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Rheological properties of Cholesteryl n-valerate, Cholesteryl decanoate and Cholesteryl myristate which are esters of cholesterol have been studied. Phase transition temperatures and rheological parameters such as viscosity, elastic modulus G${}^{\prime }$, loss modulus G${}^{″}$ as functions of temperature, shear rate and time are investigated. In frequency sweep test, a higher transition crossover region has occurred for Cholesteryl myristate, whereas for Cholesteryl n-valerate a frequency-independent plateau prevailed for both the moduli. The occurrence of blue phase in Cholesteryl decanoate during temperature sweep measurements is an indication for the rheological support. The results for steady state have informed that cholesteric esters are having non-Newtonian flow behavior in their respective cholesteric phases. The power-law model has explained well the shear rate dependence of shear stress. A few practical applications of these esters as lubricant additives are discussed, too.

The primary purpose of this study is to investigate the buoyancy mixed convection flow of non-Newtonian fluid over a flat plate. The addition of a small amount of polymers into a Newtonian solvent raises the viscosity and generates elastic properties in the resulting solution. To study the behavior of these viscoelastic fluids, finite extensible nonlinear elastic constitutive equations along with Peterlin’s closure (FENE-P model) are used. Along with mass, momentum and energy equations, viscoelastic constitutive equations are also used to examine the rheology of the resulting polymer solution. Similarity transformations are introduced to convert the governing equations into nondimensional forms. The nondimensional equations are solved using the fourth-order boundary value solver in MATLAB. The distribution of the velocity and temperature fields is displayed graphically under the impact of various involved parameters like Eckert number (Ec), Richardson number (Ri), Prandtl number (Pr). The addition of polymers increases the friction among the different fluid layers, leading to viscous dissipation in the fluid. The presented model’s validation is done with the Newtonian fluid to verify the results. The Nusselt number is also computed and analyzed to study the heat transfer rate. The effects of viscoelastic parameters like Weissenberg number (W${}_i$), polymer viscosity ratio (${\beta }_p$) and polymer extensibility parameter ($L^2$) on heat transfer rate are also shown graphically. Buoyancy parameter (Richardson number, $0\le \mathrm{\text{Ri}}\le 2$) represents the dominance of natural convection relative to that of forced convection. The temperature of the resulting fluid falls with the increase in the value of Ri. The Nusselt number tends to decrease with increasing Richardson number when viscous dissipation effects are active.

Based on nonlocal strain gradient theory, wave propagation in fluid-conveying viscoelastic single-walled carbon nanotubes (SWCNTs) is studied in this paper. With consideration of thermal effect and surface effect, wave equation is derived for fluid-conveying viscoelastic SWCNTs under longitudinal magnetic field utilizing Euler–Bernoulli beam theory. The closed-form expressions are derived for the frequency and phase velocity of the wave motion. The influences of fluid flow velocity, structural damping coefficient, temperature change, magnetic flux and surface effect are discussed in detail. SWCNTs’ viscoelasticity reduces the wave frequency of the system and the influence gets remarkable with the increase of wave number. The fluid in SWCNTs decreases the frequency of wave propagation to a certain extent. The frequency (phase velocity) gets larger due to the existence of surface effect, especially when the diameters of SWCNTs and the wave number decrease. The wave frequency increases with the increase of the longitudinal magnetic field, while decreases with the increase of the temperature change. The results may be helpful for better understanding the potential applications of SWCNTs in nanotechnology.

Load-relaxation of the human trunk following prolonged flexion has been observed earlier, yet the adverse effects of such viscoelastic behaviors on performing demanding tasks (e.g. lifting) remain poorly understood. Theoretically, trunk stiffness reduces following flexion exposures and requires a compensatory increase in paraspinal muscle activation and spine loads. Here, a multi-segment model with nonlinear viscoelastic properties was developed. After evaluating the model, it was used to predict changes, due to a range of trunk flexion exposures, in several outcome measures (i.e. peak spine load, peak axial stiffness and absorbed energy) at L5/S1 during simulated lifting. All three measures increased during lifting following flexion exposures, including a ~ 9% (~ 284 N) increase in spine loads, and these changes were magnified by increasing flexion duration and angle. These results support prior epidemiological evidence that occupational low back injury risk is elevated when prolonged trunk flexion along with lifting are required. Further, the dependency of spine loads on loading conditions was determined in response to several flexion angles and loading durations. The current modeling approach is considered as an initial step toward implementing Kelvin-solid models in future viscoelastic spine models.

