Stretch Rate Research Articles

Enhancement in ageing and functional properties of copper-coated fabrics by subsequent electroplating

This paper proposed a simple way to prepare electrically conductive multifunctional fabrics made by imparting copper nanoparticles and followed with copper electroplating. The surface and ageing properties of copper nanoparticles coated fabric were investigated. Furthermore, the problems regarding ageing properties were solved in a very simple way and various functional properties were studied. The effect of electroplating parameters (concentration of acid) against the stretch rate of fabric was studied. The influence of operating parameters on copper nanoparticles coated fabrics were characterized by Zetasizer, scanning electron micrograph, X-ray diffraction analysis, differential scanning calorimeter. Increase in electrical properties with the rate of weight gain was analyzed. The utility of simple nanoparticles coated and copper electroplated conductive fabrics were analyzed for electromagnetic shielding ability over a frequency range of 30 MHz–1.5 GHz. Furthermore, the heating performances of the fabrics were studied through measuring the change in temperature at the surface of the fabric while applying a voltage difference across the fabric. Moreover, the role coated fabrics against anti-corrosion test was performed to check the durability of electroplating.

Effect of the cavity aft ramp angle on combustion efficiency of lean hydrogen/air flames in a micro cavity-combustor

Hydrogen is an idea fuel for micro energy conversion devices. This study scrutinizes the influence of cavity aft ramp angle (θ = 90° and 135°) on the conversion ratio of lean hydrogen/air combustion in a micro-cavity combustor. It is shown that the combustion efficiencies are 95.8% and 93.5% for θ = 90° and 135° at Vin = 24 m/s, while the counterparts are 56.9% and 84.6% at Vin = 28 m/s. Numerical analysis demonstrates that at Vin = 24 m/s the intensity of elementary reactions as well as the heat release rate at flame tip is larger for θ = 90° owing to a shorter flame height and smaller stretch rate. Therefore, flame tip opening is alleviated and higher hydrogen conversion efficiency is achieved in the combustor with θ = 90° at low inlet velocities. At Vin = 28 m/s, the stretch effect becomes the key factor affecting flame stability. The maximum strain rate on the cavity ramp wall is 1.37×106s−1 for θ = 90°, which is much larger than the counterpart for θ = 135° (1.08×106s−1). The downstream flame is completely extinguished for θ = 90° at high inlet velocities. As a result, the combustion efficiency shows a sharp decrease for the combustor with θ = 90°.

On the effect of labour durations using an anisotropic visco-hyperelastic-damage approach to simulate vaginal deliveries

Injuries sustained by the pelvic floor muscles during childbirth are one of the major risk factors for the development of pelvic floor dysfunctions. The ability to predict the loss of the tissue integrity and the most affected regions prior to the childbirth would represent a compelling difference in choosing the appropriate management of labour.Previous biomechanical studies, using the finite element method, were able to simulate a vaginal delivery and analyse the mechanical effects on the pelvic floor muscles during the passage of the foetus. Complementing these studies, the aim of this work is to improve the characterization of the pelvic floor muscles, by using an anisotropic visco-hyperelastic constitutive model, including a continuum mechanics damage model. Viscoelasticity is a key feature to obtain more realistic results since biological tissues present relaxation effects that allow larger deformations without damage. This work analyses the reaction forces and the loss of tissue integrity sustained by the pelvic floor and evaluates the effects of different durations of labour. A delaying pushing technique of rest and descend is also studied in this work.The results obtained showed that the reaction forces vary with the duration of labour, with higher force levels associated with higher stretch rates. The pubovisceral muscle is the most affected of the levator ani, presenting an affected region of approximately 30%. The relaxation properties of the tissue contribute to diminish the damage levels, supporting the theory of delayed pushing applied in the second stage of labour.

Modeling the formation and growth of instabilities during spherical flame propagation

Accurate models to predict large-scale flame propagation are crucial to assessing the consequences of accidental explosions. A freely expanding spherical flame can experience significant acceleration due to the growth of the Darrieus–Landau instability, increasing the severity of the explosion hazard, and must be accounted for when modeling large-scale flames. Recent large-scale experiments have demonstrated an oscillatory rate of flame acceleration, consistent with self-similar flame propagation and the formation and growth of cells with discrete length scales. In this work, an analytical model describing the growth of multiple generations of cells on a flame surface is developed. Each generation is treated independently with a criteria for cell splitting based on a critical stretch rate. Superposition of the length scales is used to determine the global flame surface wrinkling and propagation velocity of the flame. The model is compared with experimental results and the effect of upstream flow disturbances on the development of the instability is also discussed. It is found that the model reproduces a number of features observed in the experiments, including the overall rate of flame acceleration and the frequency of oscillation. The model also captures the correct trends of flame behavior for the effect of elevated initial turbulence and the transition from positive to negative Markstein length. These results support the self-similar argument of spherical-flame acceleration and can be used in future studies to develop new models describing the behavior of large-scale flames.

