Viscous Part Research Articles

Evolutional behavior of viscoelastic materials: A formulation based on logarithmic approach

In this paper, a new formulation for large deformation of visco-elastometic materials is derived. The formulation is based on logarithmic strain, and the internal variable is defined as the viscous part of the logarithmic strain. A derivation of thermodynamically consistent formulation for visco-elastomeric materials is provided. The evolution equation which is related to the deviatoric part of the strain for viscoelastic formulation is solved by the implicit trapezoidal integration rule which leads to a recursive relation.

Near-Wall Flow Features In ZPG-TBL At Various Reynolds Numbers Using Dense 3D Lagrangian Particle Tracking

The 3D Lagrangian particle tracking method Shake-The-Box (STB) and, subsequently, the data assimilation method FlowFit3 have been applied to measure the flow field in a narrow wall-parallel volume inside the nearwall region of a zero-pressure-gradient (ZPG) turbulent boundary layer (TBL) flow at various Reynolds numbers. The STB experiments have been conducted in the 1m- wind tunnel facility of DLR in Göttingen at relatively high particle image densities (~0.07 ppp) using µm-sized DEHS particles and high-repetition pulse laser at up to 38.1 kHz. The results show that the chosen methodology is able to volumetrically resolve almost all features of the flow inside the viscous sub-, buffer- and lower logarithmic- layer in space and time at Reynolds numbers up to Re θ = 5,455. The gained data consists of time-series of spatially well resolved 3D velocity, acceleration and pressure fields, as well as a huge amount of long Lagrangian particle trajectories. Selecting the viscous sublayer part of the measurement volume provides time-series of the 2D distribution of both components of the instantaneous wall-shear stresses w,x/z . The resulting data are used for conditional and time-resolved 3D analyses of coherent structures, rare (e.g. back flow) events and two-point space-timecorrelations.

Rank of the Subfamilies Loranthoideae and Viscoideae

The family Loranthaceae has been divided into the subfamilies Loranthoideae and Viscoideae (Engler, 1888-89 ; Danser, 1929, 1933a, b). These two subfamilies show great dissimilarity in their morphological as well as their embryological characters.In the Loranthoideae flowers may be unisexual or bisexual, but a calyculus is invariably present. The ovary may contain a lobed or unlobed mamelon, or the mamelon may be extremely reduced or absent. A collenchymatous pad or tube is invariably present in the ovary. The embryo sac is of the Polygonum type. Many embryo sacs may develop simultaneously in the same ovary and their tips grow up into the style and in some cases reach the stigma. The lower end of the sac sometimes produces a caecum. The endosperm is a composite structure formed by the fusion of all the endosperms developing in the same ovary. The first division of the zygote is always vertical and is followed by transverse divisions resulting in a long biseriate proembryo. The fruit shows 4 distinct layers and the viscid layer is situated outside the vascular bundles of the corolla.In the Viscoideae, flowers are unisexual and the calyculus is absent except in Viscum orientate and V. articulation. The central ovarian papilla has 2 or more archesporial cells, each of which divides to form two dyad cells. Of these the upper dyad cell is the larger and functions, while the lower soon degenerates. Thus the development conforms to Allium type. A peculiar feature is that after the 4-nucleate stage there is a slow but steady curvature of the embryo sac, which causes its lower end to bend out of the papilla and proceed upwards into the carpellary tissue. The egg apparatus differentiates from the quartet in the originally lower pole, which is later situated at a higher level than the upper. Generally only one embryo sac develops which is said to show inverted polarity. The endosperm is derived from the primary endosperm nucleus of a single embryo sac. The first division of the zygote is transverse except in Korthalsella. The embryo lacks a suspensor. The viscous part of the fruit is situated within the vascular bundles of the perigone.Thus, the Loranthoideae and the Viscoideae show important differences in floral structure, mode of development of the embryo sac, endosperm and embryo, and in the location of the viscid zone of the fruit. These differences adequately warrant the raising of the two subfamilies to the rank of fatnilies. As proposed by Miers (see Danser, 1929), the name Loranthaceae may be retained for the Loranthoideae, and the Viscoideae may be designated Viscaceae.

