Adaptive Meshing Technique Research Articles

Evaluating Tire Tread Wear and Its Dependence on Tire Working Conditions by Using the Finite Element Method and Archard’s Wear Theory

ABSTRACT The tire industry still spends a considerable amount of resources on indoor and outdoor tests during the product development stage. Virtual tests provide conditions to complete this step faster, saving both money and time. Considering that life span and mileage are important issues, especially for truck tire consumers, virtual wear analyses provide valuable information that helps engineers to improve their products. This study aims to exemplify a way to predict tread band wear using the finite element method approach and Archard’s wear theory. In addition, it shows the importance of following the vehicle maintenance program as it has an impact on how long the set of tires will last. Tread wear simulation is implemented through user subroutine and adaptive meshing technique, whereas friction energy is calculated using a steady-state analysis at selected working conditions. Data collected from outdoor experiments provide the necessary information to check and validate the analysis. The impact of the lack of appropriate vehicle maintenance on tire wear is evaluated by changing some boundary conditions of the model such as load, inner pressure, and camber and toe angles. The simulation results show good agreement with the information found in the literature.

A long short-term memory neural network-based error estimator for three-dimensional dynamically adaptive mesh generation

Adaptive meshes are pivotal in numerical modeling and simulation, offering a means to efficiently, precisely, and flexibly represent intricate physical phenomena, particularly when grappling with their intricacies and varying scales. However, the transition from two dimensions (2D) to three dimensions (3D) poses a substantial challenge, as the computational demands of dynamically adaptive mesh techniques increase exponentially. Addressing this challenge effectively, we turn to the cutting-edge realm of artificial intelligence and neural networks. In our study, we harness the innovative power of a long short-term memory (LSTM) neural network as an error estimator for adapting unstructured meshes in both 2D and 3D scenarios. This LSTM network predicts the evolution of the adaptive grid based on specified variables, presenting itself as an artificial intelligence-driven architecture to optimize the adaptive criterion for the target variable. This is achieved by establishing a direct correspondence between the Riemann metric and these variables. To demonstrate the practical applicability of our approach, we seamlessly integrate the LSTM error estimator into the 3D adaptive atmospheric model Fluidity-Atmosphere (Fluidity-Atmos), thereby enabling real-time mesh adaptation during numerical simulations. We assess the effectiveness of this method in terms of simulation precision and computational efficiency through a series of experiments in both 2D and 3D settings. Our results not only reveal that the mesh patterns generated by the LSTM error estimator within Fluidity-Atmos closely resemble those produced by traditional error estimators but also underscore its superior performance in enhancing simulation accuracy. Notably, as the number of nodes increases, the LSTM mesh generator substantially reduces CPU time requirements by up to 50% in 3D cases compared to the conventional mesh generator within Fluidity-Atmos, highlighting its remarkable computational efficiency.

In-silico modelling of multi-strike insertion and torsional resistance of tapered revision hip stems: Insight into spline design philosophy.

Despite the clinical success of tapered splined titanium stems, a knowledge gap still exists between spline design and its primary mechanical stability, which is critical to the long-term success of revision hip arthroplasty. Additionally, almost all published pre-clinical studies relied on resource-intensive benchtop and cadaveric testing. Hence, the present study developed a novel computational model to investigate effects of spline geometry and configuration on axial and torsional stability of tapered stem. Dynamic explicit Finite Element Analysis coupled with a state-of-the-art adaptive meshing technique was used to simulate the highly non-linear contacts and large bony material deformations. Hybridising primary straight splines with secondary angled splines results in 41% and 10% increases of peak insertion force and post-seating moment than the predicate device for the same seating position. The primary straight splines cut at multiple circumferential bony locations, enhancing torsional stability; while the alternatively placed secondary angled splines form wedges with the bone, providing reliable seating and additional torsional resistance. To the best knowledge of the author, this is the first in-silico investigation of its kind to simulate multi-strike seating and torsional resistance of revision hip stems, offering an effective and efficient platform for future multi-factorial parametric study and uncertainty quantification.