In this paper, the vibration and damping of a hollow sandwich box column containing a viscoelastic layer (VEL) or an electrorheological (ER) or magnetorheological (MR) fluid core with a constraining layer are analyzed and a comparison of performance is made. The hollow sandwich box column comprises two skin plates and a VEL/ER/MR fluid core layer. The finite element method is used to study the vibration and damping behaviors of the column. The natural frequencies and modal loss factors are obtained by solving the complex eigenvalue problem. The modal dampings and natural frequencies of the column are calculated for various electric as well as magnetic fields and their performance is compared with that of the viscoelastic core layer for the clamped-free boundary condition. Effects of core thickness, electric voltage and magnetic field on the vibration behavior of the sandwich box column are investigated.

This paper analyzes the dynamic stability of an isotropic viscoelastic Euler–Bernoulli nano-beam using piezoelectric materials. For this purpose, the size-dependent theory was used in the framework of the modified couple stress theory (MCST) for piezoelectric materials. In order to capture the geometrical nonlinearity, the von Karman strain displacement relation was applied. Hamilton’s principle was also employed to obtain the governing equations. Furthermore, the Galerkin method was used in order to convert the governing partial differential equations (PDEs) to a nonlinear second-order ordinary differential one. Dynamic stability analysis was performed and the effects of such parameters as viscoelastic coefficients, size effect, and piezoelectric coefficient were investigated. The results showed that in this system, saddle points, central points, Hopf bifurcation points, and fork bifurcation points could be created, and the phase portraits connecting these equilibrium points exhibit periodic orbits, heteroclinic orbits, and homoclinic orbits.

Bio-artificial tissues are being developed as replacements for damaged biologic tissues and their mechanical properties are critical for load-bearing applications. Reconstituted dense three-dimensional (3D) fibrillar collagen matrices are promising materials for tissue engineering, at the light of their interaction with fibroblasts.^1,2 The mechanical properties of these fibrillar collagen matrices are now being characterized under unconfined compression loading for various strain rates and collagen concentrations. The data were compared to those obtained in the same conditions with a biological tissue, the rat dermis. The results show a very sensitive behavior to both the displacement rate, typical of biological soft tissues, and the collagen concentration varying between 5 and 40 mg/ml. The link between the mechanical properties and the microscopic structure of the collagen scaffolds show an increasing viscoelastic modulus with respect to the fibril density. It is found that the matrices at 5 mg/ml and the dorsal rat skin (DRS) exhibit similar stress–strain response when submitted to the same external unconfined compression load. Such results highlight the interest of these matrices as potential tissue substitutes.

This study considers a 1D fluid dynamics arterial network model with 14 vessels developed to assimilate ex vivo 0D temporal data for pressure-area dynamics in individual vessel segments from 11 male Merino sheep. A 0D model was used to estimate vessel wall parameters in a two-parameter elastic model and a four-parameter Kelvin viscoelastic model. This was done using nonlinear optimization minimizing the least squares error between model predictions and measured cross-sectional areas. Subsequently, estimated values for elastic stiffness and unstressed area were related to construct a nonlinear relationship. This relation was used in the network model. A 1D single vessel model of the aorta was then developed and used to estimate the inflow profile and parameters for total resistance and compliance for the downstream network and to demonstrate effects of incorporating viscoelasticity in the arterial wall. Lastly, the extent to which vessel wall parameters estimated from ex vivo data can be used to realistically simulate pressure and area in a vessel network was evaluated. Elastic wall parameters in the network simulations were found to yield pressure-area relationships across all vessel locations and sheep that were in ranges comparable to those in the ex vivo data.

