Viscoelastic Material Model Research Articles

An adaptive MsFEM for nonperiodic viscoelastic composites

SummaryWe present a modification of the multiscale finite element method (MsFEM) for modeling of heterogeneous viscoelastic materials and an enhancement of this method by the adaptive generation of both meshes, ie, a macroscale coarse one and a microscale fine one. The fine mesh refinements are performed independently within coarse elements adjusting the microscale discretization to the microstructure, whereas the coarse mesh adaptation optimizes the macroscale approximation. Besides the coupling of the hp‐adaptive finite element method with the MsFEM we propose a modification of the MsFEM to accommodate for the analysis of transient nonlinear problems. We illustrate the efficiency and accuracy of the new approach for a number of benchmark examples, including the modeling of functionally graded material, and demonstrate the potential of our improvement for upscaling nonperiodic and nonlinear composites.

A State Space Viscoelastic Shaft Finite Element for Stability and Response Analysis of Rotors with Structural and Frequency Dependent Damping

The present work proposes a new Euler–Bernoulli shaft element for structurally damped and viscoelastic rotors in a spinning frame. The Maxwell–Wiechert linear viscoelastic material model, having one elastic branch and several parallel Maxwell branches, is used. This model introduces additional internal displacement variables between elastic and viscous elements in the Maxwell branches. Here, the stress depends not only on the elastic strain and elastic strain rate but also on additional fictitious strains and their rates. In the present work, it is assumed that these additional strains can be derived from continuous fictitious displacement variables in the same way as the elastic strains are derived from the actual displacement variables. These continuous fictitious displacements in turn are interpolated from their nodal values using the conventional beam shape functions. Therefore, in addition to the standard degrees of freedom, extra degrees of freedom are defined at the nodes. The viscoelastic shaft element is then used in time-domain analysis of rotors with structural damping or frequency-dependent damping. Parameters of the Maxwell–Wiechert model are so selected that they appropriately represent structural damping of a mild steel rotor and frequency-dependent storage modulus and loss coefficient of a typical viscoelastic rotor. Both stability and time response analyses are performed. The results obtained through dynamic analysis of two different rotor models using both structurally damped mild steel and a typical viscoelastic material PPC as shaft material are similar to those available in the literature and justify the methods applied.

Fractional Maxwell model of viscoelastic biological materials

This article focuses on fractional Maxwell model of viscoelastic materials, which are a generalization of classic Maxwell model to non-integer order derivatives. To build a fractional Maxwell model when only the noise-corrupted discrete-time measurements of the relaxation modulus are accessible for identification is a basic concern. For fitting the original measurement data an approach is suggested, which is based on approximate Scott Blair fundamental fractional non-integer models, and which means that the data are fitted by solving two dependent but simple linear least-squares problems in two separable time intervals. A complete identification algorithm is presented. The usability of the method to find the fractional Maxwell model of real biological material is shown. The parameters of the fractional Maxwell model of carrot root that approximate the experimental stress relaxation data closely are given.

Phase-Field Modelling of Fracture in Viscoelastic Solids

The phase-field modeling has emerged as an extremely powerful numerical method to simulate crack propagation with significant success. The crack is herein modeled by a field variable that distinguishes between fully broken and undamaged material. In the proposed phase-field model for crack propagation in viscoelastic solids, a model with a fracture threshold similar to gradient damage theories is developed which can distinguish between fracture behavior in compression and tension. A viscoelastic material model in the framework of finite deformations is used for rubber-like material response. The full model is implemented in the framework of the FE program FEAP and allows both a monolithic and a staggered scheme for the numerical solution. Within FEAP a parameter study is realized. Finally, a summary of the results is presented and an outlook for improvements of the modeling for fracture in viscoelastic solids is given.

