ELASTIC PROPERTIES Subject

Many materials of practical interest (such as polymer solutions and melts, foodstuffs, and biological fluids) exhibit viscoelastic characteristics they have some ability to store and recover shear energy and therefore show some of the properties of both a solid and a liquid. Thus a solid may be subject to creep and a fluid may exhibit elastic properties. Several phenomena ascribed to fluid elasticity including die swell, rod climbing (Weissenberg effect), the tubeless siphon, bouncing of a sphere, and the development of secondary flow patterns at low Reynolds numbers, have recently been illustrated in an excellent photographic study(18). Two common and easily observable examples of viscoelastic behaviour in a liquid are ... 

We have discussed the value of struts or columns in structural mechanics and described their linear elastic properties. They have another characteristic that is not quite so obvious. When columns are subject to a compressive load, they are subject to buckling. A column will compress under load until a critical load is reached. Beyond this load the column becomes unstable and lateral deformations can grow without bound. For thin columns, Euler showed that the critical force that causes a column to buckle is given by... 

The coefficients Aj and. 44 are complex functions of the elastic properties and geometric factors of the constituents and are given in Appendix D. The solution for Eq. (4.118) is subjected to the following boundary conditions assuming an unbonded cross-section of the embedded fiber end... 

In spite of their long history, reinforcement mechanisms and elastic properties of elastomers remain the subject of numerous experimental investigations 111 116>, but... 

In Section 3.2.4 we considered the effects of an ideal mass layer on SAW response. In the model used to derive the mass-loading response, the layer was assumed to be (1) infinitesimally thick, and (2) subject only to translational motion by the SAW. Translational motion was found to induce a change in SAW velocity proportional to the areal mass density (pfc) contributed by the film — the mass loading response. Since no power dissipation arises in film translation, no attenuation response was predicted. With an actual film having finite thickness and elastic properties, it is important to also consider the effects of SAW-induced film deformation. Energy storage and power dissipation due to film deformation cause additional contributions to SAW velocity and attenuation that were neglected in the earlier treatment. 

Of course, we haven t explained precisely what we mean by viscoelasticity yet and we won t for a while. We are going to approach the subject in the conventional way, first by looking at the elastic properties of polymer solids, then the rheological properties of polymer melts. This will remind you of some basic stuff you should know, but may have forgot, or, if you ve been really sneaky, managed to avoid altogether. 

There is evidence that natural rubber was used by early Americans to make rubber balls over 2000 years ago. However, it has only been since the early twentieth century that rubber has become crucial to maintaining our standard of living in our current technology-based society. Synthetic rubbers, or elastomers as any artificial substance with elastic properties is called, have been a subject of intense research since the late 1800s. These materials were critically needed in the first half of the twentieth century to replace natural rubber in the tires for the newly invented automobile, due to shortages of natural rubber caused by wars. 

These materials exhibit both viscous and elastic properties. In a purely Hookean elastic solid, the stress corresponding to a given strain is independent of time, whereas for viscoelastic substances the stress will gradually dissipate. In contrast to purely viscous liquids, on the other hand, viscoelastic fluids flow when subjected to stress, but part of their deformation is gradually recovered upon removal of the stress. 

Acoustic and elastic properties are directly concerned with seismic wave propagation in marine sediments. They encompass P- and S-wave velocity and attenuation and elastic moduli of the sediment frame and wet sediment. The most important parameter which controls size and resolution of sedimentary structures by seismic studies is the frequency content of the source signal. If the dominant frequency and bandwidth are high, fine-scale structures associated with pore space and grain size distribution affect the elastic wave propagation. This is subject of ultrasonic transmission measurements on sediment cores (Sects. 2.4 and 2.5). At lower frequencies larger scale features like interfaces with different physical properties above and below and bed-forms like mud waves, erosion zones and ehatmel levee systems are the dominant structures imaged... 

Abstract We analyse the effect of thermal contraction of rock on fracture permeability. The analysis is carried out by using a 2D FEM code which can treat the coupled problem of fluid flow in fractures, elastic and thermal deformation of rock and heat transfer. In the analysis, we assume high-temperature rock with a uniformly-distributed fracture network. The rock is subjected to in-situ confining stresses. Under the conditions, low-temperature fluid is injected into the fracture network. Our results show that even under confining environment, the considerable increase in fracture permeability appears due to thermal deformation of rock, which is caused by the difference in temperature of rock and injected fluid. However, for the increase of fracture permeability, the temperature difference is necessary to be larger than a critical value, STc, which is given as a function of in-situ stresses, pore pressure and elastic properties of rock. 

Since treatments of the elastic properties of crystals are often very brief, or at best limited to a discussion of cubic crystals, let us begin by giving a short review of this subject as it applies to hexagonal crystals like ice. We shall follow the development given by Nye (1957), to whose book the reader is referred for a fuller treatment. 

Materials reveal their mechanical properties when subjected to forces. The apphcation of a force results in a deformation. The amount of deformation will depend on the magnitude of the force and its direction measured with respect to the crystallographic axes. Both force and deformation are vector quantities. In the discussion below, it will be assumed that all materials are isotropic in this respect and that there is no crystallographic relationship between force and deformation, which are both presumed to be scalars (numbers. See section S4.13). In fact, in much of the discussion, especially of the elastic properties of sohds, the atomic structure is ignored, and the sohds are treated as if they were continuous. This viewpoint caimot explain plastic deformation, and knowledge of the crystal structure of the sohd is needed to understand the... 

The self-consistent method is based on a classical solution of Eshelby (1957) that spawned a remarkably large number of different apphcations. It states that for an ellipsoidal isotropic elastic inclusion in an infinite elastic medium of different but uniform isotropic elastic properties the state of stress (or strain) inside the inclusion is uniform when the distant body is subjected to a uniform stress (or strain). 

The correspondence principle states that for problems of a statically determinate nature involving bodies of viscoelastic materials subjected to boundary forces and moments, which are applied initially and then held constant, the distribution of stresses in the body can be obtained from corresponding linear elastic solutions for the same body subjected to the same sets of boundary forces and moments. This is because the equations of equilibrium and compatibility that are satisfied by the linear elastic solution subject to the same force and moment boundary conditions of the viscoelastic body will also be satisfied by the linear viscoelastic body. Then the displacement field and the strains derivable from the stresses in the linear elastic body would correspond to the velocity field and strain rates in the linear viscoelastic body derivable from the same stresses. The actual displacements and strains in the linear viscoelastic body at any given time after the application of the forces and moments can then be obtained through the use of the shift properties of the relaxation moduli of the viscoelastic body. Below we furnish a simple example. 

---