Theoretical principles of modeling elastoplastic media by movable

Basic concepts of methods of discrete simulation of physical systems based on the microscopic dynamics of a certain model medium are discussed. This medium is of the same macroscopic but rougher microscopic dynamics as compared to the system under review. Examples of modeling the behavior of hydrodynamic systems, elastic media, and diffusion processes show that the model medium can have much lower spatial symmetry than the model macroscopic system and essentially simpler microscopic interaction laws than real media. This, however, leaves the correctness of the description of the macroscopic dynamics unaffected. In particular, macroscopically isotropic systems can be described using discrete models. The application of discrete simulation concepts is discussed, considering the elastoplastic medium modeling by the movable cellular automata method as an example. The method is a hybrid model, proposed in 1995 by Psakhie and co-workers, that combines ideas and advantages of molecular dynamics and cellular automaton methods. In the present paper, we will restrict ourselves to the description of macroscopically homogeneous media. The modeling principles for heterogeneous media will be examined in Part II