Simulation of Crack Pattern Formation Due to Shrinkage in a Drying Material

Crack patterns observed in nature have attracted the interest of researchers in various fields, and the mechanism of the pattern formation has been investigated. However, the phenomenon is very complicated, and many factors affect the process. Therefore, we are motivated to construct a general simulation code with a simple algorithm. In this study, crack pattern formation due to shrinkage caused by the drying of a wet material was simulated. The process was simplified as follows: tensile force is generated in the model, and a crack is generated when the tension exceeds a critical value. The tensile forces in the x and y directions are independently evaluated. A crack propagates perpendicular to the tension until it reaches another crack or a boundary. Based on this modeling, simulations with a two-dimensional square domain were performed. Consequently, a cross-divided pattern was generated. Assuming zigzag crack propagation, more realistic patterns were obtained. The effects of the boundary and domain size were also considered, and various characteristic patterns were obtained. Furthermore, the orientation dependency was simulated, and 45&#730 declined patterns and rectangularly divided patterns were generated. The model presented in this study is very simplified and is expected to be applicable to various objects.

POD analysis of the instability mode of a low-speed streak in a laminar boundary layer

The instability of one single low-speed streak in a zero-pressure-gradient laminar boundary layer is investigated experimentally via both hydrogen bubble visualization and planar particle image velocimetry(PIV) measurement. A single low-speed streak is generated and destabilized by the wake of an interference wire positioned normal to the wall and in the upstream. The downstream development of the streak includes secondary instability and self-reproduction process, which leads to the generation of two additional streaks appearing on either side of the primary one. A proper orthogonal decomposition(POD) analysis of PIV measured velocity field is used to identify the components of the streak instability in the POD mode space: for a sinuous/varicose type of POD mode, its basis functions present anti-symmetric/symmetric distributions about the streak centerline in the streamwise component, and the symmetry condition reverses in the spanwise component. It is further shown that sinuous mode dominates the turbulent kinematic energy(TKE) through the whole streak evolution process, the TKE content first increases along the streamwise direction to a saturation value and then decays slowly. In contrast, varicose mode exhibits a sustained growth of the TKE content,suggesting an increasing competition of varicose instability against sinuous instability.

Molecular Dynamics Simulation of Grain Refinement in a Polycrystalline Material under Severe Compressive Deformation

Grain refinement in a polycrystalline material resulting from severe compressive deformation was simulated using molecular dynamics. A simplified model with four square grains surrounded by periodic boundaries was prepared, and compressive deformation was imposed by shortening the length in the y direction. The model first deformed elastically, and the compressive stress increased monotonically. Inelastic deformation was then initiated, and the stress decreased drastically. At that moment, dislocation or slip was initiated at the grain boundaries or triple junction and then spread within the grains. New grain boundaries were then generated in some of the grains, and sub-grains appeared. Finally, a microstructure with refined grains was obtained. This process was simulated using two types of grain arrangements and three different combinations of crystal orientations. Grain refinement generally proceeded in a similar fashion in each scenario, whereas the detailed inelastic deformation and grain refinement behavior depended on the initial microstructure.

Phase-Field Modeling for the Three-Dimensional Space-Filling Structure of Metal Foam Materials

Phase-field modeling for three-dimensional foam structures is presented. The foam structure, which is generally applicable for porous material design, is geometrically approximated with a space-filling structure, and hence, the analysis of the space-filling structure was performed using the phase field model. An additional term was introduced to the conventional multi-phase field model to satisfy the volume constraint condition. Then, the equations were numerically solved using the finite difference method, and simulations were carried out for several nuclei settings. First, the nuclei were set on complete lattice points for a bcc or fcc arrangement, with a truncated hexagonal structure, which is known as a Kelvin cell, or a rhombic dodecahedron being obtained, respectively. Then, an irregularity was introduced in the initial nuclei arrangement. The results revealed that the truncated hexagonal structure was stable against a slight irregularity, whereas the rhombic polyhedral was destroyed by the instability. Finally, the nuclei were placed randomly, and the relaxation process of a certain cell was traced with the result that every cell leads to a convex polyhedron shape.

