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Bulk tissues
Published in A. Šiber, P. Ziherl, Cellular Patterns, 2018
On a computer, one can mimic Marvin’s method even in a soap froth because the froth is most conveniently generated starting from a set of points in space put there using a suitable algorithm, and then partitioning the space based on this set. From an idealized perspective, Marvin’s non‐shaken samples were prepared by a protocol known as random sequential adsorption (RSA) where shots are added to an existing batch one at a time such that they do not overlap with those that are already there. This generally produces a looser, small‐density packing because it does not allow a given local configuration to rearrange so as to make space for an additional shot even if such a rearrangement required an allowed displacement of a single shot to a nearby unoccupied position. On the other hand, if the shots are first poured into the container and then shaken, they can move about so as to fill space more efficiently. This leads to a denser, more compact ensemble including the random close packing (RCP); we will refer to this method by this acronym. The two methods are easily implemented on a computer, the second one involving a suitable dynamics driven by, say, a thermostat.
Surfactant Self-Assembly at Interfaces and Its Relationship to Solution Self-Assembly
Published in Victor M. Starov, Nanoscience, 2010
Zbigniew Adamczyk, Magorzata Nattich, Anna Bratek
Accordingly, the organization of this chapter is the following. In the first section, theoretical models aimed at evaluation of the initial deposition rate (limiting flux) for homogeneous interfaces and various transport conditions are discussed. Illustrative theoretical results characterizing deposition regimes are presented, especially the analytical expressions for the limiting flux for various particle sizes, flow rate, and configuration. Particle deposition at heterogeneous surfaces, as well as the structure of particle monolayers and jamming coverage, is analyzed in terms of the random sequential adsorption (RSA) approach, whose range of validity is assessed using the limiting analytical solutions. Interesting theoretical results pertinent to multilayer deposition are also reviewed. In the case of heterogeneous surfaces, the dependence of the initial flux on site coverage, the topology of particle mono- and multilayers, the jamming (maximum) coverage, and the particle density distributions are analyzed.
Polymer Dynamics at Solid–Liquid Interfaces
Published in Michel Nardin, Eugène Papirer, Powders and Fibers, 2006
The amount of polyacrylamide adsorbed is shown by a symmetrical curve peaked at pH 4.5. The rate of establishment of the polyacrylamide layer at the aluminosilicate/water interface, determined at the maximal coverage, shows two kinetic regimes which were previously interpreted on the basis of the Langmuir model, assuming two types of kinetics to be operative [16]. The recent interpretation of the experimental result based on the kinetic model of de Gennes shows the apparent kinetics coefficient K(Ns) (mL/mol×min), which represents the instantaneous rate of adsorption to be a function of 1 – θ, θ being the relative surface coverage (Figure 14.2) [24,32]. Up to a degree of coverage θ close to 2/3, the rate of adsorption decreases (1 – θ) according to the Langmuir model or the random sequential adsorption (RSA) models. The rate of further adsorption accords to the theoretical model of de Gennes: () K(Ns)∝(1−θ)1.5
Experimental Evaluation of Fatigue Properties of Carbon Fiber/Epoxy Matrix Interface and Numerical Simulation of Transverse Cracking under Cyclic Load
Published in Advanced Composite Materials, 2023
Youzou Kitagawa, Keigo Sasaki, Masahiro Arai, Akinori Yoshimura, Keita Goto
Figure 13 shows the 2D representative volume element (RVE) of the CFRP 90 unidirectional laminate. The RVE model was generated based on the microstructure generation method consisting of random sequential adsorption [15] and explicit finite element analysis developed in our previous study [16]. The number of carbon fibers was 76 and the dimensions of the RVE model were 70 × 70 µm. The simulation was performed using ABAQUS Standard 2018. The RVE model was discretized using 4-node plane strain quadrilateral, reduced integration elements (CPE4R). The RVE contained approximately 60000 elements, and its fiber volume fraction was 59.60%. Periodic boundary conditions were imposed on the RVE by using the key degrees of freedom method [17].
Predictive abilities of pseudodiscretization and pseudograin discretization schemes of the Mori–Tanaka homogenization, benchmarked against real and virtual RVEs
Published in Mechanics of Advanced Materials and Structures, 2022
Deepjyoti Dhar, Stepan V. Lomov, Atul Jain
The microstructures considered in this article are generated using the Random Sequential Adsorption (RSA) algorithm [32]. Inclusions having an aspect ratio (AR) 3 are modeled as ellipsoids whereas inclusions with AR 15 are modeled as sphero-cylinders for ease of meshing. A minimum distance of 5% of the inclusion radius is maintained between the inclusions as recommended by Pierard et al. [8]. Periodic boundary conditions were applied to the three axes of the volume element (VE) cube to approximate an infinite VE as closely as possible [33]. The periodic structure of the cuboidal cells was ensured by splitting the ellipsoids intersecting the edge of the cube into an appropriate number of parts which were then copied to the opposite face of the cube. Three faces of the cube were then meshed and then copied to the corresponding opposite face to ensure identical meshes on opposite faces. Periodic boundary conditions were applied to the cubic cell by applying Eq. (12).
Evaluation of the in-situ damage and strength properties of thin-ply CFRP laminates by micro-scale finite element analysis
Published in Advanced Composite Materials, 2020
R. Higuchi, R. Aoki, T. Yokozeki, T. Okabe
In the micro-scale simulation, the RVE considering the effect of ply thickness was established. The following is an explanation of the RVE of cross-ply laminates as a simple example. To capture damage initiation and propagation in 90° ply in the cross-ply laminate, the randomness of fiber position in 90° ply, and the constraint effect from neighboring 0° ply should be taken into account. Therefore, the fibers were individually modeled in 90° ply and their positions were determined by using the random sequential adsorption algorithm proposed by Rintoul and Torquato [26]. Additionally, the homogeneous neighboring 0° plies were modeled by the shell element and connected with the 90° ply by a cohesive element. While the solid element was used for 0° ply in Ref [19,20], this study employs the shell element to deal with the in-situ strength in an arbitrary ply of the arbitrary stacking sequence by changing the stiffness of the shell element using the classical lamination theory. Figure 1 illustrates the established RVE for cross-ply laminates. This study employs the global coordinate system x1 –x2 –x3 shown in Figure 1. Here, x1, x2, and x3 are along the longitudinal, the in-plane transverse, and the out-of-plane transverse directions of the 90° ply. The RVE size is 0.18 mm in the x2 direction and 0.001 mm in the x1 direction. Furthermore, the periodic boundary conditions (PBCs) described in Section 2.2 were applied in the x1 and x2 directions.