Method Of Movable Cellular Automata Research Articles

MODELING OSTEOCYTE UNDER SHOCK-WAVE THERAPEUTIC LOADING

Dental implants have substantial significance in modern dentistry, but their osseointegration stage remains the most crucial and time-consuming step for compensating for a lost tooth. One promising approach to improve osseointegration rates is the use of extracorporeal shock wave therapy, which has shown efficacy in treating fractures, bone defects, and bone tissue regeneration in surgical and arthroplasty procedures. To comprehend the potential of shock wave therapy in accelerating implant osseointegration, it is crucial to investigate the influence of mechanical loading on ossification processes of varying scales objectively. This study aims to study numerically the effects of low-energy shock wave therapy at different intensities on the mechanical response of a single osteocyte, the principal bone cell that corresponds to microscale of bone tissue. The investigation employs the method of movable cellular automata for modeling. The computer simulation results and analysis based on mechanobiological principles indicate that low-intensity shock wave loading creates conditions for intramembranous ossification, whereas high-intensity shock wave exposure creates conditions for endochondral ossification.

Effect of patient-specific factors on regeneration in lumbar spine at healthy disc and total disc replacement. Computer simulation

Background and ObjectiveDegenerative diseases of the spine have a negative impact on the quality of life of patients. This study presents the results of numerical modelling of the mechanical behaviour of the lumbar spine with patient-specific conditions at physiological loads. This paper aims to numerically study the influence of degenerative changes in the spine and the presence of an endoprosthesis on the creation of conditions for tissue regeneration. MethodsA numerical model of the mechanical behaviour of lumbar spine at healthy and after total disc replacement under low-energy impacts equivalent to physiological loads is presented. The model is based on the movable cellular automaton method (discrete elements), where the mechanical behaviour of bone tissue is described using the Biot poroelasticity accounting for the presence and transfer of interstitial biological fluid. The nutritional pathways of the intervertebral disc in cases of healthy and osteoporotic bone tissues were predicted based on the analysis of the simulation results according to the mechanobiological principles. ResultsSimulation of total disc replacement showed that osseointegration of the artificial disc plates occurs only in healthy bone tissue. With total disc replacement in a patient with osteoporosis, there is an area of increased risk of bone resorption in the near-contact area, approximately 1 mm wide, around the fixators. Dynamic loads may improve the osseointegration of the implant in pathological conditions of the bone tissue. ConclusionsThe results obtained in the case of healthy spine and osteoporotic bone tissues correspond to the experimental data on biomechanics and possible methods of IVD regeneration from the position of mechanobiological principles. The results obtained with an artificial disc (with keel-type fixation) showed that the use of this type of endoprosthesis in healthy bone tissues allows to reproduce the function of the natural intervertebral disc and does not contribute to the development of neoplastic processes. In the case of an artificial disc with osteoporosis of bone tissues, there is a zone with increased risk of tissue resorption and development of neoplastic processes in the area near the contact of the implant attachment. This circumstance can be compensated by increasing the loading level.

Simulation of Mechanical Processes at the Contact Region of a Dental Implant with Bone Tissues Under Shock Wave Treatment

Dental implants are becoming an increasingly important part of modern dental treatment. Developing an optimal implant surface design can improve osseointegration. Promising to increase the rate of osseointegration is the use of external shock wave therapy, which has proven itself for the treatment of fractures, bone defects, and bone tissue regeneration during surgery and arthroplasty. This work aims at a numerical investigation of the effects of low-energy shock wave therapy of various ranges on the mechanical behaviour of bone tissues, taking into account the physiological characteristics in the area of dental implant placement. Modelling was carried out using the method of movable cellular automata. Using computer simulation, it was found that the conditions for the regeneration of bone tissues at the near-contact zone with the implant of the jaw segment are created by a shock wave with an intensity of greater than 0.1 mJ/mm2.