Dynamics and burning limits of near-limit hot, warm, and cool diffusion flames of dimethyl ether at elevated pressures

The near-limit diffusion flame regimes and extinction limits of dimethyl ether at elevated pressures and temperatures are examined numerically in the counterflow geometry with and without radiation at different oxygen concentrations. It is found that there are three different flame regimes—hot flame, warm flame, and cool flame—which exist, respectively, at high, intermediate, and low temperatures. Furthermore, they are governed by three distinct chain-branching reaction pathways. The results demonstrate that the warm flame has a double reaction zone structure and plays a critical role in the transition between cool and hot flames. It is also shown that the cool flame can be formed in several different ways: by either radiative extinction or stretch extinction of a hot flame or by stretch extinction of a warm flame. A warm flame can also be formed by radiative extinction of a hot flame or ignition of a cool flame. A general €-shaped flammability diagram showing the burning limits of all three flame regimes at different oxygen mole fractions is obtained. The results show that thermal radiation, reactant concentration, temperature, and pressure all have significant impacts on the flammable regions of the three flame regimes. Increases in oxidizer temperature, oxygen concentration, and pressure shift the cool flame regime to higher stretch rates and cause the warm flame to have two extinction limits. At elevated temperatures, it is found that there is a direct transition between the hot flame and warm flame at low stretch rates. The results also show that, unlike the hot flame, the cool flame structure cannot be scaled by using pressure-weighted stretch rates due to the its significant reactant leakage and strong dependence of reactivity on pressure. The present results advance the understanding of near-limit flame dynamics and provide guidance for experimental observation of different flame regimes.

Effect of Lewis number on premixed laminar lean-limit flames stabilized on a bluff body

In this paper, we present a study on the effect of Lewis number, Le, on the stabilization and blow-off of laminar lean limit premixed flames stabilized on a cylindrical bluff body. Numerical simulations and experiments are conducted for propane, methane and two blends of hydrogen with methane as fuel gases, containing 20% and 40% of hydrogen by volume, respectively. It is found that the Le > 1 flame blows-off via convection from the base of the flame (without formation of a neck) when the conditions for flame anchoring are not fulfilled. Le ≤ 1 flames exhibit a necking phenomenon just before lean blow-off. This necking of the flame front is a result of the local reduction in mass burning rates causing flame merging and quenching of the thin flame tube formed. The structure of these flames at the necking location is found to be similar to tubular flames. It is found that extinction stretch rates for tubular flames closely match values at the neck location of bluff-body flames of corresponding mixtures, suggesting that excessive flame stretch is directly responsible for blow-off of the studied Le ≤ 1 flames. After quenching of the neck, the upstream part forms a steady and stable residual flame in the wake of the bluff body while the downstream part is convected away.

PMMA rod stagnation region flame blowoff limits at various radii, oxygen concentrations, and mixed stretch rates

Normal gravity flame blowoff limits in an axisymmetric PMMA rod geometry in upward axial stagnation flow are compared with microgravity Burning and Suppression of Solids-II (BASS-II) results recently obtained aboard the International Space Station. This testing utilized the same BASS-II concurrent rod geometry, but was done in normal gravity mixed convective flow. Cast polymethylmethacrylate (PMMA) rods of diameters ranging from 0.635 cm to 3.81 cm were burned at oxygen concentrations ranging from 15% to 18% by volume. The forced flow velocity where blowoff occurs was determined for each rod size and oxygen concentration. These blowoff limits compare favorably with the BASS-II results when the buoyant stretch rate is included and the flow is corrected by considering the flow blockage factor of the fuel. From these results, the normal gravity blowoff boundary for this axisymmetric rod geometry is determined to be linear, with oxygen concentration and flow velocity as coordinates. We describe a new normal gravity upward blowoff test method which extrapolates this linear blowoff boundary to the zero mixed stretch rate limit to resolve microgravity flammability limits—something current methods cannot do. This new test method can improve spacecraft fire safety for future exploration missions by providing a tractable way to obtain accurate but conservative estimates of material flammability in low gravity based on tests performed on Earth.