Analysis of the Electrically Large Target in Isotropic Medium by the Physical Optics Method With Adaptive Mesh Technique

In this work, the physical optics (PO) method based on multilayered medium theory is used to analyze high-frequency scattering characteristics of plasma sheath covering an aircraft. The ray intersection method is taken for occlusion judgment, but some errors occur on the edge between illuminated and shadowed regions of a target. Therefore, the iterative edge patch segmentation based on adaptive mesh technique is proposed to reduce this error, which is significant to enhance computational accuracy of the PO method. Furthermore, to simplify the computational process and validate effectiveness of adaptive mesh technique, the plasma sheath covering a RAM-C II aircraft is modeled with a five-layered isotropic medium. Compared with uniform fine segmentation, the proposed adaptive mesh technique markedly reduces the computational cost by an order of magnitude while maintaining accuracy of the PO method. Moreover, high-frequency scattering characteristics of plasma sheath covering a RAM-C II aircraft under different flight conditions are presented via the bistatic radar cross section (RCS) with observable attenuation effects. Hence, the PO method for multilayered media combined with the proposed lit region judgment method is suitable to analyze scattering features of electrically large coated target.

Application of mesh adaptive technology combined with adaptive time stepping technology under strong earthquake liquefaction

Mesh distortion caused by large deformations is a major problem that disrupts finite element (FE) analysis computations. For example, the traditional updating Lagrangian approach updates the spatial configuration of the node points, yet strong earthquakes exacerbate this issue. To address the problem, an arbitrary Lagrangian Euler (ALE) method has been developed based on the updated Lagrangian method and solid‒fluid two-phase mixing theory. This adaptive mesh technique reshapes the deformed mesh at each computational step and projects variables onto a new configuration. However, the constant modification of the mesh to avoid distortion increases the overall analysis time. To solve this problem, an adaptive time stepping methodology is introduced, which evaluates the mixed error through five control parameters and adjusts the calculation step size in real time. This method considers the effect of the time step on the required amount of time and the calculation accuracy and dynamically adjusts the time step to optimize the associated tradeoff between the two. Two FE examples demonstrate the effectiveness of the method. The results show that partitioning the time increment significantly influences the mesh distortion and calculation time and that the ALE method can maintain a nondistorted mesh. The method is optimized for accuracy and calculation time. Various working conditions and models affect the method differently, particularly regarding acceleration properties. Small excitations perform better than large excitation, and the maximum computation time can be reduced by more than 80% through adaptive solver optimization.

HLPW-4/GMGW-3: Mesh Adaptation for RANS Technology Focus Group Workshop Summary

The AIAA workshop series helps guide the computational fluid dynamics (CFD) community through publicly available test cases and impartial evaluation to establish the state-of-the-art in applied CFD. A summary of the Mesh Adaptation Technical Focus Group submissions for the joint Fourth CFD High Lift Prediction and Third Geometry & Mesh Generation Workshop is provided. The Common Research Model High-Lift variant (CRM-HL) is the target of this investigation. A 2D high-lift airfoil solution verification case was extracted from the 3D CRM-HL. Low variation is shown between 2D solutions with mesh adaptation to control estimated solution interpolation and output errors. As expected, variation for these mesh adaptation techniques is larger for the 3D CRM-HL than the 2D airfoil. More importantly, the 3D mesh-adapted results have a lower variation than expert-crafted meshes of equal or larger size. Suspected multiple solutions to Reynolds-averaged Navier–Stokes with the Spalart–Allmaras turbulence model appear to resolve into a common solution with mesh resolution.

On the effects of an optimized inlet acoustically flow on a heat storage system's performance: A numerical study

BackgroundAcoustic flows are the rotational flows that are generated near solid surfaces and vibrating components, as well as near boundary walls in a high-intensity sound field. By making the flow oscillate, this type of flow can be a good way to improve HT. Besides, phase change materials provide high cooling in a short time because they absorb the latent heat of their melting during melting. MethodThe use of the phase change material and adding some pulsing function of inlet flow have been considered to investigate the battery's performance. To this end, the finite volume method, along with interface mesh and grid adaptation techniques, has been used to achieve more accurate results. FindingThe comparisons of the obtained results were made to the existing data, and after ensuring the numerical methodology, four functions were used to investigate the effects of variations in inlet velocity. The results showed that different kinds of pulsation flows have different qualities and ways to improve HT in different situations. For instance, the sine profile helps the average temperature of the PCM unit reach the maximum value in approximately 50 percent less time.