Identification of polymer behavior from nonequibiaxial elongation test with temperature and strain rate conditions close to blow molding process

AbstractAn anisotropic visco‐hyperelastic (VHE) model for polyethylene terephthalate (PET) is used to simulate the stretch blow molding process. The biaxiality needs to be taken into account for an accurate identification of the model parameters related to the induced anisotropy. Thanks to the use of a biaxial elongation apparatus developed at MSME, nonequibiaxial tension tests on PET have been managed on optimized specimen in order to provide data complementary to the equibiaxial (EB) tension test. This last enables the correct identification of the temperature and strain rate influence, because both viscous and elastic parts of the model need to test the material in nonequibiaxial (NEB) conditions. The procedure already used for EB tension test is extended to constant width and an intermediate case, NEB cases. The VHE model developed to simulate the PET behavior in the stretch blow molding conditions is identified from these three different biaxial tests: differences and dispersions are discussed. The origin of this dispersion is found out and solved by a modification of the model. This leads to a reduction of the number of parameters in the proposed VHE model.

Effect of temperature on dynamic compressive behavior of periodontal ligament

Periodontal ligament (PDL) attaches tooth root to the surrounding bone. Its existence between tooth and jaw bone is of utmost importance due to its significant role in absorbing and distributing physiological and para-physiological loading. According to the previous studies, various mechanical tests have been performed to characterize the mechanical properties of the PDL; however, all of them have been done at room temperature. To the best of our knowledge, this is the first study in which the testing was performed at body temperature. The present research was planned to measure the dependency of PDL's viscoelastic behavior on temperature and frequency. Three different temperatures, including body and room temperature, were opted to perform the dynamic compressive tests of the bovine PDL. In addition, a Generalized Maxwell model (GMM) was presented based on empirical outcomes. At 37 °C, amounts of loss factor were found to be greater than those in 25 °C, which demonstrates that the viscous phase of the PDL in higher temperatures plays a critical role. Likewise, by raising the temperature from 25 °C to 37 °C, the model parameters show an enlargement in the viscous part and lessening in the elastic part. It was concluded that the PDL's viscosity in body temperature is much higher than that in room temperature. This model would be functional for a more accurate computational analysis of the PDL at the body temperature (37 °C) in various loading conditions such as orthodontic simulations, mastication, and impact.

Understanding the inelastic response of collagen fibrils: A viscoelastic-plastic constitutive model.

Collagen fibrils, which are the lowest level fibrillar unit of organization of collagen, are thus of primary interest towards understanding the mechanical behavior of load-bearing soft tissues. The deformation of collagen fibrils shows unique mechanical features; namely, their high energy dissipation is even superior compared to most engineering materials. Additionally, there are indications that cyclic loading can further improve the toughness of collagen fibrils. Recent experiments from Liu at al. (2018) focused on the response of type I collagen fibrils to uniaxial cyclic loading, revealing some interesting results regarding their rate-dependent and inelastic response. In this work, we aim to develop a model that allows interpreting the complex nonlinear and inelastic response of collagen fibrils under cyclic loading. We propose a constitutive model that accounts for viscoelastic deformations through a decoupled strain-energy density function (into an elastic and a viscous parts), and for plastic deformations through plastic evolution laws. The stress-stretch response results obtained using this constitutive law showed good agreement with experimental data over complex loading paths. Ultimately we use the model to gain more insights on how cyclic loading and rate effects control the interplay between viscoelastic and plastic deformation in collagen fibrils, and to extrapolate the results from experimental data, analyzing how complex cyclic load influences energy dissipation and deformation mechanisms. STATEMENT OF SIGNIFICANCE: In this work, we develop a viscoelastic-plastic constitutive model for collagen fibrils with the aim of analyzing the effects of inelasticity and energy dissipation in this material, and more specifically the competition between viscoelasticity and plasticity in the context of cyclic loading and overload. Experimental and theoretical approaches so far have not fully clarified the interplay between viscous and plastic deformations during cyclic loading of collagen fibrils. Here, we aim to interpret the complex nonlinear response of collagen fibrils and, ultimately, suggest predictive capabilities that can inform tissue-level response and injury. To validate our model, we compare our results against the stress-stretch data obtained from experiments of cyclic loaded single fibrils performed by Liu etal. (2018).

