Viscoelastic Constitutive Relation Research Articles

Three-sphere swimmer in a nonlinear viscoelastic medium

A simple model for a swimmer consisting of three colinearly linked spheres attached by rods and oscillating out of phase to break reciprocal motion is analyzed. With a prescribed forcing of the rods acting on the three spheres, the swimming dynamics are determined analytically in both a Newtonian Stokes fluid and a zero Reynolds number, nonlinear, Oldroyd-B viscoelastic fluid with Deborah numbers of order one (or less), highlighting the effects of viscoelasticity on the net displacement of swimmer. For instance, the model predicts that the three-sphere swimmer with a sinusoidal, but nonreciprocal, forcing cycle within an Oldroyd-B representation of a polymeric Boger fluid moves a greater distance with enhanced efficiency in comparison with its motility in a Newtonian fluid of the same viscosity. Furthermore, the nonlinear contributions to the viscoelastic constitutive relation, while dynamically nontrivial, are predicted a posteriori to have no effect on swimmer motility at leading order, given a prescribed forcing between spheres.

A coupled SAFE-2.5D BEM approach for the dispersion analysis of damped leaky guided waves in embedded waveguides of arbitrary cross-section

The paper presents a Semi-Analytical Finite Element (SAFE) formulation coupled with a 2.5D Boundary Element Method (BEM) for the computation of the dispersion properties of viscoelastic waveguides with arbitrary cross-section and embedded in unbounded isotropic viscoelastic media. Attenuation of guided modes is described through the imaginary component of the axial wavenumber, which accounts for material damping, introduced via linear viscoelastic constitutive relations, as well as energy loss due to radiation of bulk waves in the surrounding media. Energy radiation is accounted in the SAFE model by introducing an equivalent dynamic stiffness matrix for the surrounding medium, which is derived from a regularized 2.5D boundary element formulation.The resulting dispersive wave equation is configured as a nonlinear eigenvalue problem in the complex axial wavenumber. The eigenvalue problem is reduced to a linear one inside a chosen contour in the complex plane of the axial wavenumber by using a contour integral method. Poles of leaky and evanescent modes are obtained by choosing appropriately the phase of the wavenumbers normal to the interface in compliance with the nature of the waves in the surrounding medium. Finally, the obtained eigensolutions are post-processed to compute the energy velocity and the radiated wavefield in the surrounding domain.The reliability of the method is first validated on existing results for waveguides of circular cross sections embedded in elastic and viscoelastic media. Next, the potential of the proposed numerical framework is shown by computing the dispersion properties for a square steel bar embedded in grout and for an H-shaped steel pile embedded in soil.

Stability of axially accelerating viscoelastic Timoshenko beams: Recognition of longitudinally varying tensions

Stability of axially accelerating viscoelastic Timoshenko beams is treated. The effects of longitudinally varying tensions due to the axial acceleration are focused in this paper, while the tension was approximatively assumed to be longitudinally uniform in previous works. The dependence of the tension on the finite axial support rigidity is also modeled. The governing equations and the accurate boundary conditions for coupled planar motion of the Timoshenko beam are established based on the generalized Hamilton principle and the Kelvin viscoelastic constitutive relation. The boundary conditions were approximate in previous studies. The method of multiple scales is employed to investigate stability in parametric vibration. The stability boundaries are derived from the solvability conditions and the Routh–Hurwitz criterion for principal and summation parametric resonances. Some numerical examples are presented to demonstrate the effects of the tension variation, the viscosity, the mean axial speed, the shear deformation coefficient, the rotary inertia coefficient, the stiffness parameter, and the pulley support parameter on the stability boundaries.