The effect of gelation and the modulation of their properties with the variation of aliphatic hydrocarbon solvents, e.g., n-decane and n-dodecane have been presented for a homologous series of amides of L-alanine with fatty acids. The gelation properties of these compounds were studied by a number of physical methods including scanning electron microscopy, X-ray diffraction, differential scanning calorimetry, rheology etc. It was found that the gelation properties vary with the chain length of the host aliphatic hydrocarbons. Scanning electron microscopic images showed modulation of the fiber diameters upon changing the solvent from n-decane to n-dodecane and this has been confirmed by the results obtained from small angle X-ray scattering studies independently. Thermal properties were observed under the differential scanning calorimetric studies which showed an increase in the sol–gel transition temperatures upon increase in the chain length of the hydrocarbon solvent. The mechanical behavior of such assemblies has been observed under rheological experiments which showed a more viscoelastic response for the gels in n-decane compared to n-dodecane.

In this paper, arbitrary boundary conditions including classical and elastic ones are considered in analyzing the vibration and damping characteristics of the sandwich conical shells and annular plates using a simple and efficient modified Fourier solution. The displacement field is expressed as the linear combination of a standard Fourier series and several supplementary terms. The addition of these terms make the Fourier series expansion applicable to any boundary conditions, and the Fourier series expansions improved drastically regarding its accuracy and convergence. Instead of adopting conventional differentiation procedure, a Rayleigh–Ritz technique based on the energy function is conducted which leads to a set of algebraic equations. Then natural frequencies and loss factors can be obtained by solving the algebraic equations. Accuracy and reliability of the current method are checked by comparing the present results with the existing solutions. Influences of some vital parameters on the free vibration and damping performance of sandwich shells and plates are discussed. The detailed effect of restraints from different directions on the frequencies and loss factors is investigated. So, the method can provide a guide to design sandwich structures with desired vibration characteristic and well damping performance by reasonably adjusting the boundary condition. Some new numerical results are presented for future validation of various approximate/numerical methods.

The purpose of this study is to extend a new mixed-type finite element (MFE) model, developed earlier by the present authors for the analysis of viscoelastic Kirchhoff plates [Aköz, A. Y., Kadıoğlu, F. and Tekin, G. [2015] “Quasi-static and dynamic analysis of viscoelastic plates”, Mechanics of Time-Dependent Materials19(4), 483–503], to study the quasi-static and dynamic responses of first-order shear-deformable (FSD) linear viscoelastic Mindlin–Reissner plates. In this context, various viscoelastic material models are discussed for the plate structure to read from them possible patterns of viscoelastic behavior. The developed MFE named VPLT32 is C⁰-continuous four-node linear isoparametric plate element with eight degrees of freedom per node. Hereditary integral form of the constitutive law with constant Poisson’s ratio is used. A new functional in the Laplace–Carson domain suitable for MFE formulation in the same domain is developed by employing Gâteaux differential (GD) method. The unique aspects of this study and the possible contributions of the proposed method to the literature can be summarized as follows: by using this new functional, moment and shear force values that are important for engineers can be obtained directly without any mathematical operation. In addition, geometric and dynamic boundary conditions can be obtained easily and a field variable can be included to the functional systematically. Moreover, shear-locking problem can be eliminated by using the GD method. Dubner and Abate numerical Laplace inversion technique is adopted to transform the obtained solution from the Laplace–Carson domain into the real-time domain. A set of numerical examples are presented not only to demonstrate the validity and accuracy of the proposed MFE formulation but also to examine the effects of load, geometry and material parameters on the viscoelastic response of FSD Mindlin–Reissner plates and to give a better insight into time-dependent behavior of engineering thick plate problems.