Evidence and physical mechanism for vortex-induced vibration of a bluff body without an afterbody

Afterbody—the portion of the body downstream of shear layer separation points—was believed to be essential for the vortex-induced vibration (VIV) of a bluff body. A recent study by Zhao et al. [“Flow-induced vibration of D-section cylinders: An afterbody is not essential for vortex-induced vibration,” J. Fluid Mech. 851, 317–343 (2018)] made an important forward to demonstrate “an afterbody is not required for VIV” through water tunnel experiments of a reversed D-section prism. However, our direct numerical visualization showed that the shear layer separation appears at the curved front surface of the reversed D-section prism, leaving a part of an afterbody, which makes their evidence questionable. The present study aims to provide solid numerical and experimental evidence for the statement “an afterbody is not required for VIV” using an elastically mounted triangular prism with one vertex pointing upstream. By conducting two- and three-dimensional direct numerical simulations and water tunnel experiments, we verified that even without an afterbody, the triangular prism can freely vibrate. Furthermore, the physical mechanisms for the excitation and sustenance of the VIV of a bluff body without afterbody are investigated. By decomposing the lift force into the pressure and viscous parts, we discover that the vibration of a bluff body without an afterbody is excited and sustained by the viscous lift component acting on the forebody, in contrast to the VIV of a circular cylinder with an afterbody in which the viscous component always results in energy dissipation and damps the vibration. Some recent experiments showed that the VIV does not occur for the triangular prism. The reasons are also explained: the absence of VIV is due to either high-Re or large mass ratio (structural damping) but not owing to the lack of an afterbody.

A unified determinant-preserving formulation for compressible/incompressible finite viscoelasticity

This paper presents a formulation alongside a numerical solution algorithm to describe the mechanical response of bodies made of a large class of viscoelastic materials undergoing arbitrary quasistatic finite deformations. With the objective of having a unified formulation that applies to a wide range of highly compressible, nearly incompressible, and fully incompressible soft organic materials in a numerically tractable manner, the viscoelasticity is described within a Lagrangian setting by a two-potential mixed formulation. In this formulation, the deformation field, a pressure field that ensues from a Legendre transform, and an internal variable of state Fv that describes the viscous part of the deformation are the independent fields. Consistent with the experimental evidence that viscous deformation is a volume-preserving process, the internal variable Fv is required to satisfy the constraint detFv=1. To solve the resulting initial–boundary-value problem, a numerical solution algorithm is proposed that is based on a finite-element (FE) discretization of space and a finite-difference discretization of time. Specifically, a Variational Multiscale FE method is employed that allows for an arbitrary combination of shape functions for the deformation and pressure fields. To deal with the challenging non-convex constraint detFv=1, a new time integration scheme is introduced that allows to convert any explicit or implicit scheme of choice into a stable scheme that preserves the constraint detFv=1 identically. A series of test cases is presented that showcase the capabilities of the proposed formulation.

Energy growth of vortical, acoustic, and entropic components of the second-mode instability in the hypersonic boundary layer

The acoustic, vortical, and entropic (thermal) components of the second-mode instability, regarded as an asymptotic behavior of the free-stream counterparts, were found to interact with each other in a well-defined way. However, the mechanisms of the energy growth of each component and the resulting second mode instability remain to be clarified. The present paper provides a quantitative energy analysis of the key sources responsible for the modal growth in the momentum potential theory framework. The acoustic, vortical, and entropic components are governed by energy source effects and interexchange effects, characterized by explicit transport terms and relationships between the growth rate and the energy source. The thermal-acoustic source, induced by the interaction between the fluctuation pressure and the fluctuation entropy, is revealed to be the most pronounced cause of the second-mode instability in the hypersonic boundary layer. The thermal-acoustic source is further decomposed into the dissipative (viscous) part and the non-dissipative (inviscid) part. The dissipative thermal-acoustic source is dominant near the wall surface and destabilizes the second mode. The non-dissipative thermal-acoustic source destabilizes the second mode significantly at the critical layer, while the dissipative thermal-acoustic source stabilizes the second mode in this region.

