Non-homogeneous deformation

In order to point out the essential difference between deformations induced by body forces and surface tractions we recall Ericksen s theorem [88]. The theorem states that homogeneous deformations are the only deformations that can be achieved by the application of surface tractions alone, considering a homogeneous and isotropic material characterized by an arbitrary strain-energy function. In other words, we cannot induce diverse non-homogeneous deformations with surface tractions. In contrast to surface tractions, application of fields that act as body forces leads to non-homogeneous deformations without any additional constraints for the material. 

The experimental values of yield strain, Ey, are shown in Fig. 3. The experimentaly measured strains are higher than the theoretically predicted ones and increase in the following order SIC, TTS, and no treatment. This effect should be attributed to some non-homogeneous deformation mechanism. The yielding phenomenon in ductile filled polymers is often attributed to a crazing effect or to a de-wetting... 

The appearance of a fracture surface undoubtedly is the most convincing evidence that the fracture process has reached the phase of non-homogeneous deformation. 

X. Badiche, S. Forest, T. Guibert, Y. Bienvenu, J.D. Baitout, P. lenny, M. Croset, H. Bemet, Mechanical properties and non-homogeneous deformation of open-cell nickel foams application of the mechanics of cellular solids and of porous materials. Mater. Sci. Eng. A 289(1-2), 276-288 (2000)... 

Figure 1. Uniaxial Extension of a Non-Homogeneous Sample. The figure shows simulation results for uniaxial extension of an initially (a) square sample whose orientation is primarily left-to-right, except for the central cross-shaped region, which is isotropic. After 25% stretching (b), the cross-shaped region is deformed more than the surrounding tissue, with roughly a 5% greater increase in area.

In the extruder, not only shear flow is present, but also extensional flow occurs as well. This is illustrated in Fig. 3.20 for the deformation of a fluid element. Wherever cross-sections narrow, such as at the tips or between kneading blocks and the wall, the fluid elements are compressed and extended. This effect is particularly relevant for non-homogenous polymer melts, e.g., immiscible blends, in which the disperse phase can be split by extensional deformation. For more details, see Chapter 9. 

Frozen-in stresses due to molecular orientation may also be measured by this technique, since oriented polymers shrink rapidly above the softening temperature. Non-homogeneously oriented parts cause deformations. 

McCulloch, A.D. and Omens, I.H., Non-homogeneous analysis of three-dimensional transmural finite deformations in canine ventricular myocardium, /. Biomech., 24,539-548,1991. 

In homogeneous, non-localized deformation of a rigid plastic solid as idealized here. 

M.F. Ashby, Deformation of plastically non-homogeneous materials. Phil. Mag. 21(170),... 

There have been various models and mechanisms proposed for the Mullins Effect . Bueche proposed a model based on chains failing due to physically non-homogeneous local deformations [7,8]. His... 

In these assumptions physically non-homogeneous local deformations, a non-linear stress-strain law for each element, and the possibility of having some of the elements fail have all been taken into account. Since the desired end result of this work is accurate constitutive relations for materials exhibiting permanent memory phenomena that can be used in engineering analysis, emphasis will be placed on the behavior of elements, not necessarily on polymer thains. The resulting equations appear to be of value for describing many materials, not only amorphous polymers. 

If a semicrystalline microfibril is subjected to stresses, the resulting deformation will be non-homogeneous at the molecular level. The bulk of the deformation will be born by the amorphous regions. As discussed in Chapter 5 the largest stresses are transferred upon extended chain segments which share the strain imparted onto an amorphous region. The stress induced scission of chains must, therefore, be expected to occur within the amorphous regions. 

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