Numerical Investigation of Flow Patterns and Plug Hydrodynamics in a 3D T-junction Microchannel

A three-dimensional (3D) numerical simulation of a two-phase flow liquid/liquid is performed in a rectangular microchannel with a T-junction. The volume of fluid (VOF) method was used under ANSYS Fluent to capture the interface between the two phases. The dynamic mesh adaptation technique together with the assumption of symmetry plane helps us to reduce the computational cost. The study focuses on the flow patterns and hydrodynamics of plugs. So, the influence of the flow rate ratio $$q$$ , the capillary number $$Ca$$ , and the viscosity ratio on the liquid film, the plug/droplet shape, and velocity are examined here. Particularly, the plug/droplet lengths predicted by the simulation show good agreement with the experimental and correlation available in the literature. The results revealed six distinct flow patterns by dispersing water in a continuous phase of silicone oil. By decreasing the flow rate ratio as well as the viscosity ratio, the liquid film thickness increases in the corners and side planes. In turn, this greatly impacts the liquid film velocity and the plug velocity. Furthermore, capillary number (based on two-phase flow velocity) is also shown to have a greater impact than viscosity ratio and flow rate ratio on plug shape, with the curvature radii of the tail always larger than the front one.

An adaptive finite element method for crack propagation based on a multifunctional super singular element

The traditional finite element method (FEM) often requires a large number of refined meshes to analyze the mechanical behavior of geometric discontinuities, its computational efficiency and convergence speed are affected. In this paper, an adaptive FEM for crack propagation based on a multifunctional super singular element (MSSE) at the crack tip is proposed for the fracture process investigation of two-dimensional (2D) materials. The adaptive FEM for crack propagation divides the crack tip neighborhood into the MSSE region, the protection element (PE) region and the background element (BE) region. The MSSE is established based on the numerical eigen-solution of the singular stress field near the crack tip, and can be used for anisotropic material and interfacial crack problems. The PE and BE regions are still discretized by the conventional finite element meshes. Since the node degrees of freedom between MSSE and conventional finite element are unified, they can be assembled directly without transition element. The MSSE can be used to solve the crack tip stress intensity factor (SIF) directly without refining the crack tip mesh. The adaptive meshing technique reduces the difficulty of remeshing during crack growth, thus facilitating the simulation of crack propagation processes. The adaptive crack propagation algorithm is used to analyze the crack propagation problems in isotropic materials, anisotropic materials and bi-materials. The calculated results demonstrate the effectiveness and universality of the crack tip MSSE. The method has potential for application in the simulation study of residual strength and fatigue fracture of complex mechanical structures.

On the Eccentrically Loaded Strip Footing Resting Over a Circular Cavity in the Rock Mass: Adaptive Finite-Element Analysis, Observations, and Recommendations

In this study, the effect of an eccentric load on the ultimate bearing capacity (UBC) of a strip footing of width B resting above a circular cavity in the rock mass is investigated using upper -and lower-bound finite-element limit analysis incorporating an adaptive meshing technique. The effect of governing independent variables, such as the diameter of the circular cavity, dc, load eccentricity, e, distance of the cavity from the footing (horizontal, P, and vertical, Q), and rock mass parameters based on the generalized Hoek–Brown (GHB) failure criterion on the reduction of the UBC, is studied using a reduction coefficient, Rc. This study reveals that the influence of the cavity on the UBC is minimal for a cavity beyond a depth of Q/B ≥ 2.5 when e/B ≥ 0.3; and that Q/B ≥ 3 when 0.1 ≤ e/B ≤ 0.2, irrespective of P/B. Similarly, a cavity situated at −2 ≤ P/B ≥ 2 and Q/B ≥ 2 when e/B = 0.3–0.4, and −3.5 ≤ P/B ≥ 3.5 and Q/B ≥ 2.5 when 0.1 ≤ e/B ≤ 0.2, does not show any significant impact on the reduction of the UBC. Dominant potential failure patterns that could cover at least all the representative cases are presented and discussed to strengthen the insight into the possible mechanism of such a footing failure.