Numerical Evaluation of the Surface Energy of Polyhedral Nanoparticles

Nanoparticles have been used widely in various fields, and their size and shape greatly affect the functional properties. Therefore, controlling the morphology of the particles is important, and evaluation of the surface energy is indispensable for that purpose. In this study, the surface energy of nanoparticles was evaluated by numerical simulation and formulated in a polynomial equation. First, molecular dynamics simulations were carried out for variously shaped polyhedral nanoparticles. A cube and an octahedron were introduced as reference shapes, and truncated hexahedrons and truncated octahedrons were created by cutting out their vertices. The surface energy was plotted for various polyhedrons. The lowest energy was observed in an octahedron because of the stability of the (111) plane, and the highest energy was observed in a cube because of the relatively higher energy of the (100) plane. Then, the surface energy was formulated in a polynomial equation, in which the parameters obtained by the molecular-dynamics simulations were introduced. As a result, stability of the octahedron and relative instability of the cube were fairly captured by the proposed polynomial equation, while a slight underestimation was inevitable. Finally, the parameters were revised to continuous numbers to extend the application range. Consequently, an application for various materials, such as a cube having equivalent stability to an octahedron, was demonstrated by imposing rather exaggerated parameters.

Numerical Simulation of a Domain-Tessellation Pattern on a Spherical Surface Using a Phase Field Model

A numerical simulation scheme is proposed to analyze domain tessellation and pattern formation on a spherical surface using the phase-field method. A multi-phase-field model is adopted to represent domain growth, and the finite-difference method (FDM) is used for numerical integration. The lattice points for the FDM are distributed regularly on a spherical surface so that a mostly regular triangular domain division is realized. First, a conventional diffusion process is simulated using this lattice to confirm its validity. The multi-phase-field equation is then applied, and pattern formation processes under various initial conditions are simulated. Unlike pattern formation on a flat plane, where the regular hexagonal domains are always stable, certain different patterns are generated. Specifically, characteristic stable patterns are obtained when the number of domains, n, is 6, 8, or 12;for instance, a regular pentagonal domain division pattern is generated for n = 12, which corresponds to a regular dodecahedron.

Modeling of Adhesive Particles Using a Combination of the Two-Body Interaction and Phase-Field Methods

Discrete materials such as powders and granular materials have been widely used due to their specific characteristics. The precise evaluation is accordingly becoming important, and various numerical schemes have been developed. However, the interactions among the constituent particles are still difficult to model precisely. Especially, contact conditions, which vary with material properties and circumstances, are difficult to formulate. In this study, a computational model for simulating adhesive particles on contact in a many-particle system is proposed. The interaction between the particles was represented by a two-body repulsive force that depends on the distance between particles and an additional adhesive force at the contact point. A phase-field variable was introduced to express the surface of each particle, and the adhesive force was formulated using the phase-field distribution. As a result, the adhesion of particles was properly expressed. For a mono-particle system, neighboring particles adhered and uniformly aggregated, while for a dual-particle system, several characteristic patterns were obtained depending on the initial arrangement of the particles. Repulsive contact was also considered as a specific case, and the corresponding results were obtained.

Modeling and Simulation of Particle-Packing Structures and Their Stability Using the Distinct Element Method

A numerical method for simulating the stability of particle-packing structures is presented. The packing structures were modeled on the basis of face-centered cubic (fcc) and body-centered cubic (bcc) structures, and the stability of these structures was investigated using the distinct element method. The interaction between the particles was simplified by considering repulsive, adhesive, and damping forces, and the stability against the gravitational force was simulated. The results under a certain set of parameters showed characteristic deformation when the particles were arranged in an fcc array. Focusing on the local structure, the resulting model was divided into several domains: The bottom base, four top corners, and intermediate domains. The bottom base notably became a body-centered tetragonal (bct) structure, which corresponds to a uniaxially compressed bcc structure. Conversely, the models based on the bcc arrangement were structurally stable, as no specific deformation was observed, and a monotonously compressed bct structure was obtained. Consequently, the bcc arrangement is concluded to be more stable against uniaxial compression, such as the gravitational force, in a particle-packing system.

A Molecular Dynamics Study on the Effects of Lattice Defects on the Phase Transformation from BCC to FCC Structures

Molecular dynamics simulations of the phase transformation from body- centered-cubic (bcc) to face-centered-cubic (fcc) structures were performed. A Morse-type function was applied, and the parameters were determined so that both fcc and bcc structures were stable for the perfectcrystal model. When the fcc structure was superior to the bcc structure, the bcc model transformed to fcc. Two mechanisms, based on the Bain and Nishiyama- Wasserman (NW) relationships, were considered. Then, point or linear lattice defects, i.e., randomly scattered or regularly aligned vacancies, were introduced. Consequently, bcc models tended to transform to an fcc structure, whereas fcc models remained stable. The transformation process was also investigated in detail. BCC-to-FCC transformation is often considered as a homogeneous process based on changes in the axis lengths, and such a process was observed for the perfectcrystal model. Conversely, for the defect models, local heterogeneous deformation patterns, including cylindrical domain and planar interface formation, were observed. These behaviors are considered to be related to plastic deformation during phase transformation, and the validity of the presented model for further investigation was confirmed.

