Finite Element Method For Solving Research Articles

Effect of microstructure on dynamic compressive behavior of cellular materials

It is known that the microstructure of cellular materials has a significant impact on their compressive properties. To study these phenomena, a hierarchical Poisson disk sampling algorithm and Voronoi partitioning were used to create a 3D numerical analysis model of cellular materials. In this study, we prepared random, periodic, and ellipsoidal cell models to investigate the effects of cell shape randomness and oblateness. Numerical experiments were performed using the finite element method solver RADIOSS. In the numerical analysis, an object collided with the cellular materials at a velocity of 25 m/s. The results showed that the flow stress of the random cell model was higher than that of the periodic cell model. Further, it was found that the aspect ratio of the cell shape has a significant impact on the mechanical properties of cellular materials.

Digital blood in massively parallel CPU/GPU systems for the study of platelet transport.

We propose a highly versatile computational framework for the simulation of cellular blood flow focusing on extreme performance without compromising accuracy or complexity. The tool couples the lattice Boltzmann solver Palabos for the simulation of blood plasma, a novel finite-element method (FEM) solver for the resolution of deformable blood cells, and an immersed boundary method for the coupling of the two phases. The design of the tool supports hybrid CPU–GPU executions (fluid, fluid–solid interaction on CPUs, deformable bodies on GPUs), and is non-intrusive, as each of the three components can be replaced in a modular way. The FEM-based kernel for solid dynamics outperforms other FEM solvers and its performance is comparable to state-of-the-art mass–spring systems. We perform an exhaustive performance analysis on Piz Daint at the Swiss National Supercomputing Centre and provide case studies focused on platelet transport, implicitly validating the accuracy of our tool. The tests show that this versatile framework combines unprecedented accuracy with massive performance, rendering it suitable for upcoming exascale architectures.

Helically Grooved Gold Nanoarrows: Controlled Fabrication, Superhelix, and Transcribed Chiroptical Switching

Plasmonic chiroptical materials, coupled by chirality and surface plasmons, have been attracting great interest due to their potential applications, such as photonics, chiral recognition, asymmetri...

Advanced Modelling Techniques for Resonator Based Dielectric and Semiconductor Materials Characterization

This article reports recent developments in modelling based on Finite Difference Time Domain (FDTD) and Finite Element Method (FEM) for dielectric resonator material measurement setups. In contrast to the methods of the dielectric resonator design, where analytical expansion into Bessel functions is used to solve the Maxwell equations, here the analytical information is used only to ensure the fixed angular variation of the fields, while in the longitudinal and radial direction space discretization is applied, that reduced the problem to 2D. Moreover, when the discretization is performed in time domain, full-wave electromagnetic solvers can be directly coupled to semiconductor drift-diffusion solvers to better understand and predict the behavior of the resonator with semiconductor-based samples. Herein, FDTD and frequency domain FEM approaches are applied to the modelling of dielectric samples and validated against the measurements within the 0.3% margin dictated by the IEC norm. Then a coupled in-house developed multiphysics time-domain FEM solver is employed in order to take the local conductivity changes under electromagnetic illumination into account. New methodologies are thereby demonstrated that open the way to new applications of the dielectric resonator measurements.

Monitoring and modeling of part thickness evolution in vacuum infusion process

The main hurdles in Vacuum Infusion (VI) are the difficulty in achieving complete mold filling and uniform part thickness. This study integrates process monitoring by full field thickness measurements and resin flow modeling that accounts for compaction and permeability characterizations of fabric reinforcements to assess the evolution of part thickness during filling and post-filling stages of VI process. A Structured Light Scanning system is used for full field thickness monitoring in experiments and a Control Volume Finite Element Method solver is implemented to couple resin flow with fabric’s compaction and permeability. Two cases are studied both experimentally and numerically. Evolutions of thickness and pressure validate the developed flow solver, its accuracy in terms of predicting fill times and fill patterns, suitability and limitations of the elastic compaction models for thickness modeling.

A new method to get initial guess configuration for multi-step sheet metal forming simulations

This study aims to develop a universal, robust, and linear method to obtain an initial guess configuration for the multi-step finite element method (FEM) solver of sheet metal forming. Using the decoupling theory, the deformation at each step in the multi-step FEM solver of the sheet metal forming is decoupled into two independent deformation modes: bending-dominated deformation and stretching-dominated deformation. The configuration of the bending-dominated deformation constrained by the sliding constraint surface is considered as the initial guess configuration for the current step in multi-step FEM solver. To get an accurate initial configuration at each step, the method of Laplace-Beltrami operator (LBO) on a simplicial surface is employed to obtain the initial guess configuration effectively. Several numerical examples are provided for validation and verification of the proposed method through its applications for complicated sheet metal workpieces of finite element simulations. The results show that the proposed method on the simplicial surface for the initial guess configuration within a few iterations to be significantly effective.