Mechanical properties of silica aerogels modelled by Movable Cellular Automata simulations

In this paper the mechanical properties of silica aerogels are studied by simulations with the usage of the Movable Cellular Automata (MCA) method. In the MCA approach a sample is considered as a set of interacting cellular automata. The procedure to prepare porous samples is based on random spheres method. The resulting structures have densities in the range from 111 to 2200 kg/m3 and porosity up to 95%. The structures of the samples are studied by obtaining the fractal dimension using the FD3 program. The Young's modulus is examined in the simulation of a compression test. The elastic modulus relate to density by a power law characterized by exponent 3.83 ± 0.18 for samples with densities from 111 to 568 kg/m3 and 3.17 ± 0.11 for samples with densities from 350 to 2200 kg/m3. A comparison to previously published data from experiments and comparable computer simulations is included. The results prove that the Movable Cellular Automata method is suitable to investigate the mechanical properties of silica aerogels.

Risk assessment of resurfacing implant loosening and femur fracture under low-energy impacts taking into account degenerative changes in bone tissues. Computer simulation

Background and objectiveDegenerative diseases of the musculoskeletal system significantly reduce the quality of human life. Hip resurfacing is used to treat degenerative diseases in the later stages. After surgery, there is a risk of endoprosthesis loosening and low-energy fracture during daily physical activity. Computer modeling is a promising way to predict the optimal low-energy loads that do not lead to bone destruction. This paper aims to study numerically the mechanical behavior of the proximal femur, amenable to degenerative changes and subjected to hip resurfacing under low-energy impact equivalent to physiological loads. MethodsA numerical model of the mechanical behavior of the femur after hip resurfacing arthroplasty under low-energy impacts equivalent to physiological loads is presented. The model is based on the movable cellular automaton method (discrete elements), where the mechanical behavior of bone tissue is described using the Biot poroelasticity accounting for the presence and transfer of interstitial biological fluid. ResultsFor the first time, it is shown that a poroelastic model allows predicting the service life of endoprostheses, taking into account the individual characteristics of the bone tissues amenable to various degenerative diseases. The obtained results indicate that the changes in the bone properties have a significant influence on the critical forces corresponding to the first appearance of microcracks and the fracture formation. At the same time, their effect on the type of fracture is negligible. A much more impact on the type of fracture has the kinematic and dynamic conditions of the exposure. ConclusionsThe obtained results show the promise of using the proposed model for predicting the operational resource of resurfacing endoprostheses, taking into account the physiological features of the structure of the patient's bone tissues.

The Effect of Fluid-Saturation on Mechanical Behavior of the Coating–Substrate System under Contact Loading

The influence of the fluid saturation of a porous coating on the mechanical properties of the coating and the entire coating-substrate system is addressed. An important practical application is targeted as the wear-resistant coatings of endoprostheses of major human joints. Based on the method of movable cellular automata, a 3D-model of the mechanical behavior of a porous fluid-saturated coating on a titanium substrate is constructed. Using this model, the influence of fluid-saturation of the surface-layer of a ceramic coating on the mechanical characteristics of the coating-substrate system is studied numerically. The simulation results demonstrate that the presence of fluid in a thin surface layer of the coating can strongly affect the mechanical response of the entire coating-substrate system under sufficiently high rates of the local contact loading. In particular, the calculations without taking the fluid into account give overestimated values of strength and hardness of the coated materials under the wetting conditions. A simulation of scratching demonstrates that the material with a fluid-saturated surface layer is more stable to wear.

Физические закономерности влияния характеристик наполнителя на трибологические свойства полимерного нанокомпозита

The paper analyzes the patterns of influence of the characteristics of silica nanoparticles on the friction coefficient and wear parameters during friction of a polymer nanocomposite (PNC) on a steel counterbody. The studies were performed theoretically using the method of movable cellular automata and experimentally according to the "block-on-ring" scheme. The size and shape of silica nanoparticles and the sliding velocity were varied. The model also took into account the temperature dependence of the mechanical properties of materials. It was found that the low friction properties of PNC are caused by changing the mechanical properties of the materials of a transition tribolayer under conditions of frictional heating. It was shown also that the size of the nanofiller affects the stability of friction and wear mode.

