TOPOLOGICAL CHARACTERISTICS OF THE STRUCTURE OF COMPOSITE MATERIALS

Abstract

The article discusses methods for modeling composite materials using graph theory. For this purpose, the method of structure-oriented and structure-invariant modeling of composite materials was analyzed. As a basis for such modeling, it is supposed to use structural descriptors ‒ quantities that describe the structure of the material at different scale levels, including the molecular one. Structure-oriented modeling of hierarchical systems, which, in particular, are composite materials, can be carried out on the basis of regression statistical modeling, which takes into account the possibility of implementing the previous structural level at the next one, and, in particular, the molecular level at the microscopic or mesoscopic level. A form of experimental-statistical models, which includes descriptors of several structural levels was proposed. A simplified approach, which takes into account the regularities of two levels: molecular and subsequent (micro- and mesoscopic) was considered. Examples and algorithms for constructing a representative graph for cross-linked and branched polymers, as well as silicate materials, were considered. It is shown that the representing graph of cross-linked polymers is infinite stochastic. An experimental procedure for constructing a discrete model based on microphotographs of a hardening binder was considered and implemented. For a quantitative description of this graph, an incremental scheme was used, as well as topological indices obtained as a result of the transformation of topological indices of graphs of low molecular weight compounds. For the purpose of transformation, there is a transition to probabilistic characteristics ‒ shares and average (normalized) values. The transformed topological indices are supposed to be applied in the statistical model of the composite material.