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Fractal characteristics of defects growth in porous ceramics modeled with the Movable Cellular Automata
Abstract
In this paper Movable Cellular Automata and fractal geometry are applied to examine defects growth in porous ceramic specimens.
The Movable Cellular Automata method is applied in numerical simulations of compression loading of ceramic specimens. It allows a continuous monitoring material processes and gives physical picture of defects over the meso- and macroscopic range of scales, at any stage of evolution.
The entire structure of defects enclosed in macroscopic volume is treated as a single fractal and described by means of fractals with fractal dimension and measure.
... The method of movable cellular automata (MCA), an efficient and discrete element-based method for modeling the mechanical behavior of heterogeneous materials, was employed. It has been demonstrated that such methods are highly effective for modeling of the mechanical behavior of biomaterials and metals under dynamic loading at the macro-and mesoscales [6][7][8][9]. In the MCA method, the simulated material is represented as a packing of cellular automata (discrete elements of the same size) interacting with neighbors according to certain rules. ...
... To simulate the shock wave exposure on the model bone tissue with a tumor, the applicator was introduced to the model as a thin, square copper plate 10 × 10 mm in size located in the gum area (shown by black plate in Fig. 1b). The velocity V of the applicator automata was changed in time according to the specified energy flux density (EFD) of the shock wave (a detailed description of the loading velocity computation is presented in work [7]). ...
... The properties of the biological tissues presented in Table 1 were borrowed from works [10,11]. In this model, the biological fluid inside the tissues had the properties of salt water with the bulk modulus Kf = 2.4 GPa, the density ρf = 1000 kg/m 3 , and the viscosity ηf = 1 mPa s [7]. ...
Malignant tumors arising from mesenchymal tissues (bones or cartilages) have the worst prognosis. Currently, the development of minimally invasive and non-invasive methods for treating patients in the early stages, used separately and in combination with existing treatment methods, is relevant. In this work, we study numerically the mechanical behavior of the thoracic spine affected by osteosarcoma under shock wave treatment using an invasive applicator placement technique. The results obtained indicate that the optimal range for initiating the deactivation process with minimal risks of bone tissue destruction is the shock wave loading with energy flux density (EFD) in the range from 0.005 to 0.15 mJ/mm2. By further increasing in the amplitude of the therapeutic shock wave treatment (with invasive installation of the applicator), the formation and expressive growth of stroma around the tumor is possible.
... Some studies have been done to improve the ceramic material design by microstructure evolution simulation and the results of have been released. [2][3][4][5][6] With the phase field method, Zhou et al. [2] developed laminated ceramic composite materials, simulating the anisotropic grain growth. Aniszewska et al. [3] built a microstructure evolution model of composite ceramic material to improve the fracture toughness and flexure strength. ...
... [2][3][4][5][6] With the phase field method, Zhou et al. [2] developed laminated ceramic composite materials, simulating the anisotropic grain growth. Aniszewska et al. [3] built a microstructure evolution model of composite ceramic material to improve the fracture toughness and flexure strength. It could be seen that the grain size of the constructed model was consistent with the experimental results, indicating that the microstructure evolution of composite ceramic materials could be well simulated by the cellular automata model. ...
A microstructure evolution model for the ceramic materials was constructed, and the spark plasma sintering parameters were optimized using the model to shorten the designing period and reduce the consumption of the material. Based on the optimized sintering parameters, the ceramic tool material with a composition of Al2O3, TiB2, and TiC proved to be a success. It verified that the materials prepared under the optimized sintering parameters exhibited excellent mechanical properties. The results showed when sintered at 1600°C, under the pressure of 40 MPa and with the holding period of 7 min, the materials with 70% Al2O3, 20% TiB2, and 10% nano‐TiC possess the relatively best performance, with the hardness, fracture toughness, and flexure strength being 20.3 GPa, 10.5 MPa/m², and 839.5 MPa, respectively.
... We utilized the movable cellular automaton method (MCA), which is an improved version of the discrete element method as presented in [28][29][30]. The MCA method models materials as a collection of discrete elements, called movable cellular automata, that interact according to specific rules of multi-body interaction and can change their state. ...
