Computer elastic properties

Fiber-reinforced systems have been modeled with use of an MC method to place parallel fibers into a polymer matrix, with a finite element algorithm (FEA) then being used to compute elastic properties (274). A generic meshing algorithm for use in FEA studies of nanoparticle reinforcement of polymers has been developed (275) and applied to the calculation of mechanical properties of whisker and platelet filled systems. The method should be applicable to void-containing low dielectric materials of such great utility in the semiconductor industry. 

Monte Carlo computer simulations were also carried out on filled networks [50,61-63] in an attempt to obtain a better molecular interpretation of how such dispersed fillers reinforce elastomeric materials. The approach taken enabled estimation of the effect of the excluded volume of the filler particles on the network chains and on the elastic properties of the networks. In the first step, distribution functions for the end-to-end vectors of the chains were obtained by applying Monte Carlo methods to rotational isomeric state representations of the chains [64], Conformations of chains that overlapped with any filler particle during the simulation were rejected. The resulting perturbed distributions were then used in the three-chain elasticity model [16] to obtain the desired stress-strain isotherms in elongation. 

Bockstedte M, Kley A, Neugebaur J, Scheffler M (1997) Density-functional theory calculations for poly-atomic systems electronic structure, static and elastic properties and ab initio molecular dynamics, Comput Phys. Commun. 107 187-222... 

Matsui, M., M. Akaogi, and T. Matsumoto (1987). Computational model of the structural and elastic properties of the ilmenite and perovskite phases of MgSiO,. Phys. Chem. Mineral. 14, 101-6. 

The impact of computers on high-pressure theoretical studies may be compared with that of synchrotron facilities on high-pressure experimental studies. Steady improvements in computational methods have enabled calculations of structure, stability, and elastic properties of simple systems under pressures and temperatures of the Earth s interior (e.g., Stixrude and Brown, 1998 Boness and Brown, 1990 Sherman, 1995, 1997 Steinle-Neumann and Stixrude, 1999 ... 

The results of calculations of the effective Poisson s ratio vp dependence on the bulk concentration of a rigid phase p at various values of a = log i/C/Au) are shown in Fig. 53. The calculations were made for Poisson s ratios of the phases ranging from 0.1 to 0.4. It can be seen that at percolation threshold Poisson s ratio of the isotropic fractal composite is vp = 0.2, when K jK > 0 it is also independent of the Poisson s ratios of the individual components of the composite. The Poisson s ratio obtained by us near the percolation threshold is in agreement with computer simulation results and the conjecture of Arbabi and Sahimi [161]. It has been shown that an approximate theoretical treatment of percolation on a cubic lattice exactly reproduces the Poisson s ratio obtained in computer simulation at the percolation threshold. This result may encourage one to use this approximation to describe various elastic properties of composites. It is worth noting that some critical indices have been calculated recently with a high degree of accuracy in the context of the present model. 

It is useful to understand the microstructure of soft particle dispersions before discussing the predictions of their elastic properties and the comparison of these with experimental data. The radial distribution function is a convenient form for characterizing the microstructure since one expects radial symmetry at nearequilibrium conditions. In Fig. 7, the radial distribution function computed for the undeformed system has been plotted against the scaled radial distance. But for the first peak (Fig. 7a), this radial structure is very similar to that observed for jammed hard-sphere packings [139]. For hard spheres, g r shows a sharp rise from zero at the hard-sphere diameter, i.e., r = IR. Here, since the soft-sphere packing is... 

As yet, our reflections on the elastic properties of solids have ventured only so far as the small-strain regime. On the other hand, one of the powerful inheritances of our use of microscopic methods for computing the total energy is the ease with which we may compute the energetics of states of arbitrarily large homogeneous deformations. Indeed, this was already hinted at in fig. 4.1. 

Note that we have resorted to the use of /r and v for our description of the elastic properties for ease of comparison with many of the expressions that appear elsewhere. In order to compute the total elastic energy, we separate the volume integral of eqn (10.15) into two parts, one which is an integral over the inclusion, and the other of which is an integral over the matrix material. The reason for effecting this separation is that, external to the spherical inclusion, the displacements we have computed are the elastic displacements. On the other hand, within the inclusion, it is the total fields that have been computed and hence we must resort to several manipulations to deduce the elastic strains themselves. 

In what follows the theoretical background of the most common physical properties and their measuring tools are described. Examples for the wet bulk density and porosity can be found in Section 2.2. For the acoustic and elastic parameters first the main aspects of Biot-Stoll s viscoelastic model which computes P- and S-wave velocities and attenuations for given sediment parameters (Biot 1956a, b, Stoll 1974, 1977, 1989) are summarized. Subsequently, analysis methods are described to derive these parameters from transmission seismograms recorded on sediment cores, to compute additional properties like elastic moduli and to derive the permeability as a related parameter by an inversion scheme (Sect. 2.4). 

Dynamic force spectroscopy (DFS) was introduced [1] allowing us to understand quantitatively dissipative and non-dissipative processes in dynamic force microscopy [2]. Using a combined experimental and computer simulation technique it is possible to reconstruct force/distance ciuves without using any model potentials and parameters. This method opens the perspective to extract material parameters such as atomic densities of the surface investigated as well as local elastic properties... 

It is widely presumed that in the vicinity of insertion the elastic properties must differ from the macroscopic limit [76,89]. However, this notion has not previously been implemented in a computational model. 

Han, et al.. Molecular dynamics simulations of the elastic properties of polymer/ carbon nanotube composites. Comput Mater. Sci. 2007,39(8), 315-323. 

Thus, the density of chemical crosslinking points cannot serve as an index for the cormectivity of the macromolecular skeleton of network polymers. This makes it impossible to use to characterise the structure of network polymers in a computer simulation, which follows from the results presented previously. The d value, which provides determination of elastic properties, may serve as a suitable parameter. However, to estimate other properties, one more parameter is required, which would characterise the degree of thermodynamic nonequilibrium of the structures of vitreous polymers. This role can be played by dfOr the density of the cluster network of physical entanglements [48], or by the proportion of clusters (p [140] For instance, the necessity to take into account d, V i or [Pg.334]

The motility appears to be due to a passive piezoelectric behavior of the ceU plasma membrane [Kahnec and colleagues, 1992]. Iwasa and Chadwick [1992] measured the deformation of a ceU under pressure loading and voltage clamping and computed the elastic properties of the wall, assuming isotropy. It appears that for agreement with both the pressure and axial stiffness measurements, the ceU wall must be... 

Perhaps a sensible procedure is to consider an approach which incorporates both interatomic potentials (classical forces) and fully quantum mechanical methods. One can compute the properties of smaller systems with quantum mechanical approaches and establish the accuracy, or inaccuracy, of interatomic potentials. For example, some elastic anomalies have been reported for a-cristobalite. These elastic anomalies indicated the presence of a negative Poisson ratio in this crystalline form of silica. With the use of interatomic potentials, it is a trivial matter to compute these properties. If the anomalies are confirmed via such calculations, it is likely that the experimental measurements are accurate, and more computationally intense calculations with quantum forces are merited. Another useful role of interatomic potentials is to perform molecular dynamics simulations, e.g., to examine the amorphization of quartz under pressure. One can easily compute the free energy of large systems as a function of both temperature and pressure via interatomic potentials. Sueh calculations can be useful as guides if interpreted in a judicious fashion. 

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