Response Of Viscoelastic Materials Research Articles

Micromechanical analysis of stress relaxation response of fiber-reinforced polymers

The paper describes a micromechanical method to determine the stress relaxation response of polymer composites consisting of linearly viscoelastic matrices and transversely isotropic elastic fibers. A representative unit cell is subjected to some prescribed axial and shear loadings to study and quantify the time-dependent behavior of composite materials. Closed-form analytical expressions are derived describing the anisotropic viscoelastic response of composite materials as functions of matrix and fiber properties. The present analytical expressions are employed to determine the stress relaxation behavior of a graphite/epoxy composite and the results are compared with the finite element analysis of the micromechanical model. Very good correlation between analytical expressions and numerical results is illustrated for the linearly anisotropic viscoelastic response of composite materials.

Finer‐Scale Extraction of Viscoelastic Properties from Nanoindentation Characterised by Viscoelastic–Plastic Response

Abstract: Motivated by recent progress in viscoelastic indentation analysis, the identification of viscoelastic properties from materials exhibiting elastic, viscous and plastic material behaviour by means of nanoindentation is dealt with in this paper. Based on existing solutions for pure viscoelastic material behaviour, two methods allowing us to consider the effect of plastic deformation are presented: (i) the so‐called double‐indentation technique, with the second indentation characterised by pure viscoelastic material response and (ii) the use of spherical indenter geometries instead of commonly used pyramidal indenters avoiding plastic deformation at all. Both methods are applied to three different polymers, giving access to the model parameters of the fractional dash‐pot which is used to describe the viscoelastic behaviour. The results obtained are compared with results from standard (single) indentation tests using a Berkovich indenter. Moreover, the influence of the maximum load, determining the amount of plastic material response, on the identified model parameters is investigated. Finally, the creep‐compliance functions identified by nanoindentation are compared with the respective macroscopic creep‐compliance functions obtained from bending‐beam rheometer tests.

In situ Identification of Viscoelastic Material Parameters

Abstract: Experimental methods have proved to be useful tools in structural health monitoring, enabling in situ measurements of structural deformations. By proper mathematical/numerical evaluation of the measured data it is possible to identify the characteristic internal parameters and to observe their degradation at any time during the lifetime of the structures. Especially in case of the viscoelastic response of material it is quite important to have reliable information on the material parameters to assess the actual state of structures. In this concern it is described in the following, how to proceed in monitoring the time‐dependent response of plates‐in‐bending consisting of viscoelastic material. Based on the theory of linear viscoelasticity the fundamental relationships between the displacements on the plate surface and the material parameters are presented. To perform measurements electronic speckle interferometry is applied. The application of the described process will be demonstrated by the example of a clamped plate.

Scaling relations for viscoelastic – cohesive conical indentation

Abstract Most geomaterials exhibit both viscoelastic and plastic material response when indented by a sharp conical tip. Lacking analytical solutions for viscoelastic – plastic material response, a numerical approach based on the finite element method is proposed for backcalculation of model parameters from indentation data. Departing from the analytical solutions recently obtained by Vandamme and Ulm, viscoelastic – cohesive conical indentation of a homogeneous material halfspace is dealt with in this paper. Results from finite element analysis, i. e., the load – penetration history for a rigid, conical indenter with linearly increasing load, are presented in dimensionless form. From the results, scaling relations are constructed for application to materials exhibiting viscoelastic – cohesive behavior.

Determining the complex modulus of alginate irreversible hydrocolloid dental material

