Elasticity modulus definition

From these definitions one may corroborate the intention of HTS in chemistry and materials science. The total speed-up factor of this part of the R D (Research and Development) process, as stated earlier, is between 5 and 50, but contrary to most of the pharma applications true (semi-) quantitative answers will result. As a result, this approach is essentially applicable in any segment of R D. On the other hand, this approach requires methods of experimentation that have almost the same if not the same accuracy as in the traditional one-experiment-at-the time approach. This is key as (i) in process optimisation accuracy is key and (ii) in research, also in academic research, accuracy is important as some polymer properties do not span a wide range of values (e.g., the elastic modulus of amorphous polymers) or may depend critically on molecular weight distribution or molecular order. 

Actually, crosslinks control the molecular packing and indeed significantly affect the elastic modulus of the material. As the intermolecular energy of kink formation is also determined by elastic modulus, the yield stress will definitely vary with modulus and thus the cross -linking density. In other words, crosslinks may not seriously affect the activation segment configuration in the molecular chain but will indirectly control the yield stress. 

Note 1 The detailed definitions of K, E and G are given in Definitions 4.5, 4.7 and 4.10. Note 2 An elastic modulus or modulus of elasticity is a modulus of a body which obeys... 

According to the ASTM D-883 definition, a plasticizer is a material incorporated into a plastic to increase its workability and flexibility or dispensability. The addition of a plasticizer may lower the melt viscosity, elastic modulus, and Tg. 

However, in contrast to the cases of complex elastic modulus G and dielectric constant e, the imaginary part of the piezoelectric constant, e", does not necessarily imply an energy loss (Holland, 1967). In the former two, G"/G and e"/e express the ratio of energy dissipation per cycle to the total stored energy, but e"/e does not have such a meaning because the piezoelectric effect is a cross-coupling effect between elastic and electric freedoms. As a consequence, e" is not a positive definite quantity in contrast to G" and e". In a similar way to e, however, the Kramers-Kronig relations (Landau and Lifshitz, 1958) hold for e ... 

According with their definition the elastic modulus take into account the stress necessary to produce an unitary lengthening and the docility the strain produced due to the application of a unity stress [1-7]. 

Thus, E of the bulk solution can be used to predict the elasticity modulus of films at a definite thickness and bulk concentration. 

One of the basic mechanical properties of the foam is its compressibility (elasticity). By definition the bulk modulus of elasticity Ev is expressed by... 

In each case the attenuation of sound can be formally represented by defining a complex wavenumber, where the sound attenuation coefficient is the imaginary part of the wavenumber. The complex wavenumber also leads to the definition of a complex sound speed and a complex dynamic elastic modulus. 

In real food polymers, a distinction can be made between a viscoelastic solid, which contains some cross-links that are permanent, and a viscoelastic liquid, where, under the influence of stress, the relative movement of whole molecules will be observed. As shown in Figure 8.9, in the case of a viscoelastic solid, after application of the stress, the strain will eventually reach a constant value, and upon removal of the stress, the strain will finally return to the remaining value of food primary energy, which was not entirely dissipated. For a viscoelastic liquid, a permanent deformation will remain after removal of the stress. In the stress relaxation area, the deformation value will decay to zero for a viscoelastic liquid, whereas for a solid, it will reach a constant, nonzero value. It can also be seen as either a decreased value to the zero or a constant, nonzero value, as pointed out by the dashed line. Both values characterize the rheology parameters of foods under certain conditions. One of the reasons for this is that the factors of time-dependent foods are not necessarily related to their elastic modulus. This can be explained by the series of small deformations without rupture, which are dependent in different ways and are based on the primary molecular microstructure of foods. The time required for the stress to relax to a definite fraction of its initial value is the relaxation time. 

Tensile properties that are related to fiber stiffness can be used to measure the T of almost all fibers. The elastic modulus, that is, the sl pe of the Hookean region of the fiber stress-strain curve, is a measure of the fiber stiffness and can be used for T determination since, by definition, a glass is stlffer than rubber (Figure 6). Since the transition from a glassy to a rubbery state Involves a reduction in stiffness, the temperature at which the modulus is abruptly lowered is taken as... 

Before describing this test in more detail it might be of interest to compare the various definitions relevant to elastic modulus given in ASTM D 4848-94a. BS 4029, 1978, and Textile Terms and Definitions [1],... 

The spatially reduced property of the system is the elasticity modulus, which is an operator in the general case. This is a specific property in a system with three dimensions of space, which links the relative elongation to the stress (superficial force) according to the definition of the capacitive relationship. 

Elastic modulus is a quantitative measure of the stiffness or rigidity of a material. For example, for homogeneous isotropic substances in tension, the strain (e) is related to the applied stress (o) by the equation E = o/e, where E is defined as the elastic modulus. A similar definition of shear modulus (g) applies when the strain is shear. 

---