds.

Natural and synthetic hydrogel scaffolds exhibit distinct viscoelastic properties at various length scales and deformation rates. Laser Speckle Rheology (LSR) offers a novel, non-contact optical approach for evaluating the frequency-dependent viscoelastic properties of hydrogels. In LSR, a coherent laser beam illuminates the specimen and a high-speed camera acquires the time-varying speckle images. Cross-correlation analysis of frames returns the speckle intensity autocorrelation function, g2(t), from which the frequency-dependent viscoelastic modulus, G*(ω), is deduced. Here, we establish the capability of LSR for evaluating the viscoelastic properties of hydrogels over a large range of moduli, using conventional mechanical rheometry and atomic force microscopy (AFM)-based indentation as reference-standards. Results demonstrate a strong correlation between |G*(ω)| values measured by LSR and mechanical rheometry (r = 0.95, p < 10−9), and z-test analysis reports that moduli values measured by the two methods are identical (p > 0.08) over a large range (47 Pa – 36 kPa). In addition, |G*(ω)| values measured by LSR correlate well with indentation moduli, E, reported by AFM (r = 0.92, p < 10−7). Further, spatially-resolved moduli measurements in micro-patterned substrates demonstrate that LSR combines the strengths of conventional rheology and micro-indentation in assessing hydrogel viscoelastic properties at multiple frequencies and small length-scales.

Viscoelastic properties of a spinal posterior dynamic stabilisation device

The purpose of this study was to quantify the frequency dependent viscoelastic properties of two types of spinal posterior dynamic stabilisation devices. In air at 37°C, the viscoelastic properties of six BDyn 1 level, six BDyn 2 level posterior dynamic stabilisation devices (S14 Implants, Pessac, France) and its elastomeric components (polycarbonate urethane and silicone) were measured using Dynamic Mechanical Analysis. The viscoelastic properties were measured over the frequency range 0.01–30Hz. The BDyn devices and its components were viscoelastic throughout the frequency range tested. The mean storage stiffness and mean loss stiffness of the BDyn 1 level device, BDyn 2 level device, silicone component and polycarbonate urethane component all presented a logarithmic relationship with respect to frequency. The storage stiffness of the BDyn 1 level device ranged from 95.56N/mm to 119.29N/mm, while the BDyn 2 level storage stiffness ranged from 39.41N/mm to 42.82N/mm. BDyn 1 level device and BDyn 2 level device loss stiffness ranged from 10.72N/mm to 23.42N/mm and 4.26N/mm to 9.57N/mm, respectively. No resonant frequencies were recorded for the devices or its components. The elastic property of BDyn 1 level device is influenced by the PCU and silicone components, in the physiological frequency range. The viscoelastic properties calculated in this study may be compared to spinal devices and spinal structures.