The stability of laminar explosion flames

The paper presents the results of a fundamental experimental and theoretical study of Darrieus–Landau, thermo-diffusive, instabilities in atmospheric explosions, and, on a smaller scale, in laboratory explosions in closed vessels. Pressure dependencies were sought to exploit the leading role of the Peclet number in the phenomena, so that similar Peclet numbers were achieved in both instances. However, in large atmospheric explosions large Peclet numbers were achieved by the size of the fireball, whereas in the closed vessel explosion it was achieved at a higher pressure by a much smaller flame, but because of the higher pressure, one endowed with a small laminar flame thickness. This study covers a much wider range of fuels and of pressures and the dependencies of the phenomena on both of these were carefully studied, although, for the atmospheric explosions, the data only covered propane and methane. The roles of both Markstein and Peclet numbers become clear and give rise to a more fundamental correlating parameter, a critical Karlovitz number, Kcl, for flame stability. This is based on the flame stretch rate, normalised by its multiplication by the chemical reaction time in a laminar flame. The experimentally measured dependencies of this key parameter on pressure and Markstein number are reported for the first time for so many different fuels. The critical Karlovitz number for flame stability decreases with increase in the strain rate Markstein number. As a result, it is possible to predict the extent of the unstable regime for laminar flames as a function of Masr and pressure. Such data can be used to estimate the severity of large scale atmospheric explosions. As Masr becomes highly negative, the regime of stability is markedly reduced.

A 3-D Energy-Harvesting-Aware Routing Scheme for Space Nanosatellite Networks

Space wireless networks composed of a large number of low-cost miniaturized nanosatellites enable many promising astronautical applications such as the distributed and cooperative sensing. Data collection via multihop relay is critical for nanosatellite networks. However, due to the small size of onboard solar panels and limited attitude control, energy harvesting (EH) capability of nanosatellites is quite low and unstable. In addition, the space networks have 3-D topologies due to various orbit altitudes. In this paper, we propose a novel 3-D EH-aware routing (3DEHR) scheme for nanosatellite networks. The main idea is to establish the 3-D artificial potential field (APF) based on the EH capabilities and geographic positions of neighboring nanosatellites. A nanosatellite node determines the next hop among its neighbors based on the composite force direction obtained from the APF for data forwarding. We also design the methods in 3DEHR to solve the routing void problem and to circumvent sensitive nodes such as malicious satellites. Simulation results show that 3DEHR outperforms the existing routing schemes in hop stretch and packet delivery rate. Since the routing paths are planned based on the EH capabilities of nanosatellites, the harvested energy in the network is fully utilized and the network lifetime is extended. 3DEHR is suitable for nanosatellite networks in space and other 3-D ad hoc networks with dynamic EH capabilities and topologies.

On the validity of Damköhler's first hypothesis in turbulent Bunsen burner flames: A computational analysis

The validity of Damköhler's first hypothesis, which relates the turbulent flame speed to turbulent flame surface area under the condition where the integral length scale of turbulence is greater than the flame thickness, has been assessed using three-dimensional Direct Numerical Simulations (DNS) of turbulent premixed Bunsen burner flames over a range of values of Reynolds number, pressure and turbulence intensity. It has been found for the Bunsen configuration that the proportionality between volume-integrated burning rate and the overall flame surface area is not strictly maintained according to Damköhler's first hypothesis. The discrepancy is found to originate physically from the local stretch rate dependence of displacement speed, and this helps to explain differences observed previously between flames with and without mean curvature. Approximating the local density-weighted flame propagation speed with the unstrained laminar burning velocity is shown to be inaccurate, and can have a significant influence on the prediction of the overall burning rate for flames with non-zero mean curvature. Using a two-dimensional projection of the actual scalar gradient for flame area evaluation is shown to exacerbate the loss of proportionality between volume-integrated burning rate and the overall flame surface area. The current analysis identifies the conditions under which Damköhler's hypothesis remains valid and the necessary correction for non-zero mean flame curvature. Further, it has been demonstrated that surface-weighted stretch effects on displacement speed need to be accounted for in order to ensure the validity of Damköhler's hypothesis under all circumstances. Finally, it has been found that the volume-integrated density-weighted scalar dissipation rate remains proportional to the overall burning rate for all flames considered here irrespective of the value of Reynolds number, pressure and turbulence intensity. However, this proportionality is lost when the scalar dissipation rate is evaluated using the two-dimensional projection of the actual scalar gradient.

