Multiscale properties, analysis

Abstract We here treat a diffusion problem coupled with water flow in bentonite. The remarkable behavior originates from molecular characteristics of its constituent clay mineral, namely montmorillonite, and we show the behavior based on a unified simulation procedure starting with the molecular dynamic (MD) method and extending the obtained local characteristics to a macroscale behavior by the multiscale homogenization analysis (HA Sanchez-Palencia. 1980). Not only the macroscale effective diffusion property but also the adsorption behavior is well defined based on this method. 

For characterizing the microstructure we use a confocal laser scanning microscope (CLSM). By CLSM we can specify a 3-D configuration under atmospheric condition. Smectite minerals are extremely fine and poorly crystallized, so it is difficult to determine the properties by experiment. We inquire into the physicochemical properties by a molecular dynamics (MD) simulation method. Then, we develop a multiscale homogenization analysis (HA) method to extend the microscopic characteristics to the macroscopic behavior. We show numerical examples of a coupled water-flow and diffusion problem. 

We here showed that for bentonite clay, we can determine the nano-scale material properties such as diffusion coefficient and viscosity by molecular dynamics (MD) simulation and extend the microscale characteristics to the macroscale behavior by the multiscale homogenization analysis (HA) method. A seepage flow and diffusion problem is treated. The micro/macro problem can be simulated well by this procedure if we know the microscale geometrical characteristics. 

With the advent of nanomaterials, different types of polymer-based composites developed as multiple scale analysis down to the nanoscale became a trend for development of new materials with new properties. Multiscale materials modeling continue to play a role in these endeavors as well. For example, Qian et al. [257] developed multiscale, multiphysics numerical tools to address simulations of carbon nanotubes and their associated effects in composites, including the mechanical properties of Young s modulus, bending stiffness, buckling, and strength. Maiti [258] also used multiscale modeling of carbon nanotubes for microelectronics applications. Friesecke and James [259] developed a concurrent numerical scheme to evaluate nanotubes and nanorods in a continuum. 

Cluster analysis. In this section, the application of the simple multiscale approach to cluster analysis is demonstrated. The masking method will also be used to localise important features. There are several possible cluster analysis algorithms, however only discriminant function analysis (DFA) will be used here. Before discussing the results from the simple multiscale analysis, this section will first present DFA and how it can applied to both unsupervised and supervised classification, followed by how the cluster properties S are measured at each resolution level. 

Measures of cluster structure. To test the simple multiscale approach to cluster analysis, the independent taxonomic information available for the different objects were used either directly or indirectly in the analyses. This is similar to the situation where a taxonomic expert is faced with a data set without the true classification information. In the process of determining interesting clusters the expert is expected to make use of his external knowledge in the assessment of the observed patterns. Thus, here the external class information is used to define a cluster. Having identified taxonomically relevant clusters, the next step is to measure how they relate to each other. The three properties measured for the two data set analysed were ... 

The elastoplastic multiscale analysis requires several computational modules, including (1) a microscale computation module, which consists of a set of numerical solutions for the local constitutive equation of each subphase, (2) a micromechanical computation module, which provides numerical tools to link the mechanical properties of each of the local subphases to the macroscopic responses, and (3) a macroscale computation module, in which the continuum mechanics governing equations are enforced to simulate the overall mechanical response of the material and to identify the local loading conditions over the R VE. Each of these computational modules is discussed in the following. A flowchart of the multiscale analysis is shown in Figure 5.24. 

FIGURE 1.5 Multiscale modeling in computational pharmaceutical solid-state chemistry. Here DEM and FEM are discrete and finite element methods MC, Monte Carlo simulation MD, molecular dynamics MM, molecular mechanics QM, quantum mechanics, respectively statistical approaches include knowledge-based models based on database analysis (e.g., Cambridge Structure Database [32]) and quantitative structure property relationships (e.g., group contributions models [33a]). 

The multiscale clay mineral organization in the polymer matrix has been widely studied in the scientific literature,48,86,154 ise identified as the key feature determining the nanocomposite material properties. The analysis of the multiscale clay organization is typically focused on ... 

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