The Effects of Inhomogeneous Elasticity and Dislocation on Thermodynamics and the Kinetics of the Spinodal Decomposition of a Fe-Cr System: A Phase-Field Study

The effects of inhomogeneous elasticity and dislocation on the microstructure evolution of α′ precipitate in a Fe-Cr system was investigated using a Computer Coupling of Phase Diagrams and Thermochemistry (CALPHAD)-type free energy incorporated phase-field method. In order to simulate the precipitation behavior by phase-field modeling in consideration of inhomogeneous elasticity, a Multiphysics Object-Oriented Simulation Environment (MOOSE) framework was used, which makes it easy to use powerful numerical means such as parallel computing and finite element method (FEM) solver. The effect of inhomogeneous elasticity due to the compositional inhomogeneity or the presence of dislocations affects the thermodynamic properties of the system was investigated, such as the lowest Cr concentration at which spinodal decomposition occurs. The effect of inhomogeneous elasticity on phase separation kinetics is also studied. Finally, we analyzed how inhomogeneous elasticity caused by compositional fluctuation or dislocation affects microstructure characteristics such as ratio between maximum precipitate size with respect to the average on early stage and later stage, respectively.

The Research for Approaches to Increase Power of the Compact THz Emitters Based on Low-Temperature Gallium Arsenide Heterostructures

The design and technological conditions for the manufacture of photoconductive antennas based on low-temperature gallium arsenide (LT-GaAs) have been developed. The optimized photoconductive THz antenna is made based on LT-GaAs with the flag geometry of the contacts and with the interdigitated structure including metal closing through the dielectric of each second period. LT-GaAs samples were obtained by molecular beam epitaxy at temperatures of 210 °C, 230 °C, 240 °C on GaAs substrates (100). Dark and photocurrent were measured depending on the bias voltage of the LT-GaAs heterostructure at the EP6 probe station. Full wave finite element method solver has been used to investigate the proposed plasmon PCA electrical and optical behavior by combining the Maxwell's wave equation with the drift-diffusion/Poisson equations.

Antenna In-Situ Performance Analysis for the Hypersonic Flight Vehicle HEXAFLY: Employing measurement data in a simulation model

An antenna in-situ performance analysis for the hypersonic flight vehicle HEXAFLY is presented. Two simulation tools and a compact antenna test range (CATR) measurement facility are employed to obtain the embedded radiation characteristics of two different antenna systems. In a first step, both antenna types are simulated and measured without the impact of the flight vehicle, but in an environment supporting correct functioning, e.g., on a finite conducting ground plane or on top of a vertical conducting stabilizer. A finite-element method (FEM) solver is used for this detailed full-wave analysis of antenna structures with fine geometrical and material details. Next, the FEM solver and a method of moments (MoM) solver with multilevel fast multipole algorithm (MLFMA) acceleration are used to obtain the in-situ radiation characteristic of both antennas mounted on the flight vehicle. The FEM solver is now utilized to simulate the complete setup, whereas the MoM solver works with an equivalent radiation source, which is obtained from CATR measurements of isolated antennas. The results confirm the effectiveness of the measurement data-based two-stepapproach, which helps to overcome the limitations of pure simulations that are often not feasible for off-the-shelf antennas and allows the overall validation process to be viewed with added confidence.

GPU-based matrix-free finite element solver exploiting symmetry of elemental matrices

Matrix-free solvers for finite element method (FEM) avoid assembly of elemental matrices and replace sparse matrix-vector multiplication required in iterative solution method by an element level dense matrix-vector product. In this paper, a novel matrix-free strategy for FEM is proposed which computes element level matrix-vector product by using only the symmetric part of the elemental matrices. The proposed strategy is developed to take advantage of the massive parallelism of Graphics Processing Unit (GPU). A unique data structure is also introduced which ensures localized and coalesced memory access suitable for a GPU while storing only the symmetric part of the elemental matrices. In addition, the proposed strategy emphasizes the efficient use of register cache, uniform workload distribution, reducing thread synchronization, and maintaining sufficient granularity to make the best use of GPU resources. The performance of the proposed strategy is evaluated by solving elasticity and heat conduction problems using 4-noded quadrilateral element with two degrees of freedom (DOFs) and one DOF per node, respectively. The performance is compared with the matrix-free solver strategies on GPU from the literature. It is found that a maximum speedup of 4.9 $$\times $$ is obtained for the elasticity problem and a maximum of 3.2 $$\times $$ speedup for the heat conduction problem. Further, the proposed strategy takes the least amount of GPU memory as compared to the existing strategies.