Morphology of wrinkles along the surface of turbulent Bunsen flames – Their amplification and advection due to the Darrieus–Landau instability

The morphological development of wrinkles along the surface of a Bunsen flame in a weakly-turbulent flow is investigated, with turbulence added solely to disturb the flame front. The resulting flame-flow interactions are examined using a hybrid Navier–Stokes/front-tracking methodology within the context of the hydrodynamic theory. Topological markers based on the skewness of curvature are introduced to distinguish between sub- and super-critical conditions, or the absence/presence of the Darrieus–Landau instability, respectively. We show that for sub-critical conditions disturbances created along the flame surface are dampened when convected downstream along the flame front, and the flame surface is only weakly perturbed. For super-critical conditions, on the other hand, disturbances of the flame front are amplified when advected downstream leading to a highly corrugated surface and a flame brush of increasing thickness. A measure of these dramatic changes is included in the mean local stretch rate which, when properly modulated by a Markstein length, directly affects the turbulent flame speed.

Predicting the consumption speed of a premixed flame subjected to unsteady stretch rates

The stretched laminar flame model provides a convenient approach to embed realistic chemical kinetics when simulating turbulent premixed flames. When positive-only periodic strain rates are applied to a laminar flame there is a notable phase lag and diminished amplitude in heat release rate. Similar results have being observed with respect to the other component of stretch rate, namely the unsteady motion of a curved flame when the stretch rates are periodic about zero. Both cases showed that the heat release rate or consumption speed of these laminar-premixed flames vary significantly from the quasi-steady flamelet model. Deviation from quasi-steady behavior increases as the unsteady flow time scale approaches the chemical time scale that is set by the stoichiometry. A challenge remains in how to use such results predictively for local and instantaneous consumption speed for small segments of turbulent flames where their unsteady stretch history is not periodic.This paper uses a frequency response analysis as a characterization tool to simplify the complex non-linear behavior of premixed methane air flames for equivalence ratios from 1.0 down to 0.7, and frequencies from quasi-steady up to 2000 Hz using flame transfer functions. Various linear and nonlinear models were used to identify appropriate flame transfer functions for low and higher frequency regimes, as well as extend the predictive capabilities of these models. Linear models were only able to accurately predict the flame behavior below a threshold of when the fluid and chemistry time scales are the same order of magnitude. Other proposed transfer functions were tested against arbitrary multi-frequency stretch inputs and were shown to be effective over the full range of frequencies.

Measurement and simulation of partially-premixed cellular tubular flames

Experimental and numerical simulation results are reported of partially-premixed cellular tubular flames. Parametric measurements across stretch rate and equivalence ratio are taken by chemiluminescent imaging and are presented for the first time. Select hybrid cases with both cellular and non-cellular flame structures are examined with laser-induced spontaneous Raman scattering. Results are spatially resolved in two dimensions and radial interpolations of reaction and extinction zones are compared to numerical simulations using multicomponent transport and detailed chemical kinetics. Experimental cell structures and extinction zones are well predicted by numerical simulation, with discrepancies of temperature and H2O and temperature primarily observed in locations with moderate and high mole fractions of CO2. A novel cellular structure, denoted as a “split-cell” flame, is reported for the first time with both chemiluminescent imaging and Raman scattering. Results indicate that partially-premixed flames are valuable as experimental and numerical benchmarks to advance fundamental combustion research.

Extinguishment of counterflow diffusion flame stabilized in turbulent airflow by polydisperse water mist

In the present study, the effect of turbulence on extinguishment of counterflow diffusion flame by polydisperse water mist was investigated experimentally. A counterflow methane-air diffusion flame was stabilized in the forward stagnation region of a porous cylinder. Water mist was supplied by a pressure-type atomizer. Uniform turbulence was produced in the airflow by a grid. Mist characteristics were measured by a phase Doppler particle analyzer and turbulence properties by a hot wire anemometer. For laminar flames, the critical stretch rate at extinguishment decreases with the mass fraction of water mist and the extinguishment is not affected by the Sauter mean diameter D32 even when D32 is as large as 70 µm. Turbulence reduces significantly the critical bulk (mean flow) stretch rate at extinguishment. Effect of turbulence on extinguishment is relevant to the turbulence stretch rate, which is the inverse of the Kolmogorov time scale. Sum of the bulk stretch rate and the turbulence stretch rate is the total stretch rate that actually exerts on turbulent flame. If the relative turbulence intensity v’/V is as low as 0.06 and D32 is smaller than 30 µm, extinguishment of turbulent diffusion flame is expressed uniquely by the total stretch rate, which coincides with that of laminar flame. On the other hand, for large water mist, D32 > 30 µm or high turbulence intensity, v’/V = 0.10, non-uniformity of mist dispersion appears, of which scale is of the order of integral scale of turbulence. The locally extinguished flame by a spot of dense water mist is reignited by surrounding flame and the suppression effectiveness of water mist is deteriorated when the turbulence intensity is high or the mist diameter is large.