Coupled global dynamics of an axially moving viscoelastic beam

The nonlinear global forced dynamics of an axially moving viscoelastic beam, while both longitudinal and transverse displacements are taken into account, is examined employing a numerical technique. The equations of motion are derived using Newton′s second law of motion, resulting in two partial differential equations for the longitudinal and transverse motions. A two-parameter rheological Kelvin–Voigt energy dissipation mechanism is employed for the viscoelastic structural model, in which the material, not partial, time derivative is used in the viscoelastic constitutive relations; this gives additional terms due to the simultaneous presence of the material damping and the axial speed. The equations of motion for both longitudinal and transverse motions are then discretized via Galerkin’s method, in which the eigenfunctions for the transverse motion of a hinged-hinged linear stationary beam are chosen as the basis functions. The subsequent set of nonlinear ordinary equations is solved numerically by means of the direct time integration via modified Rosenbrock method, resulting in the bifurcation diagrams of Poincaré maps. The results are also presented in the form of time histories, phase-plane portraits, and fast Fourier transform (FFTs) for specific sets of parameters.

Stress-Strain Analysis of Composite Propellant under Cyclic Temperature Loads

Based on integral nonlinear viscoelastic constitutive relationship, stress-strain field was analyzed of composite propellant under cyclic temperature loads to ensure the stress-strain distribution and damageable locality. The simulation conditions were designed in the temperature range from-10 to 60 at three different rate-temperature. The results indicate that the stress and strain have the same trend of changing. Adhesive interphase is prone to failure because of the alternating stress.

Ballistic Impact of Twaron CT709® Plain Weave Fabrics

The ballistic impact of Twaron CT709® plain weave fabrics is studied using a three-dimensional fabric model. The model is developed by treating each individual yarn as a continuum, and the time-dependent yarn behavior is phenomenologically described using a three-dimensional linear viscoelastic constitutive relation. A user subroutine VUMAT for ABAQUS/Explicit is compiled to incorporate the constitutive behavior. By using the newly developed model, a parametric study is carried out to analyze the effects of various parameters on the impact behavior of the fabrics, which include impact velocity, inter-yarn friction, and the number of fabric layers. The simulation results obtained include bullet residual velocity, fabric deformation and damage pattern, kinetic energy of the system, fabric strain energy, and frictional dissipation energy. The residual velocities predicted by the current model correlate well with existing experimental data, and the parametric study leads to the determination of the optimal number of fabric layers and the optimized level of inter-yarn friction that are needed to achieve the maximum energy absorption in the fabrics at specified impact velocities.

Analysis of Mechanical Behavior of Red Cell Membrane in Sickle Cell Disease

Sickle cell disease (SCD) is a disease of abnormal rheology. The rheological properties of normal erythrocytes appear to be largely determined by those of the red cell membrane. In SCD, the intracellular polymerization of sickle he- moglobin upon deoxygnation leads to marked increase in intracellular viscosity and elastic stiffness and also having indirect effects on cell membrane .To examine mathematically, the abnormal cell rheology behavior due to polymerization process and that due membrane abnormalities , we mechanically modeled the whole cell deformability as viscoelastic solid and proposed a Voigt-model of nonlinear viscoelastic solid constitutive relation as mixture''of an elastic and viscous dissipative parts, with parameters of elastic and viscous moduli. The elastic part used to express stress-strain relations via strain energy function of the material and the viscous part derivation depends on strain - rate of deformation. The combination of both constitutive expressions is used to predict the viscoelastic properties of normal and sickle erythrocyte. Furthermore, sickle hemoglobin polymerization also leads to alter the osmotic behavior of the cell and to investigate such osmotic effect; we employ the van't Hoff law of osmotic pressure versus volume relation. The analysis of both formulations presented well the abnormal rheological /mechanical characterization of sickle erythrocyte membrane as we understood and concluded from our results.