This paper discusses the thermal and mechanical buckling of simply supported and clamped orthotropic viscoelastic graphene sheets (nanoplates) embedded in a visco-Pasternak elastic medium. For this purpose, the nonlocal continuum mechanical model is employed with two-variable plate theory. The material of the present nanoplate is assumed to be orthotropic and viscoelastic. The modified nonlinear Kelvin–Voigt viscoelastic model is utilized to formulate the constitutive relations depending on the viscoelastic structural damping coefficient. Moreover, the visco-Pasternak elastic medium is composed of both viscoelastic and shear layers. The viscoelastic layer includes a set of dashpots and elastic springs connected in parallel. In accordance with the two-variable theory, two governing equations are derived via Hamilton’s principle. These equations are analytically solved for various boundary conditions to obtain the explicit solution for critical buckling temperature and buckling load. The present buckling load and buckling temperature both are compared well with the published ones in the literature. In addition, various numerical studies are thoroughly carried out, concentrating on the influences of the plate geometric, nonlocal parameter, structural damping coefficient, elastic foundation parameters, foundation damping parameter and boundary conditions on the critical buckling load and temperature of the nanoplates. The results show that the involvement of the viscidity of the nanoplate and viscoelastic foundation enhances the strength of the nanoplates and therefore increases the resistance of them to external loads.

This study concerns the effect of applied velocity on the energy state and stress state related to the puncture-cutting of soft material. A finite element modeling (FEM) of combined puncture and cutting of neoprene rubber by a pointed blade was established at 17 velocities (from 10mm/min to 1500mm/min). The proposed FEM takes into consideration, the nonlinear material behavior of the elastomeric substrate. First, puncture-cutting tests are conducted and the evolution of puncture-cutting force with increased velocity is investigated. Second, the commonly used puncture-cutting energy criterion, including the fracture toughness of material and the friction energy occurring between the material and the pointed blade, are summarized and analyzed. Finally, an analysis of the stress state in the fracture process zone is proposed. Results show that the puncture-cutting force increases significantly with increasing insertion velocity. A low velocity of the pointed blade is dominated by a uniaxial tension with a constant energy, while a medium velocity causes a dominant biaxial tension with increasing energy, which may be the source of the viscoelastic deformation involved around the crack tip. However, an increase of the velocity increases the shear stress up to a maximum value and, therefore, shows a toughening of material.

This paper presents a model for microbars with variable cross-sections using the Kelvin–Voigt model for viscoelastic material, accounting for size-dependent effects based on strain gradient theory. The size-dependent dynamic equations for the rod, which consider the variable cross-sectional area, are obtained through the extended Hamilton’s principle. These equations are then reduced in order using the Galerkin method and solved in the steady state using the harmonic response form and the algebra of complex numbers. To solve the equations from the transient state to the steady state, a combined method is implemented using the Grünwald–Letnikov derivative technique and the Newmark method. Furthermore, a model and analysis based on the finite element method are presented to validate the results. In the results section, various factors such as size-dependent effects, the order of the fractional derivative, the amount of the viscoelastic coefficient, and the shape of the section area are examined through the time history graph, frequency response, and maximum displacement in terms of force. The results demonstrate that the transient response converges to the stable response after a certain period of time. Moreover, it is observed that decreasing the order of the fractional derivative in the pre-resonance range leads to a decrease in response sensitivity, while in the resonance frequency range, the sensitivity increases with the increase in order.

This study investigated the influence of temperature variations on the mechanical and dynamic behaviors of biobased composites incorporating a passive control layer. These composites, which include an external layer made up of Flax/polylactic acid (PLA) and an internal layer of rubber, were manufactured using 3D printing technique. To better understand their mechanical characteristics, bending tests were carried out on samples of Flax/PLA with and without a rubber coating at temperatures ranging from $20^{\circ }$C to $50^{\circ }$C. To evaluate the bending response of the materials under several temperatures settings, three-point bending tests were also conducted on the materials with different viscoelastic layer thicknesses. Additionally, resonance vibration studies were carried out at various temperatures to explore dynamic characteristics like frequencies and damping factors. The analysis of the data revealed the consequences of incorporating a functional rubber layer under diverse circumstances. The results demonstrated that increasing temperatures negatively impacts the mechanical and dynamic characteristics degradation of the composite with the viscoelastic layer. The main objective of this work is that under various thermal settings, passive control layers in biocomposites can display modified mechanical and dynamic behaviors. This understanding of how these biobased composites perform in different environments offers significant context for their possible applications.