Mesh deep Q network: A deep reinforcement learning framework for improving meshes in computational fluid dynamics

Meshing is a critical, but user-intensive process necessary for stable and accurate simulations in computational fluid dynamics (CFD). Mesh generation is often a bottleneck in CFD pipelines. Adaptive meshing techniques allow the mesh to be updated automatically to produce an accurate solution for the problem at hand. Existing classical techniques for adaptive meshing require either additional functionality out of solvers, many training simulations, or both. Current machine learning techniques often require substantial computational cost for training data generation, and are restricted in scope to the training data flow regime. Mesh Deep Q Network (MeshDQN) is developed as a general purpose deep reinforcement learning framework to iteratively coarsen meshes while preserving target property calculation. A graph neural network based deep Q network is used to select mesh vertices for removal and solution interpolation is used to bypass expensive simulations at each step in the improvement process. MeshDQN requires a single simulation prior to mesh coarsening, while making no assumptions about flow regime, mesh type, or solver, only requiring the ability to modify meshes directly in a CFD pipeline. MeshDQN successfully improves meshes for two 2D airfoils.

Adaptive Mesh Refinement for Dam-Break Models using the Shallow Water Equations

The 2D shallow water equations are a common tool for the simulation of free surface fluid dynamics in civil engineering. However, the nonlinear structures of the equations' straightforward implementations lead to numerical problems, such as spurious oscillations and unphysical diffusion. Therefore, this research compared several strategies to overcome these problems, using various finite element formulations and combinations of stabilization methods and mesh options. The accuracy and performance of numerous approaches are examined on models of dam-break in one and two space dimensions. The analytical solution checks the numerical, derived shock wave heights and velocities for the 1D classical benchmark. The result showed that streamlined diffusion and shock capturing stabilization deal with the classical problems of spurious oscillations and numerical diffusion but still indicate similar problems locally in the vicinity of steep fronts and shock waves when used on fixed meshes. As adaptive meshing is the most promising method to deal with such situations, several concerned options are examined in detail. It is important to fine-tune the method to the model's needs, i.e. to adapt the maximum number of mesh refinements, the indicator functions, and the starting mesh. The use of adaptive meshing techniques leads to accurate solutions for the usual parameter range in 1D and 2D, requiring less computational resources than simulations on fixed meshes. Meanwhile, meshing reduces the model size of the 2D dam break model adaptive by almost one order of magnitude and the execution time by a factor of 20.

A Hybrid Euler–Lagrange Model for the Paint Atomization Process of Air Spraying

The modeling of the paint atomization process is a barrier in computational fluid dynamics numerical simulation for the whole process of air spraying, and seriously restricts robot intelligent spray gun trajectory planning and the improvement of coating quality. Consequently, a multi-scale paint atomization model based on the hybrid Euler–Lagrange method was established in this paper, which included a large liquid micelle motion model, a particle motion model, and a turbulence flow model. The Euler method was adopted to capture the gas–liquid interface in the atomization flow field to describe the deformation and motion of large liquid micelles. The identification and transformation mechanisms of large liquid micelles and small particles were constructed by the particle motion model, and the motion of small droplets generated by paint atomization was tracked by the Lagrange method. The turbulence motion of the fluid in the process of paint atomization was described by a two-equation turbulence model. The model calculation method consisting of a finite-volume model, an adaptive hexcore mesh technique and a pressure-based coupled algorithm was established. The multi-scale atomization model was solved and model validation was carried out, which included mesh independence verification and model reliability analysis. The numerical simulation results predicted the atomization flow field parameters, paint atomization shapes, and the changing process from paint to liquid droplets, which was consistent with the experimental data. As a result, the established multi-scale atomization model in this paper is reliable for studying the paint atomization process of air spraying.