О влиянии флюидонасыщенности пористого покрытия на механическое поведение системы покрытие - подложка при контактном нагружении

The problem of the influence of the porous coating saturation with a fluid on the mechanical properties of both the coating and the coating-substrate system as a whole is considered. An important practical application of the problem under consideration is wear-resistant coating of endoprostheses of human large joints. Based on the method of movable cellular automata, a three-dimensional model of the mechanical behavior of a porous fluid-saturated coating on a titanium substrate is constructed. The effect of fluid saturation of the surface layer of a ceramic coating on the mechanical characteristics of the coating-substrate system was numerically studied. The simulation results show that the presence of fluid in a thin surface layer of the coating can have a significant effect on the mechanical response of the entire coating-substrate system at sufficiently high rates of local contact loading. Thus, calculations without taking into account the interstitial fluid lead to an overestimation of the strength and hardness of the materials with coatings in wetting conditions. Scratch simulations show that a fluid-saturated surface layer possesses higher resistant to wear.

Simulation of three-point bending test of the silicon-coated nitinol bar

Self-expanding intravascular stents made of nickel-titanium shape memory alloy (nitinol) serve to recover the lumen of vessels suffered from atherosclerotic stenosis. A novel drug-eluting stents are usually wrapping by a porous coating containing an antiproliferative drug around the stent struts. From the practical point of view, it is very important to understand the strength of the coating owing to the flexibility of the nitinol struts. In this paper, we study numerically the strength properties of a nitinol bar covered by a silicon coating, as a part of such a stent, under three-point flexural test using the method of movable cellular automata. The results show stages of the coating fracture as well as a periodic pattern of the cracks in the coating, which are confirmed by experimental evidence. The difference in computational and experimental results shows the way for future works on improving the model assumptions.

Simulation of mechanical behaviour of the proximal femur as a poroelastic solid using particles

Full understanding of the mechanical behaviour of living bone is the key to solving many important problems of modern orthopaedics and arthroplasty. An important role in the study of the mechanical behaviour of living bone belongs to the development and use of comprehensive numerical models. In this work, we model the mechanical behaviour of the proximal femur as a 3D poroelastic solid consisting of the interior cancellous part and the outer cortical part. For simplicity, both parts are assumed isotopic linear poroelastic material. However, they have different values of porosity, fluid content and elastic properties, which are taken from literature. For computer simulation, we used the so-called movable cellular automaton method, which is a representative of simply deformed discrete elements i.e. computational particle mechanics. The method allows simulating dynamics of the elastic skeleton deformation and viscous fluid flow in the skeleton pores according to Biot’s theory of linear poroelasticity. Using the model developed we study the mechanical behaviour of the proximal part of the femur in compression with different rate of loading and different permeability. The results obtained for both saturated and drained bones are discussed.

MULTILEVEL NUMERICAL MODEL OF HIP JOINT ACCOUNTING FOR FRICTION IN THE HIP RESURFACING ENDOPROSTHESIS

Friction between the moving parts of the endoprosthesis has a significant impact on the endoprosthesis operation time. Primarily, it concerns the endoprosthesis of hip and knee joints. To improve the tribological characteristics of the metal endoprosthesis, hardening nanostructured coatings are used. Usually, titanium and titanium alloys are used as metal, and titanium nitride is used as a coating. Herein, we propose an approach to multilevel modeling of the system “bone-endoprosthesis” which is based on the movable cellular automaton method and accounts for friction between the moving parts of the hip resurfacing endoprosthesis. We validated the models of the friction system materials using the instrumented scratch test simulation. Then, we simulated friction at the mesolevel, explicitly considering roughness of the coating. The results obtained at the mesolevel were used as tribological characteristics of the coating in the macroscopic model of the hip resurfacing endoprosthesis.