Full-Wave Computation of the Electric Field in the Partial Element Equivalent Circuit Method Using Taylor Series Expansion of the Retarded Green’s Function

This article presents new analytical formulas for the efficient computation of the full-wave electric field generated by conductive, dielectric, and magnetic media in the framework of the partial element equivalent circuit (PEEC) method. To this aim, the full-wave Green's function is handled by the Taylor series expansion leading to three types of integrals for which new analytical formulas are provided in order to avoid slower numerical integration. An orthogonal (Manhattan type) tessellation of the geometries is assumed, and the electrical quantities, i.e., currents, charges, and magnetization, are expanded in space through rectangular basis functions. The full-wave electric field radiated by charges, currents, and magnetization is computed analytically in the postprocessing step. The proposed closed-form computation of the electric field is tested using two examples, comparing the results obtained by the derived analytical formulas with the results from a finite element method solver.

Realistic haptic rendering of hyper-elastic material via measurement-based FEM model identification and real-time simulation

This paper presents a measurement-based FEM (finite element method) modeling and haptic rendering framework for objects with hyper-elastic deformation property. A complete set of methods covering the whole process of the measurement-based modeling/rendering paradigm is newly designed and implemented, with a special emphasis on haptic feedback realism. To this end, we first build a data collection setup that accurately captures shape deformation and response forces during compressive deformation of cylindrical material samples. With this setup, training and testing sets of data are collected from four silicone objects having various material profiles. Then, an objective function incorporating both shape deformation and reactive forces is designed and used to identify material parameters based on training data and the genetic algorithm. For real-time haptic rendering, an optimization-based FEM solver is adopted, ensuring around 500 Hz update rate. The whole procedure is evaluated through numerical and psychophysical experiments. The numerical rendering error is calculated based on the difference between simulated and actually measured deformation forces. The errors are also compared to the human perceptual threshold and found to be perceptually negligible. Overall realism of the feedback from the system is also assessed through the psychophysical experiment. A total of twelve participants rated similarity between real and modeled objects, and the results reveal the rendering quality to be at a reasonable level of realism with positive user feedback.

Modeling transport of charged species in pore networks: Solution of the Nernst–Planck equations coupled with fluid flow and charge conservation equations

A pore network modeling (PNM) framework11Computer code available on public repository https://github.com/PMEAL/OpenPNM. for the simulation of transport of charged species, such as ions, in porous media is presented. It includes the Nernst–Planck (NP) equations for each charged species in the electrolytic solution in addition to a charge conservation equation which relates the species concentration to each other. Moreover, momentum and mass conservation equations are adopted and there solution allows for the calculation of the advective contribution to the transport in the NP equations.The proposed framework is developed by first deriving the numerical model equations (NMEs) corresponding to the partial differential equations (PDEs) based on several different time and space discretization schemes, which are compared to assess solutions accuracy. The derivation also considers various charge conservation scenarios, which also have pros and cons in terms of speed and accuracy. Ion transport problems in arbitrary pore networks were considered and solved using both PNM and finite element method (FEM) solvers. Comparisons showed an average deviation, in terms of ions concentration, between PNM and FEM below 5% with the PNM simulations being over 104 times faster than the FEM ones for a medium including about 104 pores. The improved accuracy is achieved by utilizing more accurate discretization schemes for both the advective and migrative terms, adopted from the CFD literature. The NMEs were implemented within the open-source package OpenPNM based on the iterative Gummel algorithm with relaxation.This work presents a comprehensive approach to modeling charged species transport suitable for a wide range of applications from electrochemical devices to nanoparticle movement in the subsurface.

Improved air gap permeance model to characterise the transient behaviour of electrical machines using magnetic equivalent circuit method

AbstractTransient analysis of electrical machines with mixed eccentricity requires dedicated, fast and accurate solvers. This article proposes an improved air gap permeance expression which (a) is physically interpretable and (b) can be easily derived based on the rotor position. This expression is very suitable for inclusion in a solver based on the magnetic equivalent circuit (MEC) method. This allows to for example, calculate the torque and forces when vibrations act on the rotor. The results of the MEC solver agree very well with those obtained with a finite element method (FEM) solver, but are obtained with a fraction of the simulation time of the FEM solver.

A finite-element heat transfer model for orthogonal cutting

ABSTRACT It is known that the heat generated in various cutting zones during machining affects the formation of chips, the shearing mechanism, the chip-tool friction and consequently the tool wear and tool life. Therefore, determining the temperature distribution in machining is a major area of research. In the past, numerical approaches have been used by researchers which involved use of stationery heat sources to predict temperature distributions around the cutting zone in machining. This work presents a thermal model of orthogonal machining process to evaluate the temperature distribution in the work, tool and chip-tool interface. A series of numerical simulations were performed using finite element method (FEM) solver to develop a steady-state two-dimensional heat transfer model considering heat convection due to coolant applications in variety of cutting zones. The maximum temperature generated during machining has been validated using the numerical as well as experimental data. The simulations successfully captured the maximum temperature generated in machining of three different variants of Titanium alloys with an error of ~9%.

