Tetrakaidecahedron model

Shear stress for three-dimensional foams using the Kelvin s tetrakaidecahedron model is given in [29], The value of Young s modulus (modulus of extension) was calculated to be... 

Figure 10.14 (a) Tetrakaidecahedron model of intermediate-stage sintering, b) Expanded view of one of the cylindrical pore channels. The vacancies can diffuse down the grain boundary (dashed arrow) or through the bulk (solid arrows). Note that in both cases the vacancies are annihilated at the grain boundaries. 

Sullivan, Roy M., Louis J. Ghosn, and Bradley A. Lerch, "A general tetrakaidecahedron model for open-celled foams," International Journal of Solids and Structures, voL 45, no. 6, pp. 1754-1765,2008. 

Pentagonal dodecahedron [76-80], compact tetradecahedron [73,80,82] and minimal tetrakaidecahedron [67,68] are most often used as models of foam cells in the calculation of foam electrical conductivity and hydroconductivity, foam dispersity and in the process of adsorption accumulation of foam. 

Figure 9-33a shows the predicted shear stress as a function of strain for the initial foam orientation depicted in Fig. 9-32. The stress grows continuously until at y = 1.15 a T1 reorganization occurs which brings the cell structure back to its starting state, and the stress jumps back to zero. Thereafter, the stress history repeats itself. Similar periodic stress patterns and stress jumps have been predicted for the three-dimensional tetrakaidecahedron foam model (Reinelt 1993). If the initial orientation is rotated through an angle of r/12 with respect to that shown in Fig. 9-32, the stress history also has jumps, but is aperiodic (see Fig. 9-33b). Aperiodic behavior is the norm, and periodic stress histories occur only for special initial orientations (Kraynik and Hansen 1986). These unsteady, discontinuous stress...

At high shear rates in some systems, the onions become large and very monodisperse in size, and they then order into a macrocrystalline packing. At rest, it is clear that the onions are not spherical, but polyhedral, because they must fill space. In the perfectly ordered macrocrystalline state, the typical shape of the space-filling onions appears to be that of the Kelvin tetrakaidecahedron, which is a model structure for liquid foams (see Section 9.5.1). These well-defined MLVs might be important as encapsulants in the pharmaceutical or cosmetics industries (Roux and Diat 1992). 

It was repeatedly proposed to use Kelvin s tetrakaidecahedron (that is, minimal truncated octahedron) [381, 407, 479] with eight hexagonal and six quadrangular faces as the polyhedral model of a foam cell and of a cell of any three-dimensional biological tissue. Note, however, that it was statistically shown [195] that Kelvin s tetrakaidecahedron is encountered in biological tissues among other tetrakaidecahedral cells only in 10% of the cases. 

This compares to values of 1.0990 for the planar tetrakaidecahedron 1.1053 for the rhombic dodecahedron and 1.0984 for the regular pentagonal dodecahedron. The latter - though often considered as a unit cell in foam modeling - is not really a viable candidate either, as it not only violates Plateau s laws but is also not space filling.)... 

For the final stage sintering models, the powder system is treated as an array of equalsized tetrakaidecahedra with spherical pores with the same size located at the comers, as shown in Fig. 5.15d. The tetrakaidecahedron has 24 pores, with one at each comer. Because each pore is shared by four tetrakaidecahedra, the pore volume for every one tetrakaidecahedron is Vp = (24/4)(4/3)a r, with r being the radius of the pore. According to Eq. (5.153), the porosity per tetrakaidecahedron is given by... 

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