Unit Cell Models

Neal and Nader [260] considered diffusion in homogeneous isotropic medium composed of randomly placed impermeable spherical particles. They solved steady-state diffusion problems in a unit cell consisting of a spherical particle placed in a concentric shell and the exterior of the unit cell modeled as a homogeneous media characterized by one parameter, the porosity. By equating the fluxes in the unit cell and at the exterior and applying the definition of porosity, they obtained... 

Fig.20 Top row single unit-cell models of core-shell double gyroid (Q230), orthorhombic (O70), and alternating gyroid (Q214) cross-sectioned to reveal interfacial configuration. Bottom row. direct projections of cross-sectioned interfaces. Sketches of PI-fi-PS-fi-PEO chains show how each morphology is assembled. Projections appear to scale that is, the core-shell double gyroid unit cell is roughly twice the thickness of the other two. From [75], Copyright 2004 American Chemical Society...

It is interesting to note that in their first paper on cellulose (11) Meyer and Mark proposed a structural unit cell model which is classic and accepted, for the largest part, even today. They proposed a cellulose crystallite in which all... 

Figure 5.23. (a) HRTEM profile image of a CO-reacted Cu-Pd particle indicating a Pd surface. Inset Pd surface with simulated image. The flat surfaces (at B) are (100) the stepped ones (D) are (110). Away from the surface the structure has equal Cu and Pd (inset enlarged area A with image simulation), (b) Extended unit cell model used for image simulations, (a = 0.3 nm.) It minimizes wrap-around effects. 

Test Matrix for Parametric Study with Transient Filtration Unit-cell Model... 

The reconstructed digital materials previously mentioned are another way to simulate soot deposition apart from the unit-cell models. An example of soot deposition in such a digital material (reconstructed with a process-based algorithm that creates and sinters grains from a pre-computed grain library ) is shown in Fig. 19(a). As time passes the transition from deep bed to cake filtration as the top regions of the filter gets filled with soot is evident in... 

Ferguson J.R., 1992, SOFC two dimensional unit cell modeling. SOFC Stack Design Tool, International Energy Agency Final Report. 

The elasto plastic behavior of a compositionally graded metal-ceramic structure is investigated. The deformation under uniaxial loading is predicted using both an incremental Mori-Tanaka method and periodic as well as random microstructure extended unit cell approaches. The latter are able to give an accurate description of the local microfields within the phases. Furthermore, the random microstructure unit cell model can represent the interwoven structure at volume fractions close to 50%. Due to the high computational costs, such unit cell analyses are restricted to two-dimensional considerations. 

Figure 2. Predicted axial strain response for the extended unit cell models and the corresponding incremental Mori-Tanaka approach (IMT) the matrix of the center sublayer being nickel (Ni) or alumina (A1203)...

The periodic unit cell results are directly comparable to the IMT predictions, because both approaches represent the same matrix/inclusion type microstructure. However, such comparisons have to be done carefully since some assumptions regarding the finite element calculations are not equivalent for the extended unit cell approaches and the present mean-field method. The plane stress analysis of the unit cell models does not take into account the constraints in the out-of-plane direction. In contrast, within the present IMT formulation the inclusions are enclosed three-dimensionally by the matrix material. In contrast to the plane stress unit cell models, the constraint in the out-of plane direction is accounted for. Accordingly, these predictions are denoted as full internal constraint. To overcome this internal constraint in order to simulate the plane stress model assump-... 

The deformation behavior of a compositionally graded metal-ceramic structure has been investigated by numerical and (semi)analytical simulations. Random microstructure models are able to predict the response of an FGM-structure in a more accurate way than the other approaches. The interwoven structure in the middle of the FGM can be accounted for using this modeling strategy. For the extended periodic unit cell models the predicted stress strain response depends strongly on the micro-arrangement of the inclusions. Detailed information on the microfields of the stresses and strains can only be obtained by the extended unit cell models. The incremental Mori-Tanaka method... 

Figure 3.9. Section view of unit cell model displaying void growth around a particle at macroscopic longitudinal strains of (a) 0, (b) 0.1 and (c) 0.6. [Adapted, by permission, from Ognedal, A. S., Clausen, A. H., Berstad, T, Seeling, T., Hopperstad, O. S.,Int. J. Solids Structures, rapiess, 2014.]...

Figure 4.17 Equivalent two-layer unit cell model...

Fig. 19 Snapshots of coarse-grain unit cell model of PAAm and crosslinker mixture (left), and PAAm percolated structure after a few ns of MD-NVT (right)...

Based on the thin region model. Other results for the unit cell model. 

Figure 6.34. Mechanical modulus of various polymer blend phase arrangements. The cube shows a unit cell model of an idealized IPN structure. The shaded area is determined by upper- and lower-bound estimates for this model. " ...

Go to www.ibiblio.org/e-notes/Cryst/Cryst.htm using a compatible browser. Click on Face Centered Cubic (FCC) and view the interactive unit cell model, (a) Sketch the atom arrangement in the top layer, middle layer, and bottom layer. What do you observe about the arrangement of the atoms in each layer Which are the same (b) Rotate the model to view another face and redraw the atom arrangement on the three layers. Do you observe any difference ... 

In the unit cell model of HA, the distances between each clay mineral (i.e., the interlayer distance) and between the two stacks (i.e., the thickness of external water) strongly affects the calculated results. Note that the thickness of a clay mineral is... 

Fig. 10.5 A unit cell model of a stack of clay minerals...

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