In this paper, a circular three-layer flow model is proposed to study mucus transport in the airways due to air motion caused by mild forced expiration or mild coughing. Mucus is represented by four-parameter viscoelastic fluid, a combination of Maxwell and Voigt elements, whereas air and serous fluid are taken as Newtonian fluids (incompressible). The pressure gradient generated in the fluid layers is assumed to be given by a time-dependent function representing mild forced expiration or mild cough in the airways causing laminar flow. The effect of slip velocity at the mucus–serous interface caused by the presence of surfactant and at the top surface caused by immotile cilia are also taken into account. The roles of rheological properties of mucus on its transport are studied. The effect of serous fluid and its viscosity on mucus transport is also considered.

Shape memory polymers (SMPs) can keep a temporary shape after pre-deformation at a higher temperature and subsequent cooling. When they are reheated, their original shapes can be recovered. Such special characteristics of SMPs make them widely used in aerospace structures, biomedical devices, functional textiles and other devices. Increasing usefulness of SMPs motivates us to further understand their thermomechanical properties and deformation behavior, of which the development of appropriate constitutive models for SMPs is imperative. There is much work in literatures that address constitutive models of the thermo-mechanical coupling in SMPs. However, due to their complex forms, it is difficult to apply these constitutive models in the real world. In this paper, a three-element model with simple form is proposed to investigate the thermo-mechanical small strain (within 10%) behavior of polyurethane under uniaxial tension. Two different cases of heated recovery are considered: (1) unconstrained free strain recovery and (2) stress recovery under full constraint at a strain level fixed during low temperature unloading. To validate the model, simulated and predicted results are compared with Tobushi's experimental results and good agreement can be observed.

In this paper, a model of the heterogeneous anelastic seismic wave problem is proposed in three-dimensional (3D) cylindrical coordinates. We use the velocity-stress formula to describe the realistic attenuation properties of viscoelastic materials, derived from a rheological model of the generalized standard linear solid (GSLS). The equation system is completed by additional equations for the anelastic functions including the strain history of the material. We apply the staggered grid finite-difference (FD) method in 3D cylindrical coordinates to solve the equations. Moreover, to avoid the effect of gradual expansion of the grid size as the radius increases, we use a variable grid method to achieve compensation. In real drilling operations, the mud injected in the borehole is a fluid with viscous properties. The actual formation is also not elastic. In the synthetic data of acoustic logging while drilling (LWD), we find that the drill collar wave is not affected by the viscoelastic parameters of the formation. In contrast, the Stoneley wave is more sensitive to the viscosity of the drilling fluid. The phase and amplitude of the received waveform are affected by the drilling fluid as well as the formation viscoelasticity. Therefore, the development of the cylindrical variable-grid FD method provides a flexible and efficient numerical technique to solve 3D viscoelastic wave propagation problems, including realistic attenuation and complex geometry.

In the adolescent idiopathic scoliosis (AIS) treatment, a brace is prescribed to the patients who have 20 to 45° curves on their spines to prevent the disorder's advancement. For the analysis of Milwaukee brace effects during time, finite element models (FEMs) of the spine (the thoracolumbar region) and the ribcage (contained 10 pairs of the ribs and the sternum) were prepared for two patients. For modeling the spine part, a new element was used in which a disc (as viscoelastic 3D beam) and a vertebra (as rigid link) were modeled as an element and the ribs and the sternum modeled by 3D elastic beams. The gravity, Milwaukee brace constraints and the forces of the brace's different regions were considered as the FEM boundary conditions. By running the patients' FEMs, the spine deformities of each patient were predicted for 24 h. For AIS patients, the brace should not only correct the deformity of the spine by inserting the forces, but also support the spine from the bending moments being caused by the gravity forces in different spine regions. Moreover, in studying scoliosis pathomechanisms, the stresses in different levels of the vertebra are important. Therefore, the bending moments and compressive stresses, caused by the gravity forces, were calculated in each level of the vertebra and the brace forces effects on them were analyzed. According to the patients' FEM responses, for the female patient: lumbar scoliosis was increased, thoracic scoliosis was decreased and kyphosis and lordosis were increased, and for the male patient: lumbar scoliosis was increased, kyphosis was increased and lordosis was decreased. In standing position, the brace forces reduced the bending moment and the compressive stress in vertebral levels of thoracolumbar region for the female patient and increased them for the male patient.