Objectives The aim of the study is to investigate the visco-elastic response of an alginate irreversible hydrocolloid dental impression material during setting. Methods A novel squeeze film Micro-Fourier Rheometer (MFR, GBC Scientific Equipment, Australia) was used to determine the complex modulus of an alginate irreversible hydrocolloid dental impression material (Algident, ISO 1563 Class A Type 1, Dentalfarm Australia Pty. Ltd.) during setting after mixing. Data was collected every 30 s for 10 min in one study and every 10 min for a total of 60 min in another study. A high level of repeatability was observed. Results The results indicate that the MFR is capable of recording the complex shear modulus of alginate irreversible hydrocolloid for 60 min from the start of mixing and to simultaneously report the changing visco-elastic parameters at all frequencies between 1 Hz and 100 Hz. The storage modulus shows a dramatic increase to 370% of its starting value after 6 min and then reduces to 55% after 60 min. The loss modulus increases to a maximum of 175% of its starting value after 10 min and then reduces to 94% after 60 min. Significance The MFR enables the changes in the complex modulus through the complete setting process to be followed. It is anticipated this approach may provide a better method to compare the visco-elastic properties of impression materials and assist with identification of optimum types for different clinical requirements. The high stiffness of the instrument and the use of band-limited pseudo-random noise as the input signal are the main advantages of this technique over conventional rheometers for determining the changes in alginate visco-elasticity.

Shrinkage Cracking Test and Analytical Model for Concrete Considering Creep Behaviour at Early Age

Cracking due to the restrained shrinkage stress has been frequently observed at early age in concrete construction. The early-age shrinkage cracking reduce the structural performance of concrete and may accelerate deterioration to shorten the service life. Two kinds of strategies and instrumentation have been developed to assess early age cracking: ring tests with a restraining core, longitudinal tests where the restraint is at the end grips of the specimen. Early-age concrete exhibits creep or relaxation behavior that is a typical response of viscoelastic materials. Viscoelastic constitutive model should be used to analyze stress development of the restrained concrete. The assessment of the risk of cracking can be based on the model with input of the estimated concrete deformation.

Stability and bound‐exceeding elastic and viscoelastic response of composite materials having a negative‐stiffness phase

AbstractWe show that a composite material with one phase having negative bulk and Young's moduli (and therefore being unstable by itself) can be stable overall under dead traction boundary conditions if the encapsulating phase is sufficiently stiff. We also show experimental evidence that appropriate tuning of the negative‐stiffness phase can lead to bound‐exceeding elastic and viscoelastic overall material response. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

On the use of a spectrum-based model for linear viscoelastic materials

A new spectrum-based model for describing the behavior of time-dependent materials is presented. In this paper, unlike most prior modeling techniques, the time-dependent response of viscoelastic materials is not expressed through the use of series. Instead, certain criteria have been imposed to select a spectrum function that has the potential of describing a wide range of material behavior. Another consequence of choosing the spectrum function of the type used in this paper is to have a few closed form analytic solutions in the theory of linear viscoelasticity. The Laplace transform technique is used to obtain the necessary formulae for viscoelastic Lame' functions, relaxation and bulk moduli, creep bulk and shear compliance, as well as Poisson's ratio. By using the Elastic–Viscoelastic Correspondence Principle (EVCP), material constants appearing in the proposed model are obtained by comparing the experimental data with the solution of the integral equation for a simple tensile test. The resulting viscoelastic functions describe the material properties which can then be used to express the behavior of a material in other loading configurations. The model's potential is demonstrated and its limitations are discussed.

Extended capabilities of an inverted torsion pendulum

The complex elastic modulus, or its real component and the internal friction, are the mechanical variables that characterize the dynamic behaviour of linear viscoelastic materials. Free or forced oscillations produced by inverted torsion pendulums or rheometers are usually used to measure these variables. Linearity is checked sometimes by recording the stress vs. strain curve, otherwise by measuring whether the internal friction or any component of the dynamic modulus is independent of the strain amplitude. This paper demonstrates that the linear dynamic response of viscoelastic materials cannot be assured just by looking at the stress–strain amplitude detected by forced oscillation torsion devices. Furthermore, it is shown that internal friction measured at the resonance frequency of the experimental device provides an extremely accurate tool to determine the presence of nonlinear mechanical effects. This issue is shown for polycarbonate samples submitted to forced oscillations in a torsion pendulum working at resonance.

Inertial Effects in the Response of Viscous and Viscoelastic Fluids

We consider the effect of inertia on the high frequency response of a general linear viscoelastic material to local deformations. We calculate the displacement response and correlation functions for points separated by a distance r. The effects of inertia and incompressibility lead to anticorrelations in the correlation or response functions, which become more pronounced for more elastic materials. Furthermore, the stress propagation in viscoelastic media is no longer diffusive, as for simple liquids.