Stability of viscoelastic rectangular plate with a piezoelectric layer subjected to follower force

The effects of a piezoelectric layer on the stability of viscoelastic plates subjected to the follower forces are evaluated. The differential equation of motion of the viscoelastic plate with the piezoelectric layer is formulated using the two-dimensional viscoelastic differential constitutive relation and the thin plate theory. The weak integral form of the differential equations and the force boundary conditions are obtained. Using the element-free Galerkin method, the governing equation of the viscoelastic rectangular plate with elastic dilatation and Kelvin–Voigt distortion is derived, subjected to the follower forces coupled with the piezoelectric effect. A generalized complex eigenvalue problem is solved, and the force excited by the piezoelectric layer due to external voltage is modeled as the follower tensile force; this force is used to improve the stability of the non-conservative viscoelastic plate. For the viscoelastic plate with various boundary conditions, the results for the instability type and the critical loads are presented to show the variations in these factors with respect to the location of the piezoelectric layers and the applied voltages. The stability of the viscoelastic plates can be effectively improved by the determination of the optimal location for the piezoelectric layers and the most favorable voltage assignment.

On the use of linear viscoelastic constitutive relations to model asphalt

In this article, the appropriateness of modelling asphalt using linear viscoelastic constitutive relations is explored. Towards this, a rate-type nonlinear viscoelastic model recently proposed by Santoshreddy et al. (2011) is used and it is shown that the stress relaxation and creep response of asphalt are influenced by the type of experiment, initial rate of displacement (or loading) and the stress and strain measure used. Furthermore, it is shown that the creep and stress relaxation functions are not dependent functions as required by the linear viscoelastic theory, even in the range of values of engineering strain and stress in which the linearity property holds approximately. These observations lead one to conclude that linear viscoelastic models maybe inappropriate to model asphalt.

Experimental investigation on flow modes of electrospinning

Electrospinning experiments are performed by using a set of experimental apparatus, a stroboscopic system is adopted for capturing instantaneous images of the conejet configuration. The cone and the jet of aqueous solutions of polyethylene oxide (PEO) are formed from an orifice of a capillary tube under the electric field. The viscoelastic constitutive relationship of the PEO solution is measured and discussed. The phenomena owing to the jet instability are described, five flow modes and corresponding structures are obtained with variations of the fluid flow rate Q, the electric potential U and the distance h from the orifice of the capillary tube to the collector. The flow modes of the cone-jet configuration involves the steady bending mode, the rotating bending mode, the swinging rotating mode, the blurring bending mode and the branching mode. Regimes in the Q-U plane of the flow modes are also obtained. These results may provide the fundamentals to predict the operating conditions expected in practical applications.

Principal Parametric Resonance of Axially Accelerating Viscoelastic Beams: Multi-Scale Analysis and Differential Quadrature Verification

Transverse non-linear vibration is investigated in principal parametric resonance of an axially accelerating viscoelastic beam. The axial speed is characterized as a simple harmonic variation about a constant mean speed. The material time derivative is used in the viscoelastic constitutive relation. The transverse motion can be governed by a non-linear partial-differential equation or a non-linear integro-partial-differential equation. The method of multiple scales is applied to the governing equations to determine steady-state responses. It is confirmed that the mode uninvolved in the resonance has no effect on the steady-state response. The differential quadrature schemes are developed to verify results via the method of multiple scales. It is demonstrated that the straight equilibrium configuration becomes unstable and a stable steady-state emerges when the axial speed variation frequency is close to twice any linear natural frequency. The results derived for two governing equations are qualitatively the same, but quantitatively different. Numerical simulations are presented to examine the effects of the mean speed and the variation of the amplitude of the axial speed, the dynamic viscosity, the non-linear coefficients, and the boundary constraint stiffness on the instability interval and the steady-state response amplitude.

