Solids, viscoelastic

Elastic materials strain instantaneously when stretched and just as quickly return to their original state once the stress is removed. Viscoelastic materials have elements of both of these properties and, as such, exhibit time dependent strain. Whereas elasticity is usually the result of bond stretching along crystallographic planes in an ordered solid, viscoelasticity is the result of the diffusion of atoms or molecules inside of an amorphous material [3-6],... 

According to the Boltzmann superposition principle, the shear strain of a solid viscoelastic material under the action of a harmonic shear stress can be written as (2)... 

There is a need for thorough smdies of the solid viscoelastic properties of CPNCs. A single sweep of temperature at a single arbitrarily selected frequency and heating... 

The Stress relaxation experiment consists of applying a constant relative strain. Yii. and recording the shear. stress response, as shown in Fig. 12. Typical relaxation curves for elastic solids, viscoelastic solids or liquids, and Newtonian liquids are shown in the latter figure. The clastic solid is able to store energy and, in consequence, can maintain deformation and does not relax under the applied strain. The other extreme is the Newtonian flow that relaxes completely and flows. 

Polymeric materials, such as rubber, exhibit a mechanical response which cannot be properly described neither by means of elastic nor viscous effects only. In particular, elastic effects account for materials which are able to store mechanical energy with no dissipation. On the other hand, a viscous fluid in a hydrostatic stress state dissipates energy, but is unable to store it. As the experimental results reported in Part 1 have shown, filled rubber present both the characteristics of a viscous fluid and of an elastic solid. Viscoelastic constitutive relations have been introduced with the intent of describing the behavior of such materials able to both store and dissipate mechanical energy. 

This generality of the viscoelastic model is summarized in Table 1. The viscoelastic model in the classification of isotropic phase separation corresponds to viscoelastic matter in the classification of isotropic condensed matter. Corresponding to the classification of isotropic matter into solids, viscoelastic matter, and fluids, we... 

We have already discussed in the introductory chapter how polymers can behave as glassy solids, viscoelastic solids, rubbers or viscous liquids depending on the timescale or on the... 

Other passive control devices (solid viscoelastic dampers, metallic dampers, friction dampers, etc.) have a different hysteric behavior with several advantages and disadvantages also for what concerns their reliability. 

Polymers have found widespread applications because of their mechanical behaviour. They combine the mechanical properties of elastic solids and viscous fluids. Therefore, they are regarded as viscoelastic materials. Viscoelastic... 

The viscosity given by Eq. (3.98) not only follows from a different model than the Debye viscosity equation, but it also describes a totally different experimental situation. Viscoelastic studies are done on solid samples for which flow is not measurable. A viscous deformation is present, however, and this result shows that it is equivalent to what would be measured directly, if such a measurement were possible. 

A parameter indicating whether viscoelastic effects are important is the Deborah number, which is the ratio of the characteristic relaxation time of the fluid to the characteristic time scale of the flow. For small Deborah numbers, the relaxation is fast compared to the characteristic time of the flow, and the fluid behavior is purely viscous. For veiy large Deborah numbers, the behavior closely resembles that of an elastic solid. 

Schuler, K.W., Nunziato, J.W., and Walsh, E.K., Recent Results in Nonlinear Viscoelastic Wave Propagation, Internat. J. Solids and Structures 9, 1237-1281... 

Contact mechanics, in the classical sense, describes the behavior of solids in contact under the action of an external load. The first studies in the area of contact mechanics date back to the seminal publication "On the contact of elastic solids of Heinrich Hertz in 1882 [ 1 ]. The original Hertz theory was applied to frictionless non-adhering surfaces of perfectly elastic solids. Lee and Radok [2], Graham [3], and Yang [4] developed the theories of contact mechanics of viscoelastic solids. None of these treatments, however, accounted for the role of interfacial adhesive interactions. 

It has been also shown that when a thin polymer film is directly coated onto a substrate with a low modulus ( < 10 MPa), if the contact radius to layer thickness ratio is large (afh> 20), the surface layer will make a negligible contribution to the stiffness of the system and the layered solid system acts as a homogeneous half-space of substrate material while the surface and interfacial properties are governed by those of the layer [32,33]. The extension of the JKR theory to such layered bodies has two important implications. Firstly, hard and opaque materials can be coated on soft and clear substrates which deform more readily by small surface forces. Secondly, viscoelastic materials can be coated on soft elastic substrates, thereby reducing their time-dependent effects. 

Strength and Stiffness. Thermoplastic materials are viscoelastic which means that their mechanical properties reflect the characteristics of both viscous liquids and elastic solids. Thus when a thermoplastic is stressed it responds by exhibiting viscous flow (which dissipates energy) and by elastic displacement (which stores energy). The properties of viscoelastic materials are time, temperature and strain rate dependent. Nevertheless the conventional stress-strain test is frequently used to describe the (short-term) mechanical properties of plastics. It must be remembered, however, that as described in detail in Chapter 2 the information obtained from such tests may only be used for an initial sorting of materials. It is not suitable, or intended, to provide design data which must usually be obtained from long term tests. 

It is apparent therefore that the Superposition Principle is a convenient method of analysing complex stress systems. However, it should not be forgotten that the principle is based on the assumption of linear viscoelasticity which is quite inapplicable at the higher stress levels and the accuracy of the predictions will reflect the accuracy with which the equation for modulus (equation (2.33)) fits the experimental creep data for the material. In Examples (2.13) and (2.14) a simple equation for modulus was selected in order to illustrate the method of solution. More accurate predictions could have been made if the modulus equation for the combined Maxwell/Kelvin model or the Standard Linear Solid had been used. 

To complete the mechanical response description in this book, the phenomena of viscoelasticity, spall (dynamic tensile behavior), melting, and compression of porous solids are briefly considered. 

Fig. 2.18. Polymeric solids are observed to respond to shock compression in a viscoelastic behavior. The figure shows a transmitted wave profile in UVIIA PMMA as measured with an imbedded VISAR mirror. Note that the early shock is followed by a rapid relaxation to a higher velocity, and a slow relaxation to higher velocities, (after Schuler and Nunziato [74S01]).

DavkJ Ford Sims, Viscoelastic Creep and Relaxation Behavior of Laminated Composite Plates, Ph.O. dissertation. Department of Mechanical Engineering and Solid Mechanics Center, Institute of Technology, Southern Methodist University, Dallas, Texas, 1972. (Also available from Xerox University Microfilms as Order 72-27,298.)... 

In the preparation and processing of ionomers, plasticizers may be added to reduce viscosity at elevated temperatures and to permit easier processing. These plasticizers have an effect, as well, on the mechanical properties, both in the rubbery state and in the glassy state these effects depend on the composition of the ionomer, the polar or nonpolar nature of the plasticizer and on the concentration. Many studies have been carried out on plasticized ionomers and on the influence of plasticizer on viscoelastic and relaxation behavior and a review of this subject has been given 119]. However, there is still relatively little information on effects of plasticizer type and concentration on specific mechanical properties of ionomers in the glassy state or solid state. 

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