On the time-dependent mechanics of membranes via the nonlinear finite element method

In this work, the problem of finite generalized and viscoelastic deformation of thin membranes with different geometries, made of incompressible hyperelastic materials, is formulated. The multiplicative decomposition of the deformation gradient tensor into elastic and viscous parts, and making use of dissipation inequality, nonlinear evolution equations for the internal variables of the models are obtained. The mechanical behavior of the dampers is assumed to be linearly viscous. Therefore, the Cauchy-like stress in the dampers is similar to that in Newtonian fluids and includes terms for the hydrostatic pressure and viscosity. The implicit and second-order accurate trapezoidal method is employed for the time integration of the evolution equations. Due to the highly nonlinear governing differential equations including the effects of geometric nonlinearity and viscoelasticity, a nonlinear finite element formulation based on isoparametric elements is developed. The accuracy and performance of the developed formulation and time-dependent solutions are verified by studying several numerical examples. The obtained results are compared with theoretical and experimental data available in the literature. The proposed formulation can appropriately predict the experimental results of viscoelastic membranes for both in-plane and out-of-plane deformations.

Describing the dynamics of a nonlinear viscoelastic shelled microbubble with an interface energy model

The present work introduces an interesting revamp to the recently proposed interface energy model [N. Dash and G. Tamadapu, J. Fluid Mech. 932, A26 (2022)] for gas-filled encapsulated bubbles (EBs) suspended in a viscous fluid. Here, the elastic and viscous parts of the viscoelastic shell material are described by the Gent hyperelastic material model and a polymer solute following upper-convected Maxwell (UCM) constitutive relations, respectively. Using the aforementioned framework, the integrodifferential type governing equation has been derived, and the physical features of the radial dynamics of the EB model are studied in detail using numerical simulations. The nonlinear behavior and the underlying implications of the newly introduced interface energy model for EBs are also investigated. It was observed that the interface parameters arising from the interface energy formulation and the Gent material model collectively introduce a stiffening effect into the EB model and the extension limit parameter at its lower values affects the radial dynamics of the bubble. Analysis has been carried out at different relaxation time scales, where the viscoelastic shell material resembles a fluid-like or solid-like behavior. The UCM-type viscous part of the viscoelastic shell material introduces strong nonlinear effects into the bubble model and significantly influences the EB’s behavior. For the present model, a detailed study has been conducted to capture the dynamic behavior of the bubble through the time series curves, phase space analysis, and the nonlinear frequency response of the bubble.

Free vibration characteristics of viscoelastic nano-disks based on modified couple stress theory

This paper investigates the vibrational behavior of a viscoelastic and size-dependent nano-disk based on the modified couple stress theory (MCST). The material characteristics in nano-scale are modeled according to Zener viscoelastic constitutive relation. In addition, displacement components are defined based on classical plate theory. Leaderman integral is also used to determine the viscous parts of the stress tensor. Hamilton’s principle is utilized to derive the governing equations of motion for specifying the strain, kinetic energy, and viscous work. The obtained equations are discretized with the help of the Galerkin method and decoupled through the diagonalization procedure. Laplace transformation is employed to solve the resulting equations in differential–integral form. The damping ratio, the imaginary part and real part of the Eigen frequency of the considered nano-disk are calculated to investigate the effects of influential parameters on the nano-disk vibrational behavior. These parameters include nonlocal parameter boundary conditions, geometric constant, power constant, and element relaxation coefficient. Results obtained on different mode shapes indicate that increasing the dimensionless element relaxation coefficient is followed by a decrease in the imaginary part of the Eigen frequency regarding the energy dissipation as well as a decrease in the real part of the Eigen frequency. Furthermore, increasing the h/l ratio is accompanied by variations in the imaginary part, real part, and damping ratio. According to the results, the effect of damping on vibrational behavior of the nano disk is more distinguished for smaller values of h/l.

Why do ants differ in acclimatory ability? Biophysical mechanisms behind cuticular hydrocarbon acclimation across species.

