A. Yu. Smolin

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.

Dynamic vortex defects in deformed material

The paper studies the generation and evolution of dynamic vortex structures in a material on different structural scales. It is shown that the generation of dynamic vortex structures can be the main accommodation mechanism in a material under external mechanical loading. On the microscale, these structures can provide inter-granular sliding and grain boundary migration with anomalously high rates. On higher structural scales, their evolution can be the main process responsible for nucleation and propagation of cracks, fragmentation of material, formation of a “quasiliquid” layer in friction pairs, etc. The data and conclusions derived from the study are confirmed by numerical calculations for different types of materials in the framework of molecular dynamics and movable cellular automaton methods.

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.

Time-frequency analysis of acoustic signals in the audio-frequency range generated during Hadfield’s steel friction

Time-frequency analysis of sound waves detected by a microphone during the friction of Hadfield’s steel has been performed using wavelet transform and window Fourier transform methods. This approach reveals a relationship between the appearance of quasi-periodic intensity outbursts in the acoustic response signals and the processes responsible for the formation of wear products. It is shown that the time-frequency analysis of acoustic emission in a tribosystem can be applied, along with traditional approaches, to studying features in the wear and friction process.

Computer-aided examination and forecast of strength properties of heterogeneous coal-beds

One of the modern and perspective applications of computational mechanics is investigation of complex multiphase media containing components in different aggregative states. Striking examples of multiphase media are coal-beds, soils, geological medium and so on. In the present paper the new method for simulation of response and fracture of multiphase media, the hybrid cellular automaton method, is proposed. Developed approach was applied for computer-aided simulation of response and fracture of lignite under complex boundary conditions imitating real-life environment in coal beds. Simulation results show that presence of constrained boundary conditions can lead to change of lignite fracture regime in the range from brittle to quasi-viscous. In the case of hard boundary conditions increase of surrounding material hardness leads to transition from brittle fracture of fined detritus to degradation regime, which is characterized by generation and accumulation of numerous damages. As a result at slump of lateral pressure (in practice this situation is realized during mining or digging) fine detritus can demonstrate explosion-like fracture. In the case of boundary conditions realized by means of applied force (this type of boundary conditions is the most close to real conditions in coal beds) the vice versa dependency for fined detritus is observed. Here explosion-like regime is observed at lateral pressure slump in the case of soft surrounding material. Proposed hybrid cellular automata concept can be efficiently used for solving various geo-mechanical, biological, engineering and materials science tasks, which consider heterogeneous multiphase objects.

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.

Three-dimensional movable cellular automata simulation of elastoplastic deformation and fracture of coatings in contact interaction with a rigid indenter

The paper considers 3D movable cellular automata (MCA) models of contact interactions involved in nanoindentation, sclerometry, and tribospectroscopy. The system under study is a titanium substrate with a harden coating. The substrate and coating materials are both described in the elastoplastic approximation. It is shown that the MCA method of numerical simulation provides correct description of the contact interaction of elastoplastic materials under different types of loads with explicit account for fracture. The possibility to detect damages in ma surface layers from friction force estimates is assessed.

Quasi-Viscous Fracture of Brittle Media with Stochastic Pore Distribution

The development of deformation and fracture under uniaxial loading conditions in porous ceramic materials with the pore space having regular and stochastic structures of various types has been studied by method of movable cellular automata. The influence of the porous structure on the dynamics of damage nucleation and development is been analyzed, and a correlation between the effective stiffness of porous samples and the rate of damage accumulation is found. It is concluded that brittle materials can exhibit quasi-viscous fracture determined entirely by the pore space structure.

Identification of Elastic Waves Generated in the Contact Zone of a Friction Couple

A method for evaluation of the parameters of elastic waves during simulation of the interaction between solid bodies in friction is proposed. Using an analysis of the Fourier spectra of the time series of velocity components, pressure, and stress intensity, it is possible to determine frequencies characteristic of the given numerical model, the geometry of the problem under consideration, and of the real processes taking place immediately in the friction contact zone.