The study of the dependence of mechanical properties and fracture of water-saturated high-strength concrete on the parameters of pore structure

Based on the hybrid numerical method, namely, the hybrid method of movable cellular automata, we developed a computer-based two-scale mechanical model of heavy water-saturated concrete. The model takes into account the content of the liquid phase and its redistribution in networks of microscopic and capillary pores. The features of deformation and fracture of concrete samples under uniaxial compression were numerically studied in a wide range of variation of the macroscopic characteristics of the pore space, viscosity of an interstitial liquid and loading rate. Simulation results confirmed the possibility of a unified description of the dependence of the strength of heavy concrete on the sample permeability and size, fluid viscosity and the loading rate in terms of the complex dimensionless parameter that combines these characteristics.

The development of the formalism of movable cellular automata for modeling the nonlinear mechanical behavior of viscoelastic materials

The paper is devoted to the development of the formalism of the computational method of discrete elements (DEM) for describing the mechanical behavior of consolidated viscoelastic materials. We considered an advanced implementation of DEM, namely, the method of movable cellular automata (MCA). A feature of this implementation of DEM is the use of a generalized many-body formulation of the relations for the forces of element-element interaction. 3D numerical models of viscoelastic material with a spectrum of relaxation times (Kelvin and Maxwell models, the standard model of elastomers, and others) were developed within the formalism of MCA. The correctness of the developed discrete element formalism and its applicability for modeling the processes of deformation and fracture of viscoelastic materials under dynamic loading are shown using the standard model of elastomers as an example. The relevance of the results is determined by the prospects for the further development of DEM and its application to study and predict the mechanical response of viscoelastic materials of various nature under dynamic loading including contact problems.

3D simulation of dry friction of metal-based composites

A numerical 3D model of friction at mesoscale of the contact patch between steel samples and composite steel samples with carbon nanoinclusions has been developed based on the movable cellular automaton method. The response function of automata simulating steel corresponds to an elastic-plastic body with linear hardening, and the function for simulating carbon corresponds to an elastic-plastic body with bilinear hardening. Von Mises criterion is used for breaking bonds between the automata, and the criterion based on plastic heat is used for coupling the automata. The values of basic parameters of the model, as well as the loading conditions, that allow the formation of the characteristic quasi-liquid layer in the friction zone are determined. It was shown that the presence of carbon nanoinclusions in the contact region leads to decreasing of the coefficient of friction, lower values of stress, and higher shear strain in the friction zone.

Influence of fracture incubation time on dynamic crack propagation in brittle solids

The paper is devoted to theoretical study of the longitudinal shear (mode II) crack unstable growth dynamics in brittle materials. We considered two main regimes of the dynamic propagation of the crack (sub-Rayleigh and supershear) and their implementation conditions. The research was carried out by computer simulation with the Movable Cellular Automaton method, using the generalized kinetic fracture model, which takes into account the finite duration of local fracture (fracture incubation time). It is shown that the fracture incubation time is a key parameter, which determines the transition conditions of the shear crack growth process from the sub-Rayleigh regime to supershear.

Моделирование движения одноклеточного микроорганизма «Amoeba Proteus» методом подвижных клеточных автоматов

Моделирование движения одноклеточного микроорганизма «Amoeba Proteus» методом подвижных клеточных автоматов

Understanding the mechanisms of friction stir welding based on computer simulation using particles

