Mathematical Apparatus for the Synthesis of Composite Materials with Specified Properties

Abstract

The meaning of the creation and functioning of the system is defined as the achievement of extreme values of goals that unite the individual elements of the system into a single whole. Based on this, the main system attributes of composite materials are indicated. It is assumed that the systemic effect is generated by the systemic properties of quality criteria. The implementation of the technical task is initially determined at the stage of cognitive modeling with the establishment of intensive and extensive properties with the allocation of control parameters. Based on the cognitive map, hierarchical structures of quality criteria are determined, and in accordance with the selected quality criteria, the corresponding structural schemes of the system (for each selected scale level). Further, the system's quality criteria are formalized, and mathematical models are developed in accordance with each of the criteria. The main purpose of using system analysis is to apply the general principles of decomposition of the system into individual elements and establish connections between them, in determining the research goal and stages to achieve this goal (based on solving single-criterion optimization problems using the found optimal values). The formalization of the multicriteria problem and its solution are made based on the required operational values, the type of kinetic processes of the formation of the physical and mechanical characteristics of the material (determine its structure and properties). The problem of materials synthesis is reduced to the choice of the order and type of the differential equation; parametric identification within the chosen model; comparison of experimental and model kinetic processes at a given accuracy; adjusting the model (if necessary). Therefore, it is important to interpolate the kinetic processes of the formation of the main physical and mechanical characteristics of composite materials. The technological process is considered as a complex system consisting of elements of various levels of detail: from atomic to a separate process. Decomposition of the technological process consists in dividing it into basic operations (elements): preparation of materials, mixing of components, molding of a semi-finished product, heat treatment and additional operations. The effectiveness of this approach was confirmed in the development of chemically resistant sulfur composites, epoxy composites for radiation protection, etc. The initial prerequisite was the required operational values of the material and the type of kinetic processes. The results of effective use of interpolation models (including splines) of compressive strength, heat release, and shrinkage of composite epoxy materials are presented.