Phase-field simulation of hydraulic fracturing with a revised fluid model and hybrid solver

With an intrinsic advantage in describing complex fracture networks, the phase field method has demonstrated promising potential for the simulation of hydraulic fracturing processes in recent literatures. We critically examine the existing phase-field hydraulic fracturing models, and propose a hybrid solution scheme with a revised fluid model. Specifically, the formation deformation and phase field are solved using the finite element method (FEM), while the fluid flows are solved using the finite volume method (FVM). The proposed hybrid scheme is validated with the analytical solution for the toughness-dominated fracture propagation and is tested on the complex hydraulic fracturing process in a naturally fractured formation. Demonstrated by numerical examples, the proposed hybrid phase-field framework has several advantages: (1) it captures the effect of fluid pressure inside the fracture and reservoir more accurately than existing models; (2) it provides a sharper capture of formation fractures; (3) it avoids the nonphysical oscillation of fluid pressure when using a pure FEM solver; and (4) it has a superior performance in mesh and time step convergence.

Experimental and numerical analysis of a multilayer composite ocean current turbine blade

Ocean environmental corrosion and mechanical load vibration introduce considerable negative effects caused by the fluid-structure-environment interaction. A new design scheme for a blade with salinity corrosion resistance and mechanical fatigue resistance is proposed, based on numerical simulation and fatigue tests. The one-way fluid-structure interaction (FSI) model for an ocean current turbine blade was established and calculated by a computational fluid dynamics (CFD) solver and finite element method (FEM) solver. According to the FSI results, the maximum equivalent stress and deformation in extreme operating conditions are found to be within material and structural limits. On this basis, an aluminum alloy/nano particles reinforced polypropylene multilayer composite blade was designed and fatigue tested. The results show that an obvious crack-resistance effect exists within a certain stress range, and there is basically no change in the fatigue crack growth rates of NPRP in the four environmental fatigue tests. The multilayer composite blades with immersion pretreatment can stand 1 × 107 cycles of fatigue tensile loads and torque loads without failure. The results provide specific theoretical guidance for the optimization of the structural design of ocean current turbine blade in ocean environment.

One-way FSI analysis of bio-inspired flapping wings

Aerodynamics and structural dynamics of the insect wings are widely considered in flapping wing micro air vehicle (FWMAV) applications. In this paper, the aerodynamic characteristics of the three-dimensional flapping wing models mimicked from the bumblebee and hawkmoth wings are numerically investigated under steady flow conditions. This study aims to simulate the one-way fluid-structure interaction (FSI) of these bio-inspired wings by transferring the aerodynamic load obtained from the computational fluid dynamics (CFD) into the finite element method (FEM) solver as a pressure load. The static aeroelastic responses of the wings under the pressure load are compared for different materials, namely, cuticle, aluminium alloy, and titanium alloy at various angles of attack (α = 0°-90°). CFD analysis shows that the hawkmoth wing model at α = 5° has the highest lift-to-drag ratio (L/D). FSI analysis demonstrates that the cuticle hawkmoth wing model at α = 90° undergoes the highest tip deflection.

A finite element method to simulate dislocation stress: A general numerical solution for inclusion problems

We developed a simple and efficient way to simulate stress from arbitrary shape dislocations within the finite element method (FEM) framework. The new method is implemented as a single-step FEM simulation using analytic solutions in an infinite medium as input terms of FEM solver with special internal boundary treatment. It is fundamentally equivalent to the multistep “image method” proposed by Van der Giessen and Needleman [Modell. Simul. Mater. Sci. Eng. 3, 689 (1995)], but the force equilibration is achieved by a single step FEM method. The singularity at the dislocation core line is removed without mesh modification, which removes many technical difficulties to couple the dislocation stress model to other process/device simulation models.

Semi-analytical solution for deformation of elastic/viscoelastic two-layered films pressed on partially-opened substrate

This paper proposes an efficient solution procedure for the deformation of a viscoelastic film pressed by another elastic film in cases wherein the films are on partially-opened substrates. The problem is formulated as a quasi-static stress state, where the stress equilibrium is satisfied at each time instance. The instantaneous stress equilibrium is expressed by biharmonic and harmonic functions for the stress and displacement of those general solutions that can be obtained in the Fourier domain. By applying the boundary conditions mathematically everywhere but the surface, which is in direct contact with the partially-opened substrate, the total problem could be discretized and solved using the Fourier collocation method. In this manner, the total number of unknowns can be greatly reduced. The validity and effectiveness of the proposed method was confirmed by comparing the results with those obtained by a finite element method (FEM) solver. The viscoelastic deformation obtained by the proposed method was almost in complete agreement with the result obtained by the FEM. The elapsed computational time required by the proposed method was approximately 1/100 of that required by the FEM.