Local deformation

It should be noted that the normality conditions, arising from the work assumption applied to inelastic loading, ensure the existence and uniqueness of solutions to initial/boundary value problems for inelastic materials undergoing small deformations. Uniqueness of solutions is not always desirable, however. Inelastic deformations often lead to instabilities such as localized deformations. It is quite possible that the work assumption, which is essentially a stability postulate, is too strong in these cases. Normality is a necessary condition for the work assumption. Instabilities, while they may occur in real deformations, are therefore likely to be associated with loss of normality and violation of the work assumption. 

Gupta and his students have developed procedures for determining the elastic and plastic contributions to shock-deformed metals. The work explicitly recognizes that the metal sample is an inclusion in a host material which may act to cause local deformation unique to the particular host [83G01, 87G01]. 

According to a large number of experimental studies, the most stable phologen-erated species in the lowest excited stales of conjugated chains are electron-hole pairs bound by Coulomb attraction and associated to a local deformation of the backbone, i.e., polaron-excilons [18]. A good insight into the properties of these species can be provided by quantum-chemical calculations our recent theoretical... 

The present review shows how the microhardness technique can be used to elucidate the dependence of a variety of local deformational processes upon polymer texture and morphology. Microhardness is a rather elusive quantity, that is really a combination of other mechanical properties. It is most suitably defined in terms of the pyramid indentation test. Hardness is primarily taken as a measure of the irreversible deformation mechanisms which characterize a polymeric material, though it also involves elastic and time dependent effects which depend on microstructural details. In isotropic lamellar polymers a hardness depression from ideal values, due to the finite crystal thickness, occurs. The interlamellar non-crystalline layer introduces an additional weak component which contributes further to a lowering of the hardness value. Annealing effects and chemical etching are shown to produce, on the contrary, a significant hardening of the material. The prevalent mechanisms for plastic deformation are proposed. Anisotropy behaviour for several oriented materials is critically discussed. 

When the polymeric material is compressed the local deformation beneath the indenter will consist of a complex combination of effects. The specific mechanism prevailing will depend on the strain field depth round the indenter and on the morphology of the polymer. According to the various mechanisms of the plastic deformation for semicrystalline polymers 40 the following effects may be anticipated ... 

The fact that crystalline polymers are multiphase materials has prompted a new approach in characterizing their internal structure (lamellar thickness, perfection, etc.) and relating it to the hardness concept (volume of material locally deformed under a point indenter). In lamellar PE microhardness is grossly a given increasing function of lamellar thickness. In using the composite concept care must be exercised to emphasize and properly account for the non-crystalline phase and its various... 

Much slower spreading occurs with the rubbery material, with approximately 30 minutes being necessary to achieve equilibrium. This is attributed to local deformation of the substrate leading to viscoelastic braking of the spreading of TCP. The hypothesis is corroborated by line a of Figure 7. This line has been obtained by plotting the difference be-... 

Inoue, K., Komatsu, S., Trinh, X. A., Norisuye, T. and Tran-Cong-Miyata, Q. (2005) Local deformation in photo-crosslinked polymer blends monitored by Mach-Zehnder interferometry. J. Polym. Sci. Part B Polym. Phys., 43, 2898-2913. 

Irregularities of a specimen s surface will result in local deformation with accompanying deformation hardening. This may lead to erroneous hardness numbers, although such errors may be small. 

On the surfaces of polished metallic glasses, very sharp, distinct offsets are observed at room temperature, indicating large and highly localized deformation that must be associated with the propagation of dislocations (Pampillo, 1972). The experimental observations have been reviewed by Li (1976). 

The linear model can be extended to include more distant neighbours and to three dimensions. Let us consider an elastic lattice wave with wave vector q. The collective vibrational modes of the lattice are illustrated in Figure 8.6. The formation of small local deformations (strain) in the direction of the incoming wave gives rise to stresses in the same direction (upper part of Figure 8.6) but also perpendicular (lower part of Figure 8.6) to the incoming wave because of the elasticity of the material. The cohesive forces between the atoms then transport the deformation of the lattice to the... 

As suggested before, the role of the interphasial double layer is insignificant in many transport processes that are involved with the supply of components from the bulk of the medium towards the biosurface. The thickness of the electric double layer is so small compared with that of the diffusion layer 8 that the very local deformation of the concentration profiles does not really alter the flux. Hence, in most analyses of diffusive mass transport one does not find any electric double layer terms. For the kinetics of the interphasial processes, this is completely different. Rate constants for chemical reactions or permeation steps are usually heavily dependent on the local conditions. Like in electrochemical processes, two elements are of great importance the local electric field which affects rates of transfer of charged species (the actual potential comes into play in the case of redox reactions), and the local activities... 

Amorphous adsorbents, 1 587-589 for gas separation, 1 631 properties and applications, l 587t Amorphous aluminum hydroxide, 23 76 Amorphous carbohydrates, material science of, 11 530-536 Amorphous carbon, 4 735 Amorphous cellulose, 5 372-373 Amorphous films, in OLEDs, 22 215 Amorphous germanium (a-Ge), 22 128 Amorphous glassy polymers, localized deformation mechanisms in, 20 350-351... 

Some protuberances may be created on a droplet surface due to local deformations. Under favorable conditions, these bulges detach from the droplet and disintegrate into smaller droplets. 

These and other experiments imply that even reactions that proceed via bulky transition states can take place in the clathrate if the initiation is photochemical, perhaps as a result of local deformation of the host lattice, and presumably as a result of the large energy dissipation involved. However, even here there is some lattice control of the reaction pathway. 

Creep recovery response is due to freezing in local deformation of the polymer molecules when the polymer cools rapidly. The polymer molecules are frozen into shapes that distort their Gaussian spherical equilibrium shape. If the polymer is heated or allowed to relax over a very long time there will be dimensional changes as the polymer molecules assume their thermodynamic equilibrium states (Gaussian spherical equilibrium shape). 

This model (liyama, 1974) can be applied whenever trace-carrier substitution takes place in a single site within the crystal. According to this model, when trace element A substitutes for carrier B in a given lattice position, it causes local deformation of the structure in the neighborhood of the site where substitution takes place. This deformation, which increases as the crystal-chemical properties of trace element and carrier differ, prevents further substitutions from occurring in the vicinity of the site. A forbidden zone of r sites is thus created, clearly modifying the configurational properties of the phase. 

The term hardness is a relative term. Hardness is the resistance to local deformation that is often measured as the ease or difficulty for a material to be scratched, indented, marred, cut, drilled, or abraded. It involves a number of interrelated properties such as yield strength and elastic modulus. Because polymers present such a range of behavior, as they are viscoelastic... 

Dinner, A.R. Local deformations of polymers with nonplanar rigid main-chain internal coordinates. J. Comput. Chem. 2000, 21, 1132 14. 

In a hydrodynamic theory of the free, clean, surface of a turbulent liquid, Levich 19a) postulates that there exists an upper zone of liquid, of thickness X, in which the turbulent regime is so altered by the surface tension (which opposes local deformations) that within this zone the turbulence is severely damped. Right in the plane of the surface (at... 

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