The most time-consuming aspect of dental prosthesis installation is the osseointegration of a metal implant with bone tissue. The acceleration of this process may be achieved through the use of extracorporeal shock wave therapy. The objective of this study is to investigate the conditions for osseointegration of the second premolar implant in the mandibular segment through the use of a poroelastic model implemented in the movable cellular automaton method. The mandibular segment under consideration includes a spongy tissue layer, 600 µm in thickness, covered with a cortical layer, 400 µm in thickness, and a gum layer, 400 µm in thickness. Furthermore, the periodontal layers of the roots of the first premolar and first molar were considered, while the implant of the second premolar was situated within a shell of specific tissue that corresponded to the phase of osseointegration. The model was subjected to both physiological loading and shock wave loading across the three main phases of osseointegration. The resulting fields of hydrostatic pressure and interstitial fluid pressure were then subjected to analysis in accordance with the mechanobiological principles. The results obtained have indicated that low-intensity shock wave therapy can accelerate and promote direct osseointegration: 0.05–0.15 mJ/mm2 in the first and second phases and less than 0.05 mJ/mm2 in the third phase. In comparison to physiological loads (when bone tissue regeneration conditions are observed only around the implant distal end), shock waves offer the primary advantage of creating conditions conducive to osseointegration along the entire surface of the implant simultaneously. This can significantly influence the rate of implant integration during the initial osteoinduction phase and, most crucially, during the longest final phase of bone remodeling.
... As foreign research related to perceptual imagery has flowed into China, some domestic research institutes and universities in recent years have also begun to focus on related explorations of perceptual imagery theory [1][2] . The research on ceramic tea set mainly focuses on tea set design, tea culture and historical evolution of tea set, innovative design theory of tea set shape, application research of different materials of tea set, and application of some principles to tea set [3][4] . In addition to the basic function of tea drinking, the design of tea set should also meet the needs of users in pursuit of personalization, emotion, and diversity, in order to give users a sense of pleasure [5][6] . ...
Traditional ceramic tea set enterprises old tea set design, single shape.Early research scholars have not established a systematic design method and process of ceramic tea set shape image.These factors have affected the healthy development of the ceramic tea set industry.With the arrival of the perceptual consumption era, the shape and image conveyed by the appearance of the ceramic tea set directly affects the user’s perception of the ceramic tea set and becomes the key factor for people to buy the ceramic tea set.Based on computer 3D fractal model, this paper proposes and discusses the initial expression of the topological structure of plum blossom ceramic graphics based on fractal iteration and region iteration segmentation, and the iteration of the structure.Finally, the research results of this paper are applied to the making process of plum blossom ceramic pattern..
... Cellular automata (CA) are dynamic systems in time, space and variables. There are various applications of cellular automata, such as, market flows [15] , encryption [16] , application in biological systems [17] and physical systems [18,19] . Recent works investigated pedestrian evacuation models based on cellular automata [20][21][22] . ...
This study proposes a cellular automata ant memory model (CAAM) that controls a robot swarm when undertaking the foraging task in a previously known environment with nests. The floor field is well known to all robots, which share the same environment, communicating through the inverted pheromone. This substance is deposited by each swarm robot over every step in searching, which results in a repulsive force between team members. Besides, a short-term memory inspired by Tabu Search is applied to enable robots to remember their last positions and to avoid useless explorations. On the other hand, homing is based on the behavior observed in pedestrian evacuation, resulting in an attractive force through the nests. Moreover, a dynamic information is used to avoid queues of robots and bottlenecks next to the nests. Each robot step is a first choice movement with a stochastic conflict solver, which results in a non-deterministic characteristic to the model. The proposed model was implemented and submitted to several simulations to evaluate its resultant behavior. Different environmental conditions were employed to refine its intrinsic parameters. The results shown that the proposed model is able to perform the foraging task in a competitive way: in searching the swarm perform a good environment coverage and in homing robots are able to find the most adequate nests.
