Distortions elastic properties

Mechanical properties relate a material s resistance to imposed loads (i.e., forces). Mechanical properties include (1) measures of resistance to deformations and distortions (elastic properties), (2)... 

Fedders and Muller (213) have derived an estimate of the solid-inter-action parameter from another point of view, which ascribes the mixing enthalpy to bond distortions associated with the alloy formation and relates these distortions to the macroscopic elastic properties of the crystal. They concluded that the results based on elastic-crystal parameters yield a similar form for the thermodynamic properties as those estimated by DLP model based on optical-crystal parameters. 

The viscoelastic fluids represent the 3rd material dass of non-Newtonian fluids. Many liquids also possess elastic properties in addition to viscous properties. This means that the distortion work resulting from a stress is not completely irreversibly converted into frictional heat, but is stored partly elastically and reversibly. In this sense, they are similar to solid bodies. The liquid strains give way to the mechanical shear stress as do elastic bonds by contracting. This is shown in shear experiments (Fig. 1.27) as a restoring force acting against the shear force which, at the sudden ending of the effect of force, moves back the plate to a certain extent. 

Timgsten has been of keen theoretical interest for electron band-structure calculations [1.14-1.25], not only because of its important technical use but also because it exhibits many interesting properties. Density functional theory [1.11], based on the at initio (nonempirical) principle, was used to determine the electronic part of the total energy of the metal and its cohesive energy on a strict quantitative level. It provides information on structural and elastic properties of the metal, such as the lattice parameter, the equilibrium volume, the bulk modulus, and the elastic constants. Investigations have been performed for both the stable (bcc) as well as hypothetical lattice configurations (fee, hep, tetragonal distortion). 

Ab Initio Calculations of Structural and Elastic Properties. Equilibrium lattice constants, equilibrium volumes, as well as bulk and shear moduli can be assessed based on ab initio electron-structure calculations. They are obtained from the calculated total energies as a fimetion of volume in the bcc or fee crystal structure and from respective volume-conserving distortions of the lattice. In most cases, they agree well with experiments (Table 1.6). 

Crosslinking liquid crystalline polymers yield materials with exceptional properties due to the coupling between elastic properties and mesomorphous behavior. These compounds, especially the mesogenic elastomers, have attracted considerable attention in recent years. Like conventional elastomers, they can sustain very large deformations causing molecular extension and orientation, but they can also exhibit spontaneous distortions, some memory effects, an unusual mechanical response, and coupling between mechanical, optical and electric fields. 

Force is measured by converting the force into a displacement and measuring the displacement with a displacement sensor. The conversion takes place as a result of the elastic properties of a material on which the force is applied. This force distorts the material s shape, and this distortion can be measured... 

As already mentioned, for the fixed direction of the nematic director n the shear modulus is absent because the shear distortion is not coupled to stress due to the material slippage upon a translation. The compressibility modulus B is the same as for the isotropic liquid. New feature in the elastic properties originates from the spatial dependence of the orientational part of the order parameter tensor, i.e. director n(r). It is assumed that the modulus S of the order parameter Qij r) is unchanged. In Fig. 8.4 we can see the difference between the translation and rotation distortion of a nematic. 

When rubber is used as the sealing material it is its elastic properties which are particularly important, since the distorted rubber exerts a pressure on the contacting surface to maintain the seal. Unfortunately, no rubber is perfectly elastic and the stress in rubber decays or relaxes with time. This stress relaxation can be measured directly, or its existence can be implied through the measurement of permanent deformation acquired by the rubber when subjected to a constant strain for a given period of time. This property is known as the compression set or permanent set of the rubber. 

In the smectic A phase the director is always perpendicular to the plane of the smectic layers. Thus, only the splay distortion leaves the interlayer distance unchanged [7], and only the elastic modulus K i is finite while K22 and Kzz diverge when approaching the smectic A phase from the nematic phase. On the other hand, the compressibility of the layered structure and the corresponding elastic modulus B is taken into account when discussing the elastic properties of smectic phases. The free energy density for the smectic A phase, subjected to the action of an external electric field, is... 

One application of the stress theorem is the study of elastic properties of solids, which becomes straightforward when a suitable finite macroscopic strain is applied to the solid. When the wavefunctions of the distorted solid are known, the stress tensor is evaluated with the stress theorem. In the harmonic approximation elastic constants are defined as the ratio of stress to strain, and it is furthermore possible to go to large strains to obtain all nonlinear elastic properties. In general it is necessary to be concerned with internal strains that may appear microscopically owing to the lower symmetry of the strained solid. In section 6 we show in detail how this problem is solved by combining the stress and force theorems. 

A polymer responds to a pulling force (tensile stress) by being stretched (tensile strain). The mechanical properties of a polymer can be described partly by the values derived from the tensile stress-strain curve (Figure 2.10). Polymers are viscoelastic materials - that is, they can behave simultaneously as liquids with viscous flow and as elastic solids. When a polymer is stretched, the sample goes throngh varions stages. The first part of the curve describes the elastic properties of the polymer, when the sample can be stretched without permanent distortion. 

The mechanical properties of a polymer sample are determined by many factors. Resins vary from extremely flexible but shong rubbers to brittle weak materials such as the natural resins (Figure 2.11). Contrasts can be made in the ability to be stretched without permanent distortion (elasticity of cross-linked rubber), in the distortion caused by stretching (polyethene distorts if stfetched... 

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