Global stiffness properties

CNTs have extremely high stiffness and strength, and are regarded as perfect reinforcing fibers for developing a new class of nanocomposites. The use of atomistic or molecular dynamics (MD) simulations is inevitable for the analysis of such nanomaterials in order to study the local load transfers, interface properties, or failure modes at the nanoscale. Meanwhile, continuum models based on micromechan-ics have been shown in several recent studies to be useful in the global analysis for characterizing such nanomaterials at the micro- or macro-scale. 

In the second half of this article, we discuss dynamic properties of stiff-chain liquid-crystalline polymers in solution. If the position and orientation of a stiff or semiflexible chain in a solution is specified by its center of mass and end-to-end vector, respectively, the translational and rotational motions of the whole chain can be described in terms of the time-dependent single-particle distribution function f(r, a t), where r and a are the position vector of the center of mass and the unit vector parallel to the end-to-end vector of the chain, respectively, and t is time, (a should be distinguished from the unit tangent vector to the chain contour appearing in the previous sections, except for rodlike polymers.) Since this distribution function cannot describe internal motions of the chain, our discussion below is restricted to such global chain dynamics as translational and rotational diffusion and zero-shear viscosity. 

Since the stiffness of the bonds transfers to the stiffness of the whole filler network, the small strain elastic modulus of highly filled composites is expected to reflect the specific properties of the filler-filler bonds. In particular, the small strain modulus increases with decreasing gap size during heat treatment as observed in Fig. 32a. Furthermore, it exhibits the same temperature dependence as that of the bonds, i.e., the characteristic Arrhenius behavior typical for glassy polymers. Note however that the stiffness of the filler network is also strongly affected by its global structure on mesoscopic length scales. This will be considered in more detail in the next section. 

HOPE, LDPE, and LLDPE are the three main types of commercial polyethylenes with a combined global consumption of >80 Mt/year. HDPE is a strictly linear homopolymer while LDPE is a long-branched homopolymer because of the different methods of polymerization. LLDPE, on the other hand, is a linear ethylene copolymer with small amounts of a-olefin comonomers such as butene, hexene, or octene. Traditionally, polyethylenes are classified according to the densities. The density of polyethylene decreases as the branching and/or comonomer content increases. The crystallinity and the properties associated with crystallinity, such as stiffness, strength, and chemical resistance, progressively decrease from HDPE to LDPE/LLDPE to POE grades. 

Overall, other than underestimation of compressive strains, the MVLEM proves to be an effective modeling approach for the flexural response prediction of slender RC walls, as the model provides good predictions of the experimentally observed global and local responses, including wall lateral load capacity and lateral stiffness at varying drift levels, yield point, cyclic properties of the load-displacement response, rotations (average over the region of inelastic deformations), position of the neutral axis and tensile strains. 

In the SDP developed by Lee et al. (2005, 2009), the supplemental damper properties are represented by jS, which is the ratio of the damper stiffness per story in the global direction to the lateral load resisting frame story stiffness, k, without dampers and braces of the structural system. The structural system with dampers is converted into a linear elastic system characterized by the initial stiffness of the stmcture, a (the ratio of brace stiffness per story in the global direction to the lateral load resisting frame story stiffness ko), jS, and rj. a, jS, and p may vary among the stories of the stmcture. By conducting an elastic-static analysis with the RSA method, the design demand for the stmcture is determined. 

The rigorous model of batch distillation operation involves a solution of several stiff differential equations and the semirigorous model involves a set of highly nonlinear equations. The computational intensity and memory requirement of the problem increase with an increase in the number of plates and components. The computational complexity associated with these models does not allow us to derive global properties such as feasible regions of operation, which are critical for optimization, optimal control, and synthesis problems. Even if such information is available, the computational costs of optimization, optimal control, or synthesis using these models are prohibitive. One way to deal with these problems associated with these models is to develop simphfied models such as the shortcut model. 

To understand the principles at which biological systems operate, detailed studies on ultrastructure, material properties, force range, and motion pattern during locomotion are necessary. Such studies have become possible in the past several years due to new developments (1) in microscopical visualization techniques (atomic force microscopy, freezing and environmental scanning electron microscopy), (2) in characterisation of mechanical properties of biological materials and structures in situ and in vivo (measurements of stiffness, hardness, adhesion, friction) at local and global scales, and (3) in computer simulations. 

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