Modeling algorithm of acoustic waves penetrating through a medium with composite hierarchical inclusions

Abstract

New materials with a multilevel hierarchical structure, with specified strength properties, require a regular study of the stability of their state. For this purpose, a new method for modeling acoustic monitoring of a block-layered elastic medium with several inclusions of different physical-mechanical hierarchical structures has been developed. An iterative process of solving the direct problem for the case of acoustic field penetrating three hierarchical inclusions of the 1-th, m-th and s-th ranks based on the use of 2D integro-differential equations is developed. The degree of hierarchy of inclusions is determined by the values of their ranks, which can be different. The results of the study demonstrate that hierarchical inclusions are located in different layers, one on top of the other: the top is abnormally plastic, the second is anomalously elastic and the third is abnormally plastic. The degree of filling of each rank with inclusions for all the three hierarchical inclusions may be different. The simulation results can be used for monitoring studies of the stability of structures of a complex hierarchical arrangement under various mechanical influences. © 2018 Author(s).