Maintaining water balance is vital for terrestrial organisms. Insects protect themselves against desiccation via cuticular hydrocarbons (CHCs). CHC layers are complex mixtures of solid and liquid hydrocarbons, with a surprisingly diverse composition across species. This variation may translate into differential phase behaviour, and hence varying waterproofing capacity. This is especially relevant when temperatures change, which requires acclimatory CHC changes to maintain waterproofing. Nevertheless, the physical consequences of CHC variation are still little understood. We studied acclimatory responses and their consequences for CHC composition, phase behaviour and drought survival in three congeneric ant species. Colony sub-groups were kept under cool, warm and fluctuating temperature regimes. Lasius niger and Lasius platythorax, both of which are rich in methyl-branched alkanes, showed largely predictable acclimatory changes of the CHC profile. In both species, warm acclimation increased drought resistance. Warm acclimation increased the proportion of solid compounds in L. niger but not in L. platythorax. In both species, the CHC layer formed a liquid matrix of constantly low viscosity, which contained highly viscous and solid parts. This phase heterogeneity may be adaptive, increasing robustness to temperature fluctuations. In Lasius brunneus, which is rich in unsaturated hydrocarbons, acclimatory CHC changes were less predictable, and warm acclimation did not enhance drought survival. The CHC layer was more homogeneous, but matrix viscosity changed with acclimation. We showed that ant species use different physical mechanisms to enhance waterproofing during acclimation. Hence, the ability to acclimate, and thus climatic niche breadth, may strongly depend on species-specific CHC profile.

Experimental and Numerical Characterization of Violent Sloshing Flows Using a Single Degree of Freedom Approach

In this work, the most fundamental aspects of an aeronautical sloshing problem have been studied using an alternative and simplified model. This model consists of a single degree of freedom version of the original problem which keeps the essence of the fluid structure interaction and also the most relevant physical aspects of the industrial case. Two independent methodologies have been used: first an experimental rig has been designed to measure and visualize different magnitudes of the problem and also a smoothed particle hydrodynamics formulation has been adapted to obtain a local representation of the flow interaction. Two very different fluids in terms of viscosity have been tested, and the differences in terms of the characteristics of the sloshing regimes, free surface fragmentation and relative kinetic energy have been described and compared. Apart from the comparison of the results obtained by both methodologies in terms of tank acceleration, sloshing forces and free surface evolution, a deep study of the sloshing force has been performed. This study focuses on a deeper understanding of the different aspects that constitute the sloshing force, such as its synchronization with the tank movement, the relation to the movement of the liquid’s center of mass and the physical projection of the force on the pressure and viscous parts. Additionally, a reconstruction of the sloshing force as a sum of the pressure signal recorded by a finite number of pressure sensors has been also performed.

The pre-shearing effect on the rheological properties of okra mucilage

We investigated the effect of pre-shearing on the rheological properties of mucilage extracted from okra pods. Okra mucilage was extracted by using a cold water extraction protocol. The rheological properties were surveyed utilizing steady shear, oscillatory, time-dependent ramp measurements. Our findings reveal that the pre-shearing effect induced a drop in the viscosity of okra mucilage at high shear rates ranging between 100s−1 and 1,000s−1. In addition, the pre-shearing effect could partially reduce the elastic modulus of okra mucilage. In contrast, the viscous modulus part was found to be increased at the same time. Consequently, pre-shearing may affect the viscoelastic elements of okra mucilage, due to irreversible changes induced in the macro-structures of the okra mucilage. When the shearing deformation rate reached a limit, the large-sized hydrocolloid random coil group degraded into smaller crops. Therefore, addition of shear force could change the interior elastic energy consumption of the okra mucilage. Our findings may influence the preparation strategies of the okra polysaccharide process.

Rheology of partially solidified hypoeutectic aluminum copper alloys

This study presents oscillatory and rotational viscosity measurement results on Al-Cu alloys with the goal of achieving effective viscosity data of partially solidified alloys from fully liquid to nearly fully solid state. Rotational viscosity measurements indicate fragmentation of dendrites and a concomitant sudden drop in viscosity of the solid–liquid two-phase mixture upon cooling and increase in solid fraction. This measurement artifact is avoided with oscillatory measurements. The viscosity of partially solid Al-Cu over the hypoeutectic range is nearly composition independent when evaluated as a function of solid fraction. The oscillatory measurements yield a complex viscosity with the real part reflecting the elastic behavior and the imaginary part indicating the viscous part of the viscosity behavior. The measurements of the phase angle in this study reveal that the rheological behavior of the solid phase in the liquid–solid two-phase region resembles that of a liquid more than that of a solid phase.HighlightsOscillatory rheology is shown to be better suited to characterize partially solidified metal alloys than rotational rheology.The viscosity of the liquid phase does not change measurably during solidification despite an increase in the solute content.The solid phase in the liquid–solid two-phase region behaves rheologically more like a liquid than a solid.