Research on Fractional Derivative Viscoelastic Constitutive Relation of Asphalt Mixture

Based on the definition of fractional derivative, the paper proposed a unique new idea to describe the viscoelastic property of asphalt mixture with fractional calculus. According to the SPT (Simple Performance Tests) test results, the dynamic modulus and phase angle of asphalt mixture were determined. The result of the test was fitted with the classical Kelvin model, the Maxwell model, the solid model with three elements, respectively. It showed that the classical viscoelastic model did not simulate the dynamic mechanical properties of asphalt mixture properly. Since the existing constitutive relation cannot describe well the dynamic viscoelastic properties of asphalt mixture, the fractional derivative viscoelastic model with three elements was adopted and its fitting effect analyzed. The result shown a good fitting for the fractional derivative viscoelastic model with three elements, and a few test parameters were required to build the mode. In addition, these simulating parameters were significant in physics. The order  of the fractional derivative has good correlation with the phase angle, incarnating the viscoelastic proportion of asphalt mixture. So the fractional derivative viscoelastic model with three elements can accurately describe the dynamic mechanical properties of asphalt mixture.

1413 倒立型ねじり振り子試験機を用いたニッケル基超合金の粘弾性挙動に関する研究(OS15-3 諸観点からの物質・材料の特性評価III,OS15 諸観点からの物質・材料の特性評価)

Nickel-based superalloys are widely used as the heat-resistant materials in various engineering fields. Therefore, it is very important to clarify the viscoelastic properties of these materials because they are often used under elevated temperatures. The final object of this study is to clarify the viscoelastic constitutive relation of Inconel 718 which is one of the most popular nickel-based superalloys. As the preliminary research for this final object, the internal friction (logarithmic decrement) has been measured by the inverted torsion pendulum method with changing the atmospheric temperature. Prior to the measurement, three types of specimens with different grain sizes were prepared by changing the annealing temperature. As the results, it has been clarified that the logarithmic decrement of the large grain size superalloy is smaller than that of the small grain size superalloy and that in some cases, the logarithmic decrement takes a peak value at the atmospheric temperature of approximately 820-850K.

Research on Fractional Derivative Viscoelastic Constitutive Relation of Asphalt Mixture

Research on Fractional Derivative Viscoelastic Constitutive Relation of Asphalt Mixture

Parametric Stability of Axially Accelerating Viscoelastic Beams With the Recognition of Longitudinally Varying Tensions

In this paper, the parametric stability of axially accelerating viscoelastic beams is revisited. The effects of the longitudinally varying tension due to the axial acceleration are highlighted, while the tension was approximately assumed to be longitudinally uniform in previous studies. The dependence of the tension on the finite support rigidity is also considered. The generalized Hamilton principle and the Kelvin viscoelastic constitutive relation are applied to establish the governing equations and the associated boundary conditions for coupled planar motion of the beam. The governing equations are linearized into the governing equation in the transverse direction and the expression of the longitudinally varying tension. The method of multiple scales is employed to analyze the parametric stability of transverse motion. The stability boundaries are derived from the solvability conditions and the Routh-Hurwitz criterion for principal and sum resonances. In terms of stability boundaries, the governing equations with or without the longitudinal variance of tension are compared and the effects of the finite support rigidity are also examined. Some numerical examples are presented to demonstrate the effects of the stiffness, the viscosity, and the mean axial speed on the stability boundaries. The differential quadrature scheme is developed to numerically solve the governing equation, and the computational results confirm the outcomes of the method of multiple scales.

Nonlinear forced dynamics of an axially moving viscoelastic beam with an internal resonance

The aim of the study described in this paper is to investigate the forced dynamics of an axially moving viscoelastic beam. The governing equation of motion is obtained via Newton's second law of motion and constitutive relations. The viscoelastic beam material is constituted by the Kelvin–Voigt, a two-parameter rheological model, energy dissipation mechanism, in which material, not partial, time derivative is employed in the viscoelastic constitutive relation. The dimensionless partial differential equation of motion is discretized using Galerkin's scheme with hinged–hinged beam eigenfunctions as the basis functions. The resulting set of nonlinear ordinary differential equations is then solved using the pseudo-arclength continuation technique and a direct time integration. For the system with the axial speed in the sub-critical regime, the response of the system is examined when possessing an internal resonance and when not. By employing a direct time integration, it is shown how the bifurcation diagrams of the system are modified by the presence of the dissipation terms—i.e. by both the time-dependant and steady (due the simultaneous presence of the axial speed and the energy dissipation mechanism) energy dissipation terms. Moreover, the amplitude–frequency responses and bifurcation diagrams of Poincaré maps are presented for several values of the system parameters.