Viscoelastic Contact Simulation under Harmonic Cyclic Load

Characterization of viscoelastic materials from a mechanical point of view is often performed via dynamic mechanical analysis (DMA), consisting in the arousal of a steady-state undulated response in a uniaxial bar specimen, allowing for the experimental measurement of the so-called complex modulus, assessing both the elastic energy storage and the internal energy dissipation in the viscoelastic material. The existing theoretical investigations of the complex modulus’ influence on the contact behavior feature severe limitations due to the employed contact solution inferring a nondecreasing contact radius during the loading program. In case of a harmonic cyclic load, this assumption is verified only if the oscillation indentation depth is negligible compared to that due to the step load. This limitation is released in the present numerical model, which is capable of contact simulation under arbitrary loading profiles, irregular contact geometry, and complicated rheological models of linear viscoelastic materials, featuring more than one relaxation time. The classical method of deriving viscoelastic solutions for the problems of stress analysis, based on the elastic-viscoelastic correspondence principle, is applied here to derive the displacement response of the viscoelastic material under an arbitrary distribution of surface tractions. The latter solution is further used to construct a sequence of contact problems with boundary conditions that match the ones of the original viscoelastic contact problem at specific time intervals, assuring accurate reproduction of the contact process history. The developed computer code is validated against classical contact solutions for universal rheological models and then employed in the simulation of a harmonic cyclic indentation of a polymethyl methacrylate half-space by a rigid sphere. The contact process stabilization after the first cycles is demonstrated and the energy loss per cycle is calculated under an extended spectrum of harmonic load frequencies, highlighting the frequency for which the internal energy dissipation reaches its maximum.

On the Passage from Nonlinear to Linearized Viscoelasticity

We formulate a quasistatic nonlinear model for nonsimple viscoelastic materials at a finite-strain setting in the Kelvin--Voigt rheology where the viscosity stress tensor complies with the principl...

Failure Mechanism of O-Ring Seals under Extreme Operating Conditions

In this paper the behavior of an O-ring made of NBR rubber was investigated under extreme conditions. The effect of the extreme initial compression, operating pressure and extreme temperature conditions were examined. The rubber material was tested in simple tension, pure shear and equibiaxial tension modes complemented with a Dynamic Mechanical Thermal Analysis (DMTA) to capture the viscoelastic behavior of the material. For the investigation, a large-strain viscoelastic material model was developed by the authors, to take into account the large deformations caused by extreme conditions. Insufficient space during installation causes extreme initial compression consequently leading the material to crack on the contacting outer surfaces. It was found that the excessive strain and friction induced shear stress contributes primarily to this phenomenon. Extreme operating pressure causes the seal to penetrate into the gap between the shaft and the housing. This behavior damages the material and cracks appear on the seal. High strain areas were found in the proximity of the gap in the material. The analysis of the extreme operating temperature showed that during cooling the O-ring can completely loose its ability to seal at -70°C. There are three contributing factors: the speed of cooling, the temperature and the coefficient of thermal expansion.

Combining adhesive contact mechanics with a viscoelastic material model to probe local material properties by AFM.

Viscoelastic properties are often measured using probe based techniques such as nanoindentation (NI) and atomic force microscopy (AFM). Rarely, however, are these methods verified. In this article, we present a method that combines contact mechanics with a viscoelastic model (VEM) composed of springs and dashpots. We further show how to use this model to determine viscoelastic properties from creep curves recorded by a probe based technique. We focus on using the standard linear solid model and the generalized Maxwell model of order 2. The method operates in the range of 0.01 Hz to 1 Hz. Our approach is suitable for rough surfaces by providing a defined contact area using plastic pre-deformation of the material. The very same procedure is used to evaluate AFM based measurements as well as NI measurements performed on polymer samples made from poly(methyl methacrylate) and polycarbonate. The results of these measurements are then compared to those obtained by tensile creep tests also performed on the same samples. It is found that the tensile test results differ considerably from the results obtained by AFM and NI methods. The similarity between the AFM results and NI results suggests that the proposed method is capable of yielding results comparable to NI but with the advantage of the imaging possibilities of AFM. Furthermore, all three methods allowed a clear distinction between PC and PMMA by means of their respective viscoelastic properties.