Abstract Friction stir welding (FSW) is a novel technique for joining different materials without melting. In FSW the welded components are joined by stirring the plasticized material of the welded edges with a special rotating pin plunged into the material and moving along the joint line. From the scientific point of view, the key role of the FSW processes belongs to formation of the special plasticized conditions and activation of physical mechanisms of mixing the materials in such conditions to produce the strong homogeneous weld. But it is still a lack of complete understanding of what are these conditions and mechanisms. This paper is devoted to understanding the mechanisms of material mixing in conditions of FSW based on a computer simulation using particles. The movable cellular automaton method (MCA), which is a representative of the particle methods in mechanics of materials, was used to perform all computations. Usually, material flow including material stirring in FSW is simulated using computational fluid mechanics or smoothed particle hydrodynamics, which assume that the material is a continuum and does not take into account the material structure. MCA considers a material as an ensemble of bonded particles. Breaking of inter-particle bonds and formation of new bonds enables simulation of crack nucleation and healing, as well as mass mixing and micro-welding. The paper consists of two main parts. In the first part, the simulations in 2D statements are performed to study the dynamics of friction stir welding of duralumin plates and influence of different welding regimes on the features of the material stirring and temperature distribution in the forming welded joints. It is shown that the ratio of the rotational speed to the advancing velocity of the tool has a dramatic effect on the joint quality. A suitable choice of these parameters combined with additional ultrasonic impact could considerably reduce the number of pores and microcracks in the weld without significant overheating of the welded materials. The second part of the paper considers simulation in the 3D statement. These simulations showed that using tool pins of different shape like a cylinder, cone, or pyramid without a shoulder results in negligible motion of the plasticized material in the direction of workpiece thickness. However, the optimal ratio of the advancing velocity to the rotational speed allows transporting of the stirred material around the tool pin several times and hence producing the joint of good quality.

The Fundamental Regularities of the Evolution of Elastic Vortices Generated in the Surface Layers of Solids under Tangential Contact Loading

Conventionally discussed dynamic mechanisms of elastic strain energy redistribution in near-contact surface regions include P and S elastic wave pulses radiating from the contact surface. At the same time, the elastic strain energy can be transferred by localized vortex-like elastic waves (Rayleigh, Love, Stoneley wave, and so on). In the paper, we numerically studied the main features of the formation and propagation of localized vortex-like waves in the surface layers under the contact zone. The study was done using the numerical method of movable cellular automata. We showed that the initial phase of dynamic contact interaction with a nonzero tangential component of contact velocity is accompanied by the formation of a so-called elastic vortex. The elastic vortex is a fully dynamic object, which is characterized by shear stress concentration and propagates at the shear wave speed. We first revealed the ability of the elastic vortex to propagate toward the bulk of the material and transfer elastic strain energy deep into the surface layer in a localized manner. We analyzed the dependence of the direction of vortex propagation on the tangential contact velocity, contact pressure and Young’s modulus of the material. The results of the study are important for better understanding the dynamic mechanisms contributing to inelastic strain accumulation or gradual degradation of surface layers.

Mechanisms of Deformation and Fracture of Thin Coatings on Different Substrates in Instrumented Indentation

Mechanical properties of thin surface layers and coatings are commonly studied using instrumented indentation and scratch testing, where the mechanical response of the coating – substrate system essentially depends on the substrate material. It is quite difficult to distinguish this dependence and take it into account in the course of full-scale experiments due to a multivariative and nonlinear character of the influence. In this study the process of instrumented indentation of a hardening coating formed on different substrates is investigated numerically by the method of movable cellular automata. As a result of modeling, we identified the features of the substrate material influence on the derived mechanical characteristics of the coating – substrate systems and the processes of their deformation and fracture.

Multiscale model of mechanical behavior of ceramics composite with soft matter filling based on movable cellular automaton

In this paper, movable cellular automaton method (MCA) is applied to the multiscale simulation of 3D samples of ceramics composite with soft matter filler. MCA is an efficient numerical method in particle mechanics, which assumes many-particle interaction among discrete elements and makes a feasible simulation of solid behavior including deformation, crack initiation and propagation, and further fragmentation of the material at different scales. The lowest scale of the proposed model corresponds to the characteristic size of the smallest pores/inclusions. Herein we start with modeling uniaxial compression of several representative ceramics samples with an explicit account of small pores randomly distributed in space. The results are the average values of Young’s modulus, Poisson’s ratio, and strength, as well as the parameters of the Weibull distribution of these properties at the current scale. The data obtained allow us to describe the material behavior at the next scale were large cylindrical inclusions are considered explicitly, while the influence of small pores is accounted via the effective properties determined at the previous scale. The simulation results show that for each value of volume fraction of cylindrical soft inclusions there is no scattering of elastic modulus values while the scatter of strength and Poisson’s ratio values is significant. Random orientation of soft elongated inclusions results in higher strength value and does not change Young’s modulus of the model composites.