S. Yu. Korostelev

Movable cellular automata method for simulating materials with mesostructure

Mathematical formalism and applications of the movable cellular automata (MCA) method are presented for solving problems of physical mesomechanics. Since the MCA is a discrete approach, it has advantages over that of the finite element method (FEM). Simulation results agree closely with the experimental data. The MCA approach cab solves mechanical engineering problems ranging from those in material science to those in structures and constructions. Computer simulation using MCA can also provide useful information in situations where direct measurements are not possible.

METHOD OF MOVABLE CELLULAR AUTOMATA AS A TOOL FOR SIMULATION WITHIN THE FRAMEWORK OF MESOMECHANICS

ConclusionThe proposed MCA method is based on mesomechanics of heterogeneous media [4, 5, 9]. It is connected first with the ability to describe the material as a set of structural elements of deformation [9]. The role of the structural unit in the MCA method is played by the element (movable cellular automaton). The expressions of interparticle interactions used, as well as the rules of changing the state of the elements, allow us to simulate a wide range of phenomena including melting, chemical reactions, and phase transformations. The characteristic size of the element and its properties are defined based on the features of the model constructed in the framework of mesomechanics as described in [9]. Therefore the MCA method as a computational technique allows us to realize the principles of mesomechanics when simulating material response to external loading of different types. This method is highly recommended in computer-aided design of new materials.

The features of fracture of heterogeneous materials and frame structures. Potentialities of MCA design

A new promising numerical method named movable cellular automata (MCA) is described. Because this approach is based on the discrete concept, in contradistinction to FEM-based software, the software based on the MCA concept has a few clear advantages. The main one is connected with modeling of real fracture process. The MCA method has been successfully used for modeling dynamic loading of heterogeneous materials and structures. The results of simulations agree closely with the experimental data. The results show that the MCA approach could be really useful to solve a lot of civil engineering problems from materials to constructions. Special software has been developed on the basis of this method. Due to its potentially unique abilities, the MCA method could be considered as a breakthrough in numerical techniques and a new tool of engineering mechanics.

Dependence of the macroscopic elastic properties of porous media on the parameters of a stochastic spatial pore distribution

The mechanical behavior of porous ceramic materials with a stochastic structure of their pore space is numerically studied during shear loading. The calculations are performed by the mobile cellular automaton method. A procedure is proposed for a numerical description of the internal structure of such materials using the dispersion of the pore distribution in layers that are parallel to the loading direction in a sample. The dependence of the macroscopic elastic properties of porous media on their internal structure is analyzed. Samples with spherical pores and pores extended along the loading direction exhibit a correlation between their average shear modulus and the dispersion of a pore distribution. Thus, the results obtained indicate that the shear modulus of such media is a structure-sensitive property. The proposed approach can be applied to compare the elastic properties of samples using data on their pore structure.

A possible method of computer-aided design of materials with a highly porous matrix structure based on the method of moving cellular automata

The method of moving cellular automata was used to model a sample of ZrO2 ceramic with a matrix structure under conditions of uniaxial compression. Studies were made of the strength and type of damage to the initial structure and its modifications. Particular attention was devoted to studying the influence of characteristics of the matrix structure on the formation and suppression of internal stress macroconcentrators. It is shown that the method of moving cellular automata can be used for the computer-aided design of matrix materials with a complex structure by specifically influencing the formation and evolution of stress macroconcentrators.