A performance degradation analysis method for a reciprocating rod seal in the wear process under mixed lubrication conditions

The sealing performance of a reciprocating seal degrades during service. The analyses developed based on the initial state of a seal cannot express the performance degradation due to seal wear in detail. In this research, the Archard model in dry friction is extended to mixed lubrication by introducing the lubrication coefficient verified by an experiment. The nonlinear adaptive meshing technique is used in finite element analysis (FEA) to simulate the material removal to obtain the static contact pressure during the wear process. Hence, a sealing performance degradation analysis method is proposed based on the modified Archard model for reciprocating seals under mixed lubricating conditions. This method can be used to analyse the sealing, lubrication, and wear characteristics of seals at any service time. The simulation results indicate that the static pressure becomes more uniform with the occurrence of seal wear, and the lubricating property of the oil film reduces the seal wear. The variation trends of the sealing performance parameters such as contact pressure, friction, and net leakage at different service times under specific operating conditions are obtained.

An h-adaptive local discontinuous Galerkin method for second order wave equation: Applications for the underwater explosion shock hydrodynamics

The underwater explosion (UNDEX) phenomenon involves hydrodynamic behaviors with a wide range of spatial scales, from macroscopic cavitation regions to refined areas with fluid-structure interactions around the shock wavefront. Correct description of the refined shock wavefront is important for determining the shock wave position and pressure peak. In this work, the local discontinuous Galerkin (LDG) method for the two-dimensional wave equation, which allows for the local triangular meshes refinement and merging during the shock wave propagation process, is presented to model the UNDEX shock hydrodynamics. This article is an extension of our previous work, where we discretize the UNDEX total wave formulation in the LDG framework and simulate the UNDEX shock wave and cavitation phenomenon. In order to save computational cost (including CPU time and computational storage) and capture the shock wavefront more accurately, the LDG method is extended to be in combination with the mesh adaption technique. The troubled-cell indicator, depending on the local jump of the pressure, is adopted to identify elements which require to be refined or coarsened. Typical numerical examples are tested to assess the capability of the present h-adaptive LDG method for capturing the UNDEX shock wave. The numerical results clearly demonstrate that the mesh adaption technique enables us to dynamically increase the mesh resolution in close proximity to the flow discontinuities with a large pressure jump. The local increase of the mesh resolution results in a substantial increase in the accuracy of the pressure peak. In terms of the computational efficiency, the h-adaptive LDG method can save nearly half of the calculation time in comparison to the non-adaptive LDG method on uniform meshes, whose mesh resolution is the same as that of the maximum level of refinement of the h-adaptive LDG method.

Adaptive stabilized mixed formulation for phase field fracture modeling of nearly incompressible finite elasticity

The recently proposed mixed displacement-pressure-phase field formulation characterized by damage-mitigating incompressibility constraints excels in fracture modeling of nearly incompressible hyperelastic materials. However, such formulations generally call for mixed finite element (FE) allocations that satisfy the inf-sup condition, denying the popular lower equal-order linear FE pairs, like linear polynomial (P1) interpolation for all fields. To overcome this drawback, we develop a stabilized mixed formulation (P1/P1S) by resorting to a pressure projection technique. The lure of this formulation lies in its simplicity and versatility, allowing low-order P1 interpolation for all field variables. With this trait in mind, an efficient adaptive meshing strategy is designed, thereby speeding up computation by more than 15 times. For better coping with the adaptive scenarios involving crack nucleation, we also propose a novel energy-based mesh refinement criterion. The numerical treatment of the stabilized mixed FE formulation is elaborated, as well as the core operations of the adaptive meshing technique. The accuracy, efficiency, and robustness of the proposed formulation are validated by several representative numerical examples. Remarkably, a mixed I/II fracture test thereof is in good agreement with the experiment and thus promises to be a new benchmark.

Experiment-based numerical evaluation of the surface recession of C/C–SiC composites under the high-energy laser

In this paper, we developed a multi mechanism coupling finite element model to predict the surface recession of C/C–SiC composites on the basis of the ablation phenomena. In particular, we took into account temperature-dependent properties of component materials, heat convection, and radiation in the ultra-high temperature range. By combining a user-defined subroutine and arbitrary Lagrangian-Eulerian adaptive meshing technique, the surface recession of C/C–SiC composites was captured. The predicted ablation depth agreed well with experimental results. The trend of the ablation rate between simulations and experiments was almost the same. Meanwhile, the effects of the laser powers on ablation behaviors of C/C–SiC composites were investigated. It was found that low laser powers had little effect on the ablation rate while the ablation rate increased first and then decreased for high laser powers.