High-speed video analysis of flame oscillations along a PMMA rod after stagnation region blowoff

During blowoff extinction of clear cast PMMA rods in concurrent axial flow for microgravity BASS-II experiments, a dynamic flame oscillation was observed after the flame was blown off of the stagnation point but briefly stabilized on the periphery of the rod. Complementary normal gravity experiments were conducted and flame oscillations were tracked using a high-speed color camera at 240 frames per second. The side-stabilized flame oscillated up and down the rod with increasing amplitude until the entire flame extinguished. In none of the BASS-II or normal gravity tests could the side-stabilized flames persist (Hopf subcritical bifurcation). Since the oscillations occurred even in microgravity, the mechanism does not depend on gravity. For the larger fuel radius tests, the flame developed asymmetric oscillation (pitchfork bifurcation). The oscillation time and the number of oscillations scale with the inverse square of the rod radius (∼ Fourier no.) for the preheated microgravity rods. The average flame oscillation frequency is found to be linearly dependent on the mixed convective stretch rate (inverse of the flow time). The flame intensity varied in concert with its direction, either increasing or decreasing as the flame moved upstream or downstream, respectively. The oscillation frequency decreased as the amplitude increased and the flame slipped slightly farther down the rod with each oscillation. The flame speed increased with each subsequent oscillation, both flashing forward upstream and retreating downstream. The oscillations were found to closely follow a power law log-periodic dependence similar to those that describe systems approaching a critical point, such as diffusion-limited aggregation clusters, earthquakes, ruptures, and even stock market crashes. The net flame speeds varied linearly with ambient oxygen concentration, and linearly with the mixed convective stretch rate. Based on these observations, a mechanistic theory of the oscillations is described, and is consistent with the thermodiffusive instability.

Stationary combustion regimes and extinction limits of one-dimensional stretched premixed flames in a gap between two heat conducting plates

Abstract Stationary combustion regimes, their linear stability and extinction limits of stretched premixed flames in a narrow gap between two heat conducting plates are studied by means of numerical simulations in the framework of one-dimensional thermal-diffusion model with overall one-step reaction. Various stationary combustion modes including normal flame (NF), near-stagnation plane flame (NSF), weak flame (WF) and distant flame (DF) are detected and found to be analogous to the same-named regimes of conventional counterflow flames. For the flames stabilized in the vicinity of stagnation plane at moderate and large stretch rates (which are NF, NSF and WF) the effect of channel walls is basically reduced to additional heat loss. For distant flame characterized by large flame separation distance and small stretch rates intensive interphase heat transfer and heat recirculation are typical. It is shown that in mixture content / stretch rate plane the extinction limit curve has e-shape, while for conventional counterflow flames it is known to be C-shaped. This result is quite in line with recent experimental findings and is explained by extension of extinction limits at small stretch rates at the expense of heat recirculation. Analysis of the numerical results makes possible to reveal prime mechanisms of flame quenching on different branches of e-shaped extinction limit curve. Namely, two upper limits are caused by stretch and heat loss. These limits are direct analogs of the upper and lower limits on conventional C-shaped curve. Two other limits are related with weakening of heat recirculation and heat dissipation to the burner. Thus, the present study provides a satisfactory explanation for the recent experimental observations of stretched flames in narrow channel.

Investigation on spherically expanding flame temperature of n-butane/air mixtures with tunable diode laser absorption spectroscopy

Abstract A joint schlieren imaging, pressure recording and tunable diode laser absorption spectroscopy (TDLAS) thermometry technique was developed to simultaneously determine the flame radius, pressure and line-of-sight averaged temperature of spherically expanding flames of n-butane/air mixtures at initial temperature of 298 K, initial pressure of 1 atm and equivalence ratios of 0.9–1.5. To probe the flame temperature, a mid-infrared interband cascade laser at 4.2 µm was used to measure the time-resolved direct absorption spectra of CO2 which are strongly related to flame temperature, CO2 mole fraction, flame radius and pressure. Quantitative line-of-sight averaged temperatures of burnt gas were obtained by fitting the normalized absorbance spectra. Three typical stages, including the spark affected initial stage, quasi-steady stage and the pressure induced growing stage are determined from the evolution of measured temperature as a function of time and flame radius. The relation between flame temperature, stretch rate and burning velocity of burnt gas are analyzed. Stretch rate is found to have minor effect on the measured temperature in the quasi-steady stage. The relative variation of temperature is much smaller than that of velocity. The flame with lower normalized temperature tends to propagate slower.

