Green elastic

H. Hagimara and D.J. Green, "Elastic Behavior of Open-Cell Alumina," J. 

The simplest (and weakest ) definition of an elastic material is one for which the stress depends only on the current strain these materials are termed Cauchy elastic. A subset of these materials is occupied by those for which the strain energy depends only on the current strain. These are termed Green elastic or hyperelastic and for these the strain energy is a function of the current strain only, and fully defines the material behaviour. For Cauchy... 

When it is assumed, as is usually done, that the stiffiiess and compliance tensors are additionally symmetric with respect to their diagonals, the total number of independent components is reduced from 36 to 21 (so-called Green elasticity or hyperelasticity, in contrast to the so-called Cauchy elasticity, where this is not the case). Thus in the most general case of well-defined anisotropy (triclinic monociystals) the (6 x 6) stiffness or compliance matrices or, alternatively, the fourth-order stiffness or compliance tensors, have 36 elastic constants or coefficients, respectively, 21 of which can be assumed to be independent, cf. [Pabst Gregorova 2003a]. For reasons of convenience we confine ourselves to the stiffiiess matrices in the sequel. It is understood, however, that completely analogous relations and symmetry considerations are valid in the case of the compliance matrices. 

For the off-diagonal elements in this stiffness matrix and the following ones we automatically assume validity of the symmetry condition for Green elasticity (hyperelasticity),... 

The dynamical elastic and inelastic scattering ofhigh-energy electrons by solids may be described by three fundamental equations [5]. The first equation determines the wave amplitude G ( r, r, E), or the Green function, at point r due to a point source of electrons at r in the averaged potential (V (r)) ... 

Greene, Moursund, and Ross). Scattering, Elastic, of High-Energy Beams Repulsive 10 135... 

Fig. 5.2 Immunofluorescent demonstration of smooth muscle actin (FITC, green channel) in the blood vessel wall of the human kidney. Red autofluorescence of erythrocytes, elastic lamellae and kidney tubules was captured with a filter exciting the autofluorescence in red spectrum under a longer exposure than with the filter exciting specific fluorescence in the green spectrum. Nuclei are counterstained with DAPI (blue channel)...

Elastic Scattering in Chemically Reactive Systems (Greene, Moursund,... 

Greene, A., and A. Ciferri Elastic properties of networks formed from oriented chain molecules of fibrous natural rubber. Kolloid-Z. 186, 1 (1962). 

Milk fat plays a very important role in the development of texture in cheese. Reduced-fat cheeses tend to be firmer and more elastic than cheeses with a higher fat content. Undoubtedly the presence of a more dense protein matrix results in a firmer cheese. The precise role of fat in cheese texture is not well understood, since problems of increased firmness can be partially overcome by increasing the MNFS. Studies by Green et al (1981) on the texture of cheeses made from concentrated milk suggest a possible role of fat in cheese firmness. Reduced fat in the curd would result in a smaller fat-protein interfacial area and an increased separation between fat globules. The capacity of the fat and protein phases of cheese to move in relation to each other would be reduced and would consequently result in a firmer cheese. 

Viscoelastic properties of molten polymers conditioning the major regularities of polymer extension are usually explained within the framework of the network concept according to which the interaction of polymer molecules is localized in individual, spaced rather far apart, engagement nodes. The early network theories were developed by Green and Tobolsky 49) and stemmed from successful network theories of rubber elasticity. These theories were elaborated more fully in works by Lodge50) and Yamamoto S1). The major elasticity. These theories is their simplicity. However, they have a serious drawback the absence of molecular weight in the theory. 

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