Tetrakaidecahedral cell

The effect of gas compression on the uniaxial compression stress-strain curve of closed-cell polymer foams was analysed. The elastic contribution of cell faces to the compressive stress-strain curve is predicted quantitatively, and the effect on the initial Young s modulus is said to be large. The polymer contribution was analysed using a tetrakaidecahedral cell model. It is demonstrated that the cell faces contribute linearly to the Young s modulus, but compressive yielding involves non-linear viscoelastic deformation. 3 refs. 

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. 

Mills and Zhu (1999) developed the closed-cell and opened-cell foams using the BBC lattice tetrakaidecahedral cell model were as shown in Table 5.1 where 0s is the volume fraction of solids in the cell edges (Zhu et al. 1997a, b Mills and Zhu 1999). Roberts and Garboczi (2001, 2002) investigated the modulus for both opened-cell and closed-ceU foam stracture of random models based on Voronoi tessellations and level-cut Gaussian random fields for a closed-cell tetrakaidecahedral model shown in Fig. 5.2. Lu et al. (1999) proposed macro-mechanic model to evaluate the modulus for low porosity. 

Zhu, H.X., J.F. Knott, and N.J. Mills. 1997a. Analysis of the elastic properties of open-cell foams with tetrakaidecahedral cells. Journal of the Mechanics and Physics of Solids 45(3) 319-343. Zhu, H.X., N.J. Mills, and J.E. Knott. 1997b. Analysis of the high strain compression of open-cell foams. Journal of the Mechanics and Physics of Solids 45(11-12) 1875-1904. 

Glathrate Formation. Ethylene oxide forms a stable clathrate with water (20). It is non stoichiometric, with 6.38 to 6.80 molecules of ethylene oxide to 46 molecules of water iu the unit cell (37). The maximum observed melting poiat is 11.1°C. An x-ray stmcture of the clathrate revealed that it is a type I gas hydrate, with six equivalent tetrakaidecahedral (14-sided) cavities fully occupied by ethylene oxide, and two dodecahedral cavities 20—34% occupied (38). 

The total number of water molecules per unit-cell would be 46 and the number of available voids 8, i.e., 2 small and 6 slightly larger ones, located at the center of the dodecahedral and tetrakaidecahedral cages, respectively. These two kinds of voids could be fully or partially occupied by gas molecules and the corresponding formula would be Gg(H20)46 or G6(H20)46 if the smallest voids remained empty. The calculated H2O/G ratios of 5.75 and 7.67 were in good agreement with the experimental values. 

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