Viscoelastic response of dry and wet fibrous materials during infusion processes

The deformation response of fibrous materials to transverse compressive forces plays an important role in the Liquid Composite Molding (LCM) processes. The objective of this study was to characterize this response and to create a model of the response for inclusion in simulations of LCM processes. A series of compression tests were carried out on both dry and resin impregnated samples. A model of fibrous material deformation was developed, incorporating the observed viscoelastic response and the difference in behavior between the dry and wet samples. The same model is used for both compaction and relaxation phases, and matches well experimental data over a range of fiber volume fractions and compression speeds.

Multiple-frequency dynamic nanoindentation testing

A new method of dynamic nanoindentation testing is introduced in this paper. Conventional dynamic nanoindentation testing involves the superposition of a single frequency sinusoidal force or displacement onto the quasi-static load–displacement curve. However, the viscoelastic response of many materials depends upon the frequency of the deformation of the material. This paper describes a method whereby the storage and loss modulus of viscoelastic solids can be determined using a multi-frequency dynamic oscillatory motion mode of deformation. In this method, the applied load is modulated by a pseudo-random force signal comprising multiple frequencies. A Fourier analysis is then used to deconvolute the signal into frequency-dependent values of storage and loss modulus for the specimen material as a function of frequency. The instrument response is cancelled by the use of a reference transfer function using an equalization process. Established modeling equations can then be used to extract the modulus of elasticity and the viscosity of the specimen material.

Nested nonlinear viscoelastic and micromechanical models for the analysis of pultruded composite materials and structures

The present study introduces analytical and numerical formulations in order to derive the effective nonlinear viscoelastic response of pultruded composite materials and structures. The studied pultruded composite system consists of two alternating layers reinforced with E-glass roving and continuous filament mat (CFM). Two 3D micromechanical models are used for the layers with roving and CFM, each having a unit-cell with four fiber and matrix subcells. A sublaminate model is also used to generate a nonlinear equivalent continuum of the layered medium. A new recursive-iterative procedure is introduced to integrate the Schapery nonlinear viscoelastic model used for the isotropic matrix subcells of the micromodels. An iterative numerical algorithm with predictor–corrector type steps is formulated for the sublaminate model and is used to interface with a nonlinear finite-element (FE). Off-axis creep compression and tension tests, with and without a circular hole, are performed for E-glass/vinylester and polyester pultruded plates to calibrate and predict the nonlinear viscoelastic response. The multiscale modeling approach shows good linear and nonlinear viscoelastic prediction compared with the experimental results.

Rheological microscopy: local mechanical properties from microrheology.

We demonstrate how tracer microrheology methods can be extended to study submicron scale variations in the viscoelastic response of soft materials; in particular, a semidilute solution of lambda-DNA. The polymer concentration is depleted near the surfaces of the tracer particles, within a distance comparable to the polymer correlation length. The rheology of this microscopic layer alters the tracers' motion and can be precisely quantified using one- and two-point microrheology. Interestingly, we found this mechanically distinct layer to be twice as thick as the layer of depleted concentration, likely due to solvent drainage through the locally perturbed polymer structure.

Measurement of Creep Compliance of Solid Polymers by Nanoindentation

Methods to measure the local surface creep compliance of time-dependent materials are proposedand validated in the regime of linear viscoelasticity using nanoindentation. Two different bulkpolymers, Polymethyl Methacrylate (PMMA) and Polycarbonate (PC), were employed in thevalidation study; though it is expected that the methods developed herein can be applied for verysmall amounts of materials and heterogeneous materials. Both Berkovich and sphericalnanoindenters were used to indent into the material in nanoindentation tests. Two loading historieswere used: (1) a ramp loading history, in which the indentation load and displacement wererecorded; and (2) a step loading history, in which the indentation displacement was recorded as afunction of time. Analysis of the linearly viscoelastic material response was performed to measurethe creep compliance functions for the two materials under two different loading histories. The limitof linearly viscoelastic behavior for each of the two materials was determined through theobservation of the indent impression recovery after complete unloading; it is postulated that linearityis achieved if indentation impression is fully recovered after unloading. Results fromnanoindentation tests generally agree well with data from conventional tension and shear tests. It hasthus validated the techniques of measuring linear creep compliance in the glassy state usingnanoindentation with the Berkovich and spherical indenter tips.