Green and intelligent manufacturing has become the key direction of industrial production development. In-situ measuring and sintering simulation technologies play a key role in the modification of ceramic materials and the optimization of the sintering process. These two techniques can significantly alleviate the problems of wasted energy and resources in the ceramics production process, thus promoting the green development of the ceramics industry. Although both techniques have been widely used in the field of ceramic sintering, there is a lack of a comprehensive review of their applications. To better promote the application of these two technologies, this paper provides the first overview of the progress of the application of ceramic sintering in-situ measuring technology and systematically reviews the current research status of ceramic sintering simulation technology. Then it looks forward to the application prospect of these two technologies, synthesizes these two technologies, constructs the framework of digital twin ceramic sintering system for the first time, and analyzes the important role of these two technologies in the digital twin ceramic sintering system.
For kinematically redundant robots, self-motion manifolds that represent all the inverse kinematic solutions for a given end-effector location play a significant role in global motion planning. However, the efficient computation of self-motion manifolds, especially the computation of high-dimensional manifolds, is still a problem that needs to be solved. In this paper, the grid elements modeling criteria are formulated, and the specific modeling method of a grid element in the configuration space is developed. Based on the idea of cellular automata, the problem of computing self-motion manifolds is transformed into a dynamic model searching problem, and an evolution strategy is proposed to realize the efficient computation of self-motion manifolds. Finally, two examples are used to verify the effectiveness of the proposed method in computing high-dimensional self-motion manifolds. The results show that compared to the conventional methods, the proposed method can correctly identify all the self-motion manifolds with 94% reduced computational time on average.
Considering the self-similar characteristic of irregular pore network of materials during the damage evolution process, a pore ubiquitiform model (PUM) is developed to characterize the multiscale pore or microcrack network of quasi-brittle materials, and then based on the PUM, the ubiquitiform damage model (UDM) is proposed to describe the damage evolution process of quasi-brittle materials under quasi-static uniaxial tensile loading. The values of porosity and pore specific surface area estimated from the PUM and the stress-deformation curves including the softening curve calculated from the UDM are in good agreement with previous experimental data, respectively. It can be found that, the PUM can be adopted to characterize the self-similar multiscale pore network and estimate the porosity and pore specific surface area, and the UDM can describe the damage evolution process of quasi-brittle materials under quasi-static uniaxial tensile loading. Meanwhile, the UDM can characterize the self-similar characteristic of pore network during the damage evolution process of quasi-brittle materials through the evolving ubiquitiform complexity.
We critically review dissipative particle dynamics (DPD) as a mesoscopic simulation method. We have established useful parameter ranges for simulations, and have made a link between these parameters and χ-parameters in Flory-Huggins-type models. This is possible because the equation of state of the DPD fluid is essentially quadratic in density. This link opens the way to do large scale simulations, effectively describing millions of atoms, by firstly performing simulations of molecular fragments retaining all atomistic details to derive χ-parameters, then secondly using these results as input to a DPD simulation to study the formation of micelles, networks, mesophases and so forth. As an example application, we have calculated the interfacial tension σ between homopolymer melts as a function of χ and N and have found a universal scaling collapse when σ/ρkBTχ0.4 is plotted against χN for N>1. We also discuss the use of DPD to simulate the dynamics of mesoscopic systems, and indicate a possible problem with the timescale separation between particle diffusion and momentum diffusion (viscosity).
Most of technical surfaces show roughness on different space scales. When pressed against each other, they initially come into contact only in small number of micro-contacts. Our aim was to study the processes occurring in a single micro-contact between two rubbing bodies. The solids were simulated in the frame of the method of movable cellular automata (MCA). The main finding of our simulations is formation of a boundary layer where intensive plastic deformation and mixing processes occur. The boundary layer is well localized and does not spread to deeper layers.We investigated how the thickness of the boundary layer and the friction force stemming from the processes in this layer do depend on parameters of material and loading. To this end, all the parameters involved in the numerical model have been varied and the average friction coefficient as well as thickness of the layer determined for each set of parameter. We found that at velocities much smaller than velocity of sound and normal pressures much smaller than the yield stress, the thickness of the quasi-fluid layer is proportional to effective viscosity of the medium and the friction coefficient does depend only on two dimensionless parameters: κ1=ρv2E/σ02 and κ2=PE/σ02.