Combination and principal parametric resonances of axially accelerating viscoelastic beams: Recognition of longitudinally varying tensions

Abstracts Nonlinear parametric vibration is investigated for axially accelerating viscoelastic beams subject to parametric excitations resulting from longitudinally varying tensions and axial speed fluctuations. The effects of the longitudinally varying tension due to the axial acceleration are highlighted, while the tension was assumed to be longitudinally uniform in previous studies. The dependence of the tension on the finite axial support rigidity is also modeled. The governing equations of coupled planar vibration and the associated boundary conditions are derived from the generalized Hamilton principle and the viscoelastic constitutive relation. The equation is simplified into a governing equation of transverse nonlinear vibration in small but finite stretching problems. The governing equation of transverse vibration is a nonlinear integro-partial-differential equation with time-dependent and space-dependent coefficients. The method of multiple scales is employed to analyze the combination and the principal parametric resonances with the focus on steady-state responses. In the difference resonance, there is only trivial zero response which is always stable. In the summation and the principal resonances, the trivial responses may become unstable and bifurcate into nontrivial responses for certain excitation frequencies. Some numerical examples indicate that the longitudinal tension variation makes the instability frequency intervals of trivial responses small and the nontrivial response amplitudes large (small) in the summation (principal) resonance. It is also found that the nontrivial responses are not sensitive to the axial support rigidity. Numerical solutions are calculated via the differential quadrature to support results via the method of multiple scales.

Approximate and numerical analysis of nonlinear forced vibration of axially moving viscoelastic beams

Steady-state periodical response is investigated for an axially moving viscoelastic beam with hybrid supports via approximate analysis with numerical confirmation. It is assumed that the excitation is spatially uniform and temporally harmonic. The transverse motion of axially moving beams is governed by a nonlinear partial-differential equation and a nonlinear integro-partial-differential equation. The material time derivative is used in the viscoelastic constitutive relation. The method of multiple scales is applied to the governing equations to investigate primary resonances under general boundary conditions. It is demonstrated that the mode uninvolved in the resonance has no effect on the steady-state response. Numerical examples are presented to demonstrate the effects of the boundary constraint stiffness on the amplitude and the stability of the steady-state response. The results derived for two governing equations are qualitatively the same, but quantitatively different. The differential quadrature schemes are developed to verify those results via the method of multiple scales.

The Analyses and Calculation for Thermal Stresses of SBR Modified Asphalt Pavement

Based on the viscoelasticity theory and the data of creep test, Burgers model was established, which was used to study the viscoelastic property of SBR asphalt mixtures, and the viscoelastic constitutive relation was obtained. Using the finite element method, the temperature stresses field was calculated under the environmental conditions and the thermal stresses of SBR modified asphalt pavement was given at the last part of this paper. The study indicated that SBR modified asphalt mixtures have the advantage over common asphalt mixture in low-temperature performance.

Stability of a Cracked Viscoelastic Plate of Varying Thickness Subjected to Follower Force

The stability of the cracked visoelastic rectangular plate of varying thickness subjected to uniformly distributed tangential follower force is investigated. Two models describing thickness variation are parabolic and linear variations along one edge of the plate. This is done in order to show how critical loads for cracked visoelastic thin plate subjected to follower force can be obtained using the two-dimensional viscoelastic differential constitutive relation and the thin-plate theory. The differential equations in the Laplace domain are established. The complex eigen-value equations are derived by the differential quadrature method. The generalized eigen-value under different boundary conditions is calculated. The effects of the plate parameters, the crack parameters and the dimensionless delay time on the stability of the viscoelastic plates are analyzed. The crack is found to change the type of instability and reduce the stability of varying thickness viscoelastic plate.