Two Way Stiffness Tuning Of Magnetorheological Elastomer- Shape Memory Alloy Composite

Structural vibration control by tuning structural material modulus through external stimuli is great deal of interest for researchers. Shape memory alloy (SMA) is kind of smart material whose modulus can be varied by changing its temperature. Temperature dependent change in modulus of SMA during phase transformation is stiff and nonlinear which inducts difficulties for getting smooth structural stiffness change to alter its dynamic behavior. This paper deals with the work wherein, SMA is combined with magnetorheological elastomer (MRE) to form composite. MRE is another smart material whose shear modulus consequently stiffness can be changed by exposing it to variable magnetic field. Smart MRE-SMA composite has been studied analytically for stiffness variation by combining Maxwell form of three parameter constitutive viscoelastic material model, model for magnetic field dependent change in shear modulus for anisotropic MRE and temperature dependent modulus of SMA. The composite is fabricated, tested for stiffness change with respect to external stimuli by natural frequency measurement method and the results are compared with analytical study. The result show that the stiffness nonlinearity exists in SMA during transformation phase has been minimized by wisely selecting values of temperature and strength of magnetic field simultaneously. Significant level of smooth stiffness change is achieved by proper tuning of SMA temperature and strength of magnetic field.

Nonlinear vibration analysis of a fractional dynamic model for the viscoelastic pipe conveying fluid

• A new non-linear, fractional dynamic model of the viscoelastic pipe is established. • Analytical solutions of the fractional model are derived using the method of multiple scales. • The amplitude predicted by the fractional model is much larger than that predicted by the previous model. • With the fractional order increase, the nonlinear frequency increases at first and then diminishes. • The fractional order can change the variation trend of the amplitude versus the fluid velocity. The nonlinear free vibration of a fractional dynamic model for the viscoelastic pipe conveying fluid is studied in this paper. The dynamic equations of coupled planar motion for the pipe are derived by employing the Euler beam theory and the generalized Hamilton principle when we consider both the fractional material model and the geometric non-linearity. Then the equations are simplified into a new nonlinear, fractional order dynamic model governing transverse vibration of the pipe in small but limited stretching issues. The method of multiple scales is directly applied for the analysis and simulation of the nonlinear vibration. Numerical results show the influence of the factional order, the mass ratio, the fluid velocity and the nonlinear coefficient on the nonlinear amplitudes and frequencies of the viscoelastic pipe. It is noticeable that the amplitudes of the fluid-conveying pipe constituted by the fractional viscoelastic material model display much higher than those predicted by the previous models.

Advanced Rebar Formulation within a Thermo‐Mechanically Coupled Tire Simulation

AbstractAs shown in various experiments, coupling between the thermal and the mechanical field of a rolling tire in contact with a rigid surface can be observed. An increase of its temperature over time when rolling with a constant velocity can be seen. This phenomenon is caused by the viscoelastic material properties, where the dissipated energy will lead to a heating of the rubber. Also the constitutive behaviour will change, when the temperature increases. A nonlinear viscoelastic material model is chosen to model an amplitude dependency of the time dependent behaviour of the rubber, proposed by Bergström and Boyce [1].Another important part of a tire are the reinforcements, which are embedded inside the rubber. These consist mostly of steel or polyester. These materials are not known for a dissipative behaviour and will not contribute to the heating of the tire. However, they also change their properties with increasing temperature and have a significant influence on the overall tire properties. Even without a contribution to the heating, the reinforcements will change its conductivity and have to be taken into account.For an accurate and efficient way to model the thermo‐mechanical coupling, an in‐house framework [2] will be presented, by use of the Arbitrary Langrangian Eulerian formulation and a commercial code. It is assumed, that the temperature in circumferential direction will stay constant and instant coupling effects are negligibly small. Therefore, the problem is split into a thermal and a mechanical part, and the coupling quantities (dissipated energy and temperature) are updated in a sequential manner.A common practise to model the reinforcements in tires is to use smeared layers, which leads to some difficulties. First of all, the modelling is only valid for a really small spacing between the bars. Another problem is, that the smeared layers have to fit with the nodes of the rubber matrix. Because of that, the mesh has to be refined, which leads to an increasing computation time and can cause numerical difficulties, due to too small elements.In this contribution, a different way of modelling the rebars within a thermo‐mechanical coupled algorithm is presented without the assumption of a smeared layer and treat them as single rebars. In numerical examples, the advantages of the proposed method are presented and the difference to the classical approach is shown. Also, the influence of the reinforcements on the stiffness, heat generation and rolling resistance of the tire, will be discussed. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Arterial pulse attenuation prediction using the decaying rate of a pressure wave in a viscoelastic material model