Development of surface topography of two solids in a frictional contact is studied with the method of movable cellular automata. After the running-in process, the bodies are separated and the surface power spectra of both bodies are determined. The power spectra show a dependence on the wave vector, which is typical for fractal surfaces. It is shown, that roughness parameters of friction surface depend on relative velocity of sliding and external pressure.
Many aspects of wear are still far from understanding. The paper proposes theoretical approach exploring
the mechanisms of friction and wear on the basis of combining micro- and macro-modelling. In a macroscopic
phenomenological model processes of wear are considered as stochastic processes in the surface
layers of contacting bodies, including spalling of wear microparticles, local stochastic transport due to
plastic deformation as well as processes of nano-welding. We show that parameters of this model can be
obtained as a result of direct simulation of a microscopic tribological contact. In the paper, the method of
movable cellular automata is used for this aim. The results show a stochastic migration of a friction layer
in the direction perpendicular to the sliding velocity. Estimation of the effective diffusion coefficient of
the friction layer migration for different contacting materials, and construction of corresponding surface
power spectra were done. The results help to identify the parameters of the macroscopic model and help
to connect the micro- and macro-scales.
The 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.
We present a molecular dynamics computer simulation method for calculating equilibrium constants for the formation of physical clusters of molecules. The method is based on Hill’s formal theory of physical clusters. In the method, a molecular dynamics calculation is used to calculate the average potential energy of a cluster of molecules as a function of temperature, and the equilibrium constants are calculated from the integral of the energy with respect to reciprocal temperature. The method is illustrated by calculations of the equilibrium constants for the formation of clusters of two to five water molecules that interact with each other by an intermolecular potential devised by Watts. The method is compared with other procedures for calculating the thermodynamic properties of clusters.
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 ®nite 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. Ó 2001 Published by Elsevier Science Ltd.
Ceramics is widely used material in engineering practice because of its great strength, high heat resistance and low density. The strength is a subject of our investigations. It can be significantly decreased by small defects, such as scratches, inclusions, pores, and surface roughness. The aim of this article is to demonstrate an application of the Movable Cellular Automata (MCA) method in 3D to simulate static compression test of ceramic material with various type of defects. As results we can observe damage evolution and cracks propagation leading to sample failure.
The tribological properties of nanostructured surface films formed during dry sliding, for example during automotive braking, were determined by modelling using the method of movable cellular automata. Starting from a basic model structure, consisting of magnetite with 13% graphite inclusions, the impact of additional soft and hard particles of different size and volume fraction was studied systematically. It was revealed that agglomerates of soft particles decomposed and finally mixed with the oxide in the same way as single nanoparticles. On the other hand, agglomerates of hard particles mixed with the other components without decomposing. Whereas increasing the amount of soft components in the third body lowered the coefficient of friction, the opposite occurred with the hard particles. The boundary conditions for obtaining smooth sliding conditions with minor fluctuations between friction forces at successive time steps could be defined. In addition to features of the nanostructure, the applied normal pressure impacted modelling results. Within the parameter range of smooth sliding behaviour, increasing pressure induced thicker granular interface layers, which lead to a slight decrease of the coefficient of friction. Changing the amount of soft or hard particles did not change this pressure dependency but only the friction level.
Introduced is FD3, a program for estimation of fractal dimensions that may indicate the presence of chaos. The program, written in C computer language, will run on a variety of computers (e.g., Macintosh(r), IBM compatible, Next workstation) as long as they have a C compiler. Specific application is shown with the estimation of the fractal dimension of Bender-Gestalt. Included are the values for capacity, information, and correlation dimension for the nine drawings.
The paper presents the application of cellular automata (CA) method for simulations of fibers breaking process in composites. Cellular automata (CA) method is described in the first part of this paper. The next part includes the description of CA method used for fibre breaking process in composites and few examples of application. The last part presents possibility of simultaneous usage, acoustic emission and CA simulations.
