By Yves R?mond, Said Ahzi, Majid Baniassadi, Hamid Garmestani

ISBN-10: 1119307562

ISBN-13: 9781119307563

ISBN-10: 1119307570

ISBN-13: 9781119307570

ISBN-10: 1119307635

ISBN-13: 9781119307631

ISBN-10: 1848219016

ISBN-13: 9781848219014

Statistical correlation capabilities are a widely known type of statistical descriptors that may be used to explain the morphology and the microstructure-properties courting. A accomplished learn has been played for using those correlation services for the reconstruction and homogenization in nano-composite fabrics. Correlation services are measured from various recommendations akin to microscopy (SEM or TEM), small attitude X-ray scattering (SAXS) and will be generated via Monte Carlo simulations. during this ebook, various experimental options similar to SAXS and photo processing are provided, that are used to degree two-point correlation functionality correlation for multi-phase polymer composites.

Higher order correlation services has to be calculated or measured to extend the precision of the statistical continuum strategy. to accomplish this goal, a brand new approximation method is applied to acquire N-point correlation services for multiphase heterogeneous fabrics. The two-point capabilities measured through assorted strategies were exploited to reconstruct the microstructure of heterogeneous media.

Statistical continuum conception is used to foretell the potent thermal conductivity and elastic modulus of polymer composites. N-point likelihood features as statistical descriptors of inclusions were exploited to unravel powerful distinction homogenization for potent thermal conductivity and elastic modulus houses of heterogeneous fabrics. Finally, reconstructed microstructure is used to calculate powerful homes and harm modeling of heterogeneous materials.

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**Additional info for Applied RVE reconstruction and homogenization of heterogeneous materials**

**Example text**

Garmestani and others [GAR 98, GAR 01, GOK 05, LI 06, LIN 00, SAH 04] have further extended the statistical continuum approach to both composites and polycrystalline materials using two-point functions. Mikdam et al. [MIK 09] have developed an approximation for the three- Approximate Solution for N-Point Correlation Functions for Heterogeneous Materials 45 point correlation functions based on two-point functions. In other research, Mikdam et al. [MIK 09] and Baniassadi et al. [BAN 11b, BAN 11c] have applied the strong-contrast formulation to predict the effective electrical and thermal conductivity of a two-phase composite material where the distribution, shape and orientation of the two phases are taken into account using two-point and three-point correlation functions.

In this approach, the nanotubes were described as a chain of links and the reconstruction was performed by the optimization of the waviness, geometry and preferential distribution of CNTs. Characterization of mechanical, magnetic, electrical and thermal properties can be performed directly from descriptors such as N-point statistics. Different statistical continuum approaches (weak-contrast and strong-contrast) have been developed to account for the material heterogeneity through probability functions (Kröner [KRÖ 86]; Beran [BER 68]; Phan-Thien and Milton [PHA 82]; Dederichs and Zeller [DED 73], Willis [WIL 81]; McCoy [MCC 79]; Torquato [TOR 02, TOR 85, TOR 97]; Sen and Torquato [SEN 89]).

The analysis of the scattering signal enables characterization of the size and shape of the particles (form factor) as well as their relative ordering (structure factor) [GUN 55]. 54 Å (Cu K), at 45 kV and 40 mA was generated by an X-ray tube operating at 40 kV and 45 mA. A focused parallel mirror and a PIXcel detector were employed with specific slits in order to obtain the highest resolution at small-angle. e. the scattering curve of neat PS, was systematically subtracted. The last treatment of the curves consisted of assessing the intensity of the primary beam that passes through the nanoparticles (absorption correction).

### Applied RVE reconstruction and homogenization of heterogeneous materials by Yves R?mond, Said Ahzi, Majid Baniassadi, Hamid Garmestani

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