Estudo de sistemas particulados e contínuos: uma abordagem com métodos de elementos discretos, pontos materiais e otimização topológica

Abstract

This work performs a comparison between two fundamental methods in simulating complex physical systems: the Discrete Element Method (DEM) and the Material Point Method (MPM). Both methods have been widely applied to model behaviors of discrete and continuous materials in various fields of science and engineering. DEM is recognized for its ability to accurately represent the behavior of individual particles, considering their interactions and movements, particularly effective in analyzing problems involving granular interactions. For MPM relies on discretizing the continuous material into material points distributed in a mesh, allowing for the representation of deformations and movements with greater precision in situations of large deformations, especially in continuous material. The fundamental and applied aspects of both methods were explored, analyzing their advantages, limitations, and areas of application. Additionally, it directly compares the performance and results of these methods in specific scenarios, aiming to evaluate their capabilities and limitations in different contexts. Two topological optimization algorithms in continuous models were used, one for MPM and one for DEM, to understand and define the current limitations of each method, given the recent development of the methods. The results obtained in this research significantly contribute to understanding the nuances of each method, highlighting their strengths and weaknesses. The direct comparison between DEM and MPM provides a comprehensive insight into their modeling and simulation capabilities for both continuous and discrete and offers various applications for both methods.