With appropriate numerical methods of composites modelling we can observe defects growth without using invasive experimental methods. In this paper we present results of simulation of quasi-static process of fracture in composite using cellular automata and fractal characteristics of defects growth based on box-counting method. Defects evolution in composite are treated as a dynamical system depending on external and internal conditions and properties of fibres.
Shear failure and deformation localization are studied for tungsten alloy undergoing impact failure and “self-sharpening” in ordnance. Movable cellular Automata (MCA) method is employed to simulate the interior-structure of tungsten alloy such that shear deformation failure at mesoscale level under shear loading can be analyzed. The results show that the velocity of every automaton would vary continuously with deformation. A large velocity vortex sweeping throughout the specimen occurs at the initial loading stage. This corresponds to uniform deformation. Subsequently, the deformation adopts a pattern with more localized vortices. The vortex-morphology would change continually to sustain the global deformation field. The contact between the local vortices induces stress concentration. This means that the deformation of certain automaton pairs would not accommodate the equilibrium of vortex rotation. The different mechanisms of micro-damage mechanisms along the interface between the W grain and matr
The scope of the present paper is the study of structures involving boundaries and interfaces of fractal geometry. The geometry is analysed here by a sequence of classical geometry problems formulated by means of C0 and C1-interpolating functions. These approximations of the fractal geometry are combined with the FEM and the BEM in order to calculate the stress and displacement fields in fractal structures.
A new algorithm is used to determine fractal dimensions by box counting for dynamic and iterated function systems. This method is fast, accurate, and less dependent on data specific curve fitting criteria than the correlation dimension.
A groundwater management problem is presented involving pumping cost minimization with both well discharges and well locations as decision variables. A grid of candidate well locations is set up and optimal arrangements of wells are sought within this discrete space. A genetic algorithm approach is presented with the following particular features: (a) A suitable scaling is applied to the objective function in order to alleviate its regionally flat behavior. (b) No penalty functions are involved in constraint handling. Instead, the feasible region is transformed into a rectangular domain. The transformation introduced is proved to be bijective. (c) A binary representation of well configurations is presented and compared to a combinatorial one. The binary representation necessitates the introduction of specially designed genetic operators. Besides purely genetic algorithms, the concept of cellular automaton is introduced as the basis of an alternative formulation of the optimization problem. The lattice of the cellular automaton provides the discrete set of candidate well positions. The well configuration is represented by a group of agents occupying an equal number of lattice sites. The agents change positions as dictated by the structure of the automaton and, also, by an associated genetic algorithm, which directs the evolution of the whole scheme toward an optimal configuration. An improved performance of this approach is noted and discussed in comparison to the purely genetic algorithm schemes of the present work. A simulated annealing approach is also applied to the same problem for comparison purposes. Finally, a new and more efficient hybrid annealing–genetic approach is introduced and discussed.
Fuzzy cellular automata (FCA) are continuous cellular automata where the local rule is defined as the “fuzzification” of the local rule of a corresponding Boolean cellular automaton in disjunctive normal form. In this paper, we are interested in the relationship between Boolean and fuzzy models and, for the first time, we analytically show the existence of a strong connection between them by focusing on two properties: density conservation and additivity.We begin by showing that the density conservation property, extensively studied in the Boolean domain, is preserved in the fuzzy domain: a Boolean CA is density conserving if and only if the corresponding FCA is sum preserving. A similar result is established for another novel “spatial” density conservation property. Second, we prove an interesting parallel between the additivity of Boolean CA and oscillations of the corresponding fuzzy CA around its fixed point. In fact, we show that a Boolean CA is additive if and only if the behaviour of the corresponding fuzzy CA around its fixed point coincides with the Boolean behaviour. Finally, we give a probabilistic interpretation of our fuzzification which establishes an equivalence between convergent fuzzy CA and the mean field approximation on Boolean CA, an estimation of their asymptotic density.These connections between the Boolean and the fuzzy models are the first formal proofs of a relationship between them.