Constitutive modeling of damage-induced stress softening in electro-magneto-viscoelastic materials

This work presents a continuum physics-based constitutive model for a damaged electro-magneto-viscoelastic (EMV) material class. An extended theory of electro-magneto-viscoelasticity is employed by incorporating the balance laws of micro-forces for continuum damage in physical and material space. Multiplicative decomposition of the deformation gradient tensor into elastic and viscous parts is incorporated to characterize the rheological behavior of EMV materials. The incorporated deformation gradient decomposition enables the intermediate configuration to set up the evolution equation of EMV deformation. The overall stress is disintegrated into equilibrium stress and viscosity-induced overstresses in the proposed modeling framework. In addition, an alternative invariant-based damage function is introduced to incorporate the damage-induced stress softening into the proposed model. The findings of the model agree well with the existing experimental results. At last, the present study successfully enables the damage-induced stress softening in electro-magneto-viscoelasticity with the least material parameters.

Objective momentum barriers in wall turbulence

We use the recent frame-indifferent theory of diffusive momentum transport to identify internal barriers in wall-bounded turbulence. Formed by the invariant manifolds of the Laplacian of the velocity field, the barriers block the viscous part of the instantaneous momentum flux in the flow. We employ the level sets of single-trajectory Lagrangian diagnostic tools, the trajectory rotation average and trajectory stretching exponent, to approximate both vortical and internal wall-parallel momentum transport barrier (MTB) interfaces. These interfaces provide frame-indifferent alternatives to classic velocity-gradient-based vortices and high-shear boundaries between uniform momentum zones (UMZs). Indeed, we find that these elliptic manifold approximations and MTBs outperform standard vortices and UMZ interfaces in blocking diffusive momentum transport, which suggests our momentum barriers are physical features that may be the cause of coherence signatures in statistical and non-objective diagnostics. We also introduce normalized trajectory metrics that provide unprecedented visualizations of objective coherent structures by avoiding strong turbulence biases.

Resonance-like enhancement of forced nonlinear diffusion as a nonequilibrium phase transition

We describe the phenomenon of a resonance-like, giant enhancement of diffusion in a basic model of nonlinear diffusion featured by a nonlinear in velocity friction and the corresponding multiplicative thermal noise. The model is consistent with thermal equilibrium in the absence of driving. Different from previous studies of this phenomenon, where the crucial nonlinearity originates from a periodic external potential while friction is linear, we focus on the case of a constant force driving, whereas the crucial nonlinearity stems from the friction. The basic model of such friction considered interpolates between linear viscous Stokes friction at small velocities and dry Coulomb-like friction at large velocities corresponding to a stress plateau in some nonlinear viscoelastic materials. Recently, a nonequilibrium phase transition to super-diffusion and super-transport was discovered within this basic model. We show that adding a tiny viscous friction part to major nonlinear friction regularizes in part this behavior. Diffusion becomes asymptotically normal. However, the phase transition translates into a giant enhancement of normal diffusion and mobility of particles at the transition point over the intuitively expected large force limit, where the linearization of friction occurs. Such a giant enhancement of diffusion is closely related to the largely enhanced kinetic temperature of the particles at and beyond the critical point. We provide analytical results obtained within an effective mass approximation which nicely agree with stochastic numerics.

A Cell-Centered Semi-Lagrangian Finite Volume Method for Solving Two-Dimensional Coupled Burgers’ Equations

A cell-centered finite volume semi-Lagrangian method is presented for the numerical solution of two-dimensional coupled Burgers’ problems on unstructured triangular meshes. The method combines a modified method of characteristics for the time integration and a cell-centered finite volume for the space discretization. The new method belongs to fractional-step algorithms for which the convection and the viscous parts in the coupled Burgers’ problems are treated separately. The crucial step of interpolation in the convection step is performed using two local procedures accounting for the element where the departure point is located. The resulting semidiscretized system is then solved using a third-order explicit Runge-Kutta scheme. In contrast to the Eulerian-based methods, we apply the new method for each time step along the characteristic curves instead of the time direction. The performance of the current method is verified using different examples for coupled Burgers’ problems with known analytical solutions. We also apply the method for simulation of an example of coupled Burgers’ flows in a complex geometry. In these test problems, the new cell-centered finite volume semi-Lagrangian method demonstrates its ability to accurately resolve the two-dimensional coupled Burgers’ problems.