Laser light-induced deformation of free surface of oil due to thermocapillary Marangoni phenomenon: Experiment and computational fluid dynamics simulations

Remote light-induced free liquid surface deformation has been studied in various systems for decades. One of the mechanisms able to do this task is driven by the thermocapillary Marangoni effect. The strength of the light–matter interaction, which is usually weak, here is amplified by the light absorption and heat production that changes surface tension. Here, we report on an experimental study aimed at dynamical aspects of the deformation induced under conditions of chopped laser excitation light. The light-induced deformations are usually in the range of several micrometers. Therefore, we applied the interferometric technique to measure deformation profiles in real time. Experiments were performed in the shallow bath of the rapeseed oil with an azo-dye and excited with 514.5 nm and probed with 650 nm coherent laser beams, respectively. The mechanism of deformation driven by Marangoni effect was carefully modeled in 3D by computational fluid dynamic numerical simulations within the COMSOL Multiphysics package. The adaptive mesh technique used in the simulation together with solving the time-dependent coupled Navier–Stokes and heat transport differential equations allowed us to replicate the experimental findings. A satisfactory agreement between the results of the simulations and those of the experiment in terms of the dynamics, shape, and depth of the deformation has been obtained. The toroidal-like whirls accompanying the thermocapillary Marangoni effect were identified by the simulation results. We then experimentally proved that these toroidal-like vortices, which accompany laser heating in dyed oil, formed a kind of novel hydrodynamic trap, in the center of their quiet zone, in which microcrystals can be trapped.

Numerical Simulation of 3-D Internal Crack Propagation in Rock under Semi-circle Bending

Semi-circle bending (SCB) test is an important test in the field of rock fracture. In order to investigate the propagation process of 3-D internal cracks under semi-circular bending, numerical simulations of SCB specimens were carried out based on the finite element method and adaptive mesh technique. The results show that the numerical simulation results of this method are in good agreement with the previous laboratory test. The symmetrical loading model belongs to the pure I loading where the value of KI is positively related to the bottom load span S/R. The asymmetric loading model belongs to mix-mode loading. With the increase of unilateral load span S2/R, there is a decline and then a rise of the value of SIF at the same point at the crack tip. The S2/R is an important factor affecting the mechanical properties of rock specimens. The crack propagation path was obtained based on the maximum tensile stress (MTS) criterion. In-plane propagation of the internal crack in the symmetrically loading model leads to failure of the specimen. Wing propagation of the internal crack in the asymmetrically loading model causes the specimen to fracture into two asymmetrical parts. Quantitative analysis of the internal crack propagation of the symmetrical loading model shows that the growth rate of the lower end of the crack is the largest, and the upper end of the crack is the smallest. The above results can provide a reference for the research on the propagation of 3-D internal cracks of SCB specimens.

Thermomechanical analysis of induction assisted friction stir welding of Inconel 718 alloy: A finite element approach

Friction stir welding (FSW) of hard and high melting point materials such as Nickel and Titanium based alloys is challenging due to excessive tool wear and low weld quality. Various auxiliary energy sources have been proposed in the past decade as an assistance to conventional FSW process. In this work, a modified 3D Finite element (FE) model was developed to simulate the induction preheated FSW of Inconel 718 alloy using ABAQUS/Explicit software package. Investigation of temperature distribution and residual stress generation was carried out for induction assisted FSW (IAFSW) process and compared with those of FSW process. Features such as Arbitrary Lagrangian–Eulerian (ALE) formulation, adaptive meshing technique, mesh sensitivity analysis and mass scaling techniques have been utilised in order to develop a reliable and computationally efficient FE model. Experimental study was carried out with Induction assistance as a preheating method to FSW process. The thermal history of the numerical model was fairly validated with experimental results. Results showed that temperature increased by 138 °C in IAFSW process and was more uniformly distributed as compared to FSW. Residual stresses decreased by 15% on an average in the IAFSW joints. In addition to that, plastic strain and tool reaction forces were also predicted using the FE model proposed in this work. Plastic strain values were higher in IAFSW process with a maximum difference of 55% over the average plastic strain value of FSW at the beginning of the traverse period when temperature was highest. Reaction forces on probe tip reduced by 23% in IAFSW process during the plunge stage.