{'fraction_non_alphanumeric': 0.012142857142857143, 'fraction_numerical': 0.0007142857142857143, 'mean_word_length': 6.184615384615385, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Optimized Packings in Analysis of 3D Nanocomposites with Inclusion Systems

Mathematical models of three-dimensional representative volume elements (RVE) with systems of periodic and random located nanoinclusions are developed. The models are used for analyzing stress-strain state of nanocomposite and estimating average elastic characteristics. Matrices of nanocomposites in the form of parallelepipeds with spherical or cylindrical nanoinclusions of different sizes are considered as typical RVE. Finite elements method to determine effective elastic modulus of various RVE of three-dimensional nanocomposites is elaborated. It allows studying the influence of shapes and relative dimensions of inhomogeneities and matrixes of RVE on effective elastic modulus of nanocomposites. Mathematical models and methods of optimized packing are proposed for computer simulation of filling a given volume with spherical and cylindrical nanoinclusions. The proposed approach is suitable for estimating the influence of fraction's volume of nanoscale inclusions, permits analyzing packing the collection of inclusions and provides the possibility for synthesis of multifunctional nanoscale structures with desired properties. Advanced numerical methods are used instead of expensive full-scale experiments. This allows studying high defecting nanocomposites with novel mechanical and technological properties.