Mathematical Model of the Dynamics of Spherical Elements

This paper presents a study in the field of modelling the dynamics of spherical elements. The results obtained indicate the successful use of the discrete element method (DEM) as a numerical tool for analysing the behaviour of the system studied with the help of spheres. The results are based on the importance of correct consideration of the boundary conditions for the spheres, which determine the key aspects of modelling with the developed three-dimensional model. The developed model solves a number of important tasks, expanding the field of scientific research. Firstly, it allows studying the main parameters of the formation of a heterogeneous medium by analysing the compaction of spherical elements in different media. Next, the three-dimensional model is used to study the process of changing the structure of a heterogeneous medium from a static to an oscillatory state, which allows for a deeper understanding of this process. By modelling the mathematical behaviour of spherical elements under the influence of external and additional factors, a detailed understanding of their dynamics and contact interaction can be obtained. The application of the developed model to analyse the contact interaction of spherical elements in heterogeneous media allows predicting the main parameters of spheres and their heterogeneous environment with a reliable accuracy of up to ±1 %. It should be noted that the results obtained on the basis of the three-dimensional model are effective and indicate a number of practical applications in various fields.