Analysis of Selecting Gated Community as Opening Its Micro-Inter-Road Network

The opening of gated community to expand the micro-road network in the urban traffic system is a hot topic on the urban congestion. To satisfy the demand of opening early choosing case, this paper proposed a comprehensive selecting framework on qualified communities and its appropriate opening time. Firstly, the static influential factors on internal road structure, boundary road structure and traffic flow are qualitatively analyzed. Then, an evaluation opening state index system based on describing accurately traffic flow state is obtained, which takes the opening factors into account at the boundary road network. In this structure, the modified fuzzy C-means (FCM) method calculates the fuzzy entropy weight and range of each opening states index. Finally, the simulation results show that the proposed method is capable of selecting qualified community and the optimum opening time.

Simulation of Polyhedral Crystal Growth Based on the Estimated Surface Energy of Crystallographic Planes

Polyhedral shapes can be found in crystalline materials ranging from macroscopic natural mineral solids to microscopic or nanoscopic particles. These shapes originate from the crystallographic properties of the constituting material, and the outer shape depends on several unique habit planes. In this study, polyhedral crystal growth was simulated considering the surface energy and crystallographic characteristics. A series of polyhedrons, including cube, truncated hexahedron, cuboctahedron, truncated octahedron, and regular octahedron, was targeted. First, the polyhedron’s static surface energy and dynamic energy variation during crystal growth were computed. Then, the crystal-growth process was simulated based on the energy minimization policy. Interestingly, when the simulation began with truncated hexahedral nucleus, the shape changed to a cuboctahedron;however, a certain type of truncated octahedron was obtained when starting with different types of truncated octahedrons. In addition, once converged cuboctahedron abruptly changed the shape to a truncated octahedron as the crystal became larger. These results were supported by the static and dynamic energy curves. Furthermore, the method was applied to different materials by assuming virtual parameters, yielding various morphologies.

Tomographic particle image velocimetry measurement on three-dimensional swirling flow in dual-stage counter-rotating swirler

Three-Dimensional(3D)swirling flow structures,generated by a counter-rotating dualstage swirler in a confined chamber with a confinement ratio of 1.53,were experimentally investigated at Re=2.3×10^(5)using Tomographic Particle Image Velocimetry(Tomo-PIV)and planar Particle Image Velocimetry(PIV).Based on the analysis of the 3D time-averaged swirling flow structures and 3D Proper Orthogonal Decomposition(POD)of the Tomo-PIV data,typical coherent flow structures,including the Corner Recirculation Zone(CRZ),Central Recirculation Zone(CTRZ),and Lip Recirculation Zone(LRZ),were extracted.The counter-rotating dual-stage swirler with a Venturi flare generates the independence process of vortex breakdown from the main stage and pilot stage,leading to the formation of an LRZ and a smaller CTRZ near the nozzle outlet.The confinement squeezes the CRZ to the corner and causes a reverse rotation flow to limit the shape of the CTRZ.A large-scale flow structure caused by the main stage features an explosive breakup,flapping,and Precessing Vortex Core(PVC).The explosive breakup mode dominates the swirling flow structures owing to the expansion and construction of the main jet,whereas the flapping mode is related to the wake perturbation.Confinement limits the expansion of PVC and causes it to contract after the impacting area.

Computer Simulation of Microscopic Stress Distribution in Complex Microstructure Using a Phase Field Model

Microscopic stress distribution in a metallic material which has complex microstructure is simulated using a phase field model.The fundamental equations which take into account the coupling effects among phase transformation,temperature and stress/strain are used,while thermal effects are neglected to focus on the volumetric change due to phase transformation in this paper.A two-dimensional square region is considered,and the evolution of microscopic stress and the resultant residual stress distribution are calculated using the finite element method.As the phase transformation progresses and grains grow larger,stress is generated around the growing interface.When a grain collides with another one,specifically large stress is observed.Residual stress is finally distributed in the microstructure formed,and apparently large stresses are retained along the grain boundaries. Subsequently,dependency of the stress distribution on microstructure pattern is investigated.First,variously sized square grains are tested,and it reveals that the maximum stress tends to decrease as the grain size becomes smaller.Next,the shapes of the grains are varied.As a result,the stress distribution is remarkably affected,while the maximum stress value does not change so much.More complicated grain arrangement is finally tested with eight or nine grain models.Then,it is revealed as a common feature that large stress is generated along the grain boundaries and that the stress distribution is dependent on the grain arrangement.