The present study examines the possibility of attenuating blood pulses by means of introducing prosthetic viscoelastic materials able to absorb energy and damp such pulses. Vascular prostheses made of polymeric materials modify the mechanical properties of blood vessels. The effect of these materials on the blood pulse propagation remains to be fully understood. Several materials for medical applications, such as medical polydimethylsiloxane or polytetrafluoroethylene, show viscoelastic behavior, modifying the original vessel stiffness and affecting the propagation of blood pulses. This study focuses on the propagation of pressure waves along a pipe with viscoelastic materials using the Maxwell and the Zener models. An expression of exponential decay has been obtained for the Maxwell material model and also for low viscous coefficient values in the Zener model. For relatively high values of the viscous term in the Zener model, the steepest part of the pulse can be damped quickly, leaving a smooth, slowly decaying wave. These mathematical models are critical to tailor those materials used in cardiovascular implants to the mechanical environment they are confronted with to repair or improve blood vessel function.

Modeling the Performance of Horizontal Anchor Lines During Fall Arrest

The basic materials used for the construction of anchor lines for personal equipment protection against falls from a height are ropes and textile webbing. During fall arrest, horizontal anchor lines significantly affect the forces acting on the worker and the work site elements, as well as the fall arrest distance. Manufacturers of the equipment are required to estimate those parameters for various conditions of use by numerical simulations with a validated model. The model discussed in this paper reflects the mechanical structure of the line (whether singles-span or multi-span) taking into account Maxwell’s and Kelvin–Voigt’s non-linear rheological models for viscoelastic materials. The model consists of a system of seven non-linear differential equations with the parameters describing static load-elongation characteristics and time-courses of dynamic loading forces for selected ropes and textile webbing. The numerical model developed was used to simulate the performance of horizontal anchor lines of different constructions. The model was validated by comparing the numerical calculations with laboratory test results and was shown to be sufficiently accurate to be used for designing fall protection equipment.

Rayleigh-type wave propagation on a transversely isotropic viscoelastic layer with yielding and rigid foundations

ABSTRACTThe present study investigates the propagation of Rayleigh-type wave in a transversely isotropic viscoelastic layer in effect of yielding foundation and rigid foundation in two different cases for two considered models. Numerical computation and graphical demonstration have been carried out for the case when layer is comprised of transversely isotropic viscoelastic Mesaverde clay shale material (Model I) and simply isotropic viscoelastic material (Model II). Closed-form expression of phase velocity and damped velocity for both the cases are deduced analytically. Obtained result is found in well agreement to the established standard results existing in the literature. Significant effect of dilatational viscoelasticity, volume viscoelasticity and yielding parameter on phase and damped velocities for both the considered models has been traced out. The comparative study has been performed to unravel the effect of viscoelasticity over elasticity and anisotropy over isotropy in the context of the present problem. Moreover, comparison of phase and damped velocities for the case of layer with stress-free foundation, layer with rigid foundation and layer with yielding foundation serve as a major highlight of the present work.

Viscoelastic Behavior of Shear-Deformable Plates

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 Materials 19(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.

Dynamic characterization and modeling of rubber shock absorbers: A comprehensive case study

Rubber or elastomeric materials are widely used for shock absorbers having elastic and viscous properties such as high inherent damping, deflection capacity, and energy storage. The dynamic properties of these components are of primary concern in designing rubber absorbers to reduce the shock loading given as well as the structure-borne noise transmissibility. Besides, the dynamic response of the mechanical systems, at where the rubber shock absorbers are used, is directly associated with the properties of the shock absorbers. In order to determine these properties of the rubber, mathematical models are created in terms of hyperelasticity and viscoelasticity. The hyperelastic and viscoelastic material models represent the nonlinear elastic and strain rate dependencies of the overall rubber behavior, respectively. Hyperelastic material model captures the material’s nonlinear elasticity with no-time dependence whereas viscoelastic model describes the material response which contains an elastic and viscous part depending on time, frequency, and temperature. This paper presents the dynamic characterization of rubber shock absorbers, having different shore hardness values, in terms of hyperelastic and viscoelastic constitutive models. The parameters of the constitutive models are determined from the uniaxial tensile and relaxation tests. These parameters are used for the numerical model of the rubber components and the accuracy of the characterization is presented by means of a numerical case study.

