Author(s)

Olga Hachay¹, Andrey Khachay², Oleg Khachay²

¹Department Name of Organization, Institute of Geophysics, Ural Branch of Russian Academy of Sciences, Ekaterinburg, Rus-sia.
²Institute of Natural Sciences and Mathematics, Ural Federal University, Ekaterinburg, Russia.

In the enormous and still poorly mastered gap between the macro level, where well developed continuum theories of continuous media and engineering methods of calculation and design operate, and atomic, subordinate to the laws of quantum mechanics, there is an extensive meso-hierarchical level of the structure of matter. At this level unprecedented previously products and technologies can be artificially created. Nano technology is a qualitatively new strategy in technology: it creates objects in exactly the opposite way—large objects are created from small ones [1]. We have developed a new method for modeling acoustic monitoring of a layered-block elastic medium with several inclusions of various physical and mechanical hierarchical structures [2]. An iterative process is developed for solving the direct problem for the case of three hierarchical inclusions of l, m, s-th ranks based on the use of 2D integro-differential equations. The degree of hierarchy of inclusions is determined by the values of their ranks, which may be different, while the first rank is associated with the atomic structure, the following ranks are associated with increasing geometric sizes, which contain inclusions of lower ranks and sizes. Hierarchical inclusions are located in different layers one above the other: the upper one is abnormally plastic, the second is abnormally elastic and the third is abnormally dense. The degree of filling with inclusions of each rank for all three hierarchical inclusions is different. Modeling is carried out from smaller sizes to large inclusions; as a result, it becomes possible to determine the necessary parameters of the formed material from acoustic monitoring data.

Nano Hierarchic Objects, Algorithms of Modeling, İntegral-Differential Equations, İterative Process, Block Layered Medium, Combined Hiererachical

Hachay, O. , Khachay, A. and Khachay, O. (2019) Mathematical Modeling Algorithms for Creating New Materials with Desired Properties Using Nano-Hierarchical Structures. Advances in Materials Physics and Chemistry, 9, 211-217. doi: 10.4236/ampc.2019.911016.