Enhancement of hydrogen combustion efficiency by helium dilution in a micro-combustor with wall cavities

For very lean H2/air flames in a micro-combustor with cavity flame holders, the combustion efficiency decreases rapidly at sufficiently high inlet velocity due to the occurrence of "flame tip opening". To suppress this undesirable phenomenon, we used helium (He) to replace nitrogen (N2) as dilution in the oxidant. Numerical simulation was conducted under an equivalence ratio of 0.4 for both N2 and He dilutions. The results show that the combustion efficiency is greatly improved, remaining above 98% at 32 m/s in the case of He dilution. The analysis reveals that several reasons are responsible for these results. Firstly, the heat capacity of He is smaller than N2, which leads to a higher temperature level of the gaseous mixture in reaction zone. Second, the effective Lewis number of the H2/O2/He mixture is larger than that of the H2/O2/N2 mixture. Thirdly, the magnitude of stretch rate at the flame tip for He dilution is less than the N2 counterpart. The combined effects of three aspects result in intensified reaction rate and heat release rate at the flame tip. As a consequence, the flame tip opening phenomenon can be significantly suppressed and combustion efficiency be notably increased.

Physical Biology of Axonal Damage.

Excessive physical impacts to the head have direct implications on the structural integrity at the axonal level. Increasing evidence suggests that tau, an intrinsically disordered protein that stabilizes axonal microtubules, plays a critical role in the physical biology of axonal injury. However, the precise mechanisms of axonal damage remain incompletely understood. Here we propose a biophysical model of the axon to correlate the dynamic behavior of individual tau proteins under external physical forces to the evolution of axonal damage. To propagate damage across the scales, we adopt a consistent three-step strategy: First, we characterize the axonal response to external stretches and stretch rates for varying tau crosslink bond strengths using a discrete axonal damage model. Then, for each combination of stretch rates and bond strengths, we average the axonal force-stretch response of n = 10 discrete simulations, from which we derive and calibrate a homogenized constitutive model. Finally, we embed this homogenized model into a continuum axonal damage model of [1-d]-type in which d is a scalar damage parameter that is driven by the axonal stretch and stretch rate. We demonstrate that axonal damage emerges naturally from the interplay of physical forces and biological crosslinking. Our study reveals an emergent feature of the crosslink dynamics: With increasing loading rate, the axonal failure stretch increases, but axonal damage evolves earlier in time. For a wide range of physical stretch rates, from 0.1 to 10 /s, and biological bond strengths, from 1 to 100 pN, our model predicts a relatively narrow window of critical damage stretch thresholds, from 1.01 to 1.30, which agrees well with experimental observations. Our biophysical damage model can help explain the development and progression of axonal damage across the scales and will provide useful guidelines to identify critical damage level thresholds in response to excessive physical forces.

A transverse isotropic constitutive model for the aortic valve tissue incorporating rate-dependency and fibre dispersion: Application to biaxial deformation.

This paper presents a continuum-based transverse isotropic model incorporating rate-dependency and fibre dispersion, applied to the planar biaxial deformation of aortic valve (AV) specimens under various stretch rates. The rate dependency of the mechanical behaviour of the AV tissue under biaxial deformation, the (pseudo-) invariants of the right Cauchy-Green deformation-rate tensor Ċ associated with fibre dispersion, and a new fibre orientation density function motivated by fibre kinematics are presented for the first time. It is shown that the model captures the experimentally observed deformation of the specimens, and characterises a shear-thinning behaviour associated with the dissipative (viscous) kinematics of the matrix and the fibres. The application of the model for predicting the deformation behaviour of the AV under physiological rates is illustrated and an example of the predicted σ-λ curves is presented. While the development of the model was principally motivated by the AV biomechanics requisites, the comprehensive theoretical approach employed in the study renders the model suitable for application to other fibrous soft tissues that possess similar rate-dependent and structural attributes.