Characterization and modeling of poly(methyl methacrylate) and thermoplastic polyurethane for the application in laminated setups

Transparent polymeric laminates are increasingly used for the substitution of conventional glass and laminated safety glass respectively and thus require reliable and efficient prediction and modeling techniques, in particular for numerical simulations. In the present work, the components of a polymeric laminate consisting of poly(methyl methacrylate) (PMMA) plies combined with a thermoplastic polyurethane (TPU) interlayer were subjected to experimental and numerical investigation. Uniaxial tensile tests and dynamic mechanical thermal analysis (DMTA) were used to determine the strain-rate and temperature dependent material behavior. Adiabatic heating of the interlayer was observed using infrared (IR) surveillance. Based on the experimental basis, viscoelastic material models were applied for both materials. The corresponding parameter identification was performed in two ways. One was based on the DMTA master curve, the other on uniaxial tensile test data. The material models were able to capture the temperature and time dependent behavior of both materials adequately and enable their usage in a laminated structure.

Reliability Assessment of Solid-Propellant Rocket Motors Under Storage and Transportation Loads

A methodology for the assessment of the service life of solid-propellant rocket motors under random storage and transportation loads is presented. In storage conditions, the propellant grain is subject to random thermal environments while during transportation to vibration loads, both of which induce strain and stress. Over long periods of time, storage and transportation cause damage accumulation in the propellant. Aging mechanisms also contribute to the accumulated damage. Thermal loading is modeled as a harmonic function of time and vibratory loads of different transportation scenarios, such as ground, air, and sea transportation are used with the corresponding acceleration spectral density functions. The loading and material parameters are taken into consideration with their uncertainties. A linear viscoelastic material model is used for the propellant. Degradation of the structural capability is represented using Laheru’s cumulative damage model and the aging effect is simulated with Layton’s model. To find the stress and strain accumulated in the grain, the finite element method is used. The response surface method is used to use the surrogate mathematical models for the induced stress and strain. The limit-state functions are formed to predict failure. The instantaneous reliability is calculated within a confidence interval using a first-order reliability method.

Proper Orthogonal Decomposition–Radial Basis Function Surrogate Model-Based Inverse Analysis for Identifying Nonlinear Burgers Model Parameters From Nanoindentation Data

This study explores the application of a proper orthogonal decomposition (POD) and radial basis function (RBF)-based surrogate model to identify the parameters of a nonlinear viscoelastic material model using nanoindentation data. The inverse problem is solved by reducing the difference between finite element simulation-trained surrogate model approximation and experimental data through genetic algorithm (GA)-based optimization. The surrogate model, created using POD–RBF, is trained using finite element (FE) data obtained by varying model parameters within a parametric space. Sensitivity of the model parameters toward the load–displacement output is utilized to reduce the number of training points required for surrogate model training. The effect of friction on simulated load–displacement data is also analyzed. For the obtained model parameter set, the simulated output matches well with experimental data for various experimental conditions.

Cure-state dependent viscoelastic Poisson’s ratio of LY5052 epoxy resin

It is shown, using thermodynamically consistent linear viscoelastic material model that accounts for properties dependence on test temperature and cure state parameters, that for rheologically simple materials the cure and temperature related reduced times and shift factors are the same for all viscoelastic compliances, relaxation modulus, and Poisson’s ratio as well as for the storage and loss modulus. A necessary condition for that is that the cure and temperature parameters are affecting the reduced time only. This means that the Poisson’s ratio of polymeric materials, which for simplicity is often assumed constant, in fact exhibits a small dependence on time which is affected by temperature and state of cure. In this work, the evolution of the viscoelastic Poisson’s ratio of the commercial LY5052 epoxy resin is studied in relaxation test subjecting the specimen to constant axial strain. Specimens at several cure states are studied and Poisson’s ratio, defined as the lateral and axial strain ratio, is shown to evolve from 0.32 to 0.44 over time. Moreover, the data confirm that the cure state-dependent reduced time controlling the Poisson’s ratio development leads to the same shift functions as those identified in DMTA tests for storage modulus. The latter measurements also confirmed that the total shift can be considered as a sum of two shifts in the frequency domain, which means that function for reduced time calculation can be written as a product of two functions: one dependent on the test temperature and another one dependent on the cure state.