Axisymmetric dynamic stability of sandwich circular plates

The axisymmetric dynamic stability of sandwich circular plates with a constrained damping layer treatment subjected to a periodic uniform radial loading along the outer edge of the host plate is studied by the discrete layer annular finite element method. The viscoelastic material with frequency dependent properties in the damping layer is assumed to be incompressible, and the extensional and shear moduli are described by complex quantities. The regions of dynamic instability are determined by Bolotin’s method while two eigenvalue problem systems with frequency dependent parameters are formed. The modified complex eigensolution method is employed to solve the eigenvalue problems. Numerical results are shown that the constrained damping layer attached to circular plates tends to stabilize the circular plate system. The effects of various parameters, such as types of viscoelastic material response, treatment thickness and area, on dynamic stability are also investigated.

High Strain-Rate Constitutive Models for Solid Rocket Propellants

A constitutive model that incorporates mechanical damage and nonlinear viscoelastic material response for solid composite rocket propellants has been developed for high strain-rate impact loading conditions. The numericalconstants in this model could be related to the physics of the propellant and were obtained by nonlinear least-squares fitting of the data obtained from Hopkinson Bar experiments in the strain-rate range from 10 3 to 10 4 s - 1 . Damage was taken into account using an approach based on correcting the viscoelastic function with a stress softening function. A simple method for calibrating the stress softening function using the recoverable strain energy density has been developed. This energy-based approach has the advantage of being able to capture damage more adequately and allows for bulk inelastic behavior. Predictions of the stress response of two different composite propellants for different loading conditions (temperature and strain rate) and histories (and, therefore, different damage levels) were made using the constitutive model. Good agreement between the predicted and experimentally measured stresses for strain levels up to 30-40% was obtained. The model was able to predict the stress response quite reasonably outside the temperature range used to develop the constitutive equation, but inside the range of the reduced strain-rate, indicating the validity of the time-temperature superposition principle for high strain-rate conditions. The model was also able to reproduce quite well the mechanical deformation (both in magnitude and shape of the stress-strain curve) of predamaged propellants.

Viscoelastic response of sonic band-gap materials

A brief report is presented on the effect of viscoelastic losses in a high density contrast sonic band-gap material of close-packed rubber spheres in air. The scattering properties of such a material are computed with an on-shell multiple scattering method, properties which are compared with the lossless case. The existence of an appreciable omnidirectional gap in the transmission spectrum, when losses are present, is also reported.

Hot topics in structural acoustics: Optical imaging of surface vibrations—Some new developments and applications

Laser Doppler vibrometry is routinely used for a vast range of applications to measure surface vibrations in the nanometer range. Some new developments include the use of laser vibrometers with continuous tracking on moving targets, the detection of the vector displacement of a surface (either with multiple beam interferometry or with a photo-emf probe), and the direct measurement of torsional vibrations on rotating shafts. Electronic speckle pattern interferometry (ESPI) is a full-field optical technique that is also commonly used to image surface vibrations. An interesting development of ESPI is electronic shearography. Some applications of these optical techniques will be discussed. These include calibrations of transducers and MEMS devices, imaging of rotating parts, mapping of structural intensity, characterization of the dynamic response of viscoelastic materials, as well as some more exotic applications such as damage assessment of frescoes and painting, three-dimensional vibration imaging of the ossicular chain in cats, and dynamic characterization of human teeth.

Mechanical response of polymers: an introduction

Preface 1. Discussion of response of a viscoelastic material 2. Constitutive equations for one-dimensional response of viscoelastic materials: mechanical analogs 3. Constitutive equations for one-dimensional linear response of a viscoelastic material 4. Some features of the linear response of viscoelastic materials 5. Histories with constant strain or stress rates 6. Sinusoidal oscillations 7. Constitutive equation for three dimensional linear isotropic viscoelastic materials 8. Axial load, bending and torsion 9. Dynamics of bodies with viscoelastic support 10. Boundary value problems for linear isotropic viscoelastic materials 11. Influence of temperature Appendices References Index.