Finite Element Method Model Research Articles

Numerical-experimental analysis of laser-welded small energy absorbers with direct impact Hopkinson method

This research paper presents a comprehensive numerical-experimental analysis of the phenomena observed during the compression of small energy absorbers (EAs) with dimensions 23 × 23 mm and a thickness of 0.6 mm. This study uses the direct impact Hopkinson (DIH) method. The locus is the detailed prediction of the strength of laser-welded joints in terms of energy absorption under both quasi-static and dynamic loading conditions. Furthermore, the paper explores the potential utility of the described methodology for modeling and predicting the failure mechanisms of small energy absorbers. This investigation delves into key factors that affect the distribution of cracks in deformed energy absorbers. These include: the detail of the reproduction of the absorber geometry, the impact of finite element formulations and modeling method (2D/3D elements) and the complexity of the material model for propagated cracks. Two material models are considered, the simplified Johnson–Cook model and the tabulated Johnson-Cook with Hockett–Shelby extrapolation model, which incorporate linear damage dependent on the stress triaxiality and Lode angle. The study also highlights the advantages and disadvantages of the DIH test method. Some features cannot be effectively observed through experimental testing alone. The experimental procedure involved initial testing and calibration of the material models for both the parent material and the welded joints at three different strain rates. Subsequently, the validated energy absorber models are subjected to static and dynamic crushing. The results are subsequently compared with the virtual results obtained using the gravity hammer method, which is a more readily accessible testing approach. Remarkably, a very high correlation between the numerical simulation and experimental data is observed, providing a comprehensive understanding of the research problem related to laser-welded absorbers.

Revealing the grain boundary effect on interfacial adhesion in polycrystal Fe/Ni interfaces by using a multi-scale CZM-CPFEM approach

In layered structure, interface plays a significant role in property improvement, whereas its multiple factors at various length scales restricted further understanding. Previous research found a novel grain boundary (GB)-interface interaction: crack initiation locally occurred at the junctions between pre-existing GBs and interface. This leads to decreased interfacial strength. To clarify the mechanisms of such GB-interface interaction, the present study proposed a multi-scale cohesive zone model-crystal plasticity finite element method (CZM-CPFEM) model to investigate the effect of pre-existing GB on intrinsic bonding strength at atomic scale and interfacial stress distribution at micro scale, respectively. At atomic scale, interfacial fracture criteria were modelled according to Molecular Dynamics (MD)-based traction-separation relationships. The accuracy of CZMs was improved by considering both isothermal holding and tilting configuration effects. At micro scale, a practical interfacial microstructure was used to construct CPFEM models. Tensile simulations showed that the local stress concentration occurred at junctions, attributed to the anisotropic plastic deformation behaviours across the GB. On the other hand, weak bonding adhesion at the junction only affects the local crack initiation strength, showing insignificant impacts on the overall interfacial fracture behaviour.

Real-time prediction method of carbon concentration in carburized steel based on a BP neural network

ABSTRACT Gears are key components of mechanical transmission systems. They need to be carburized and quenched to meet the requirements of internal toughness and external hardness, to obtain higher hardness and wear resistance. Heat treatment engineers can calculate carbon concentration distribution through the finite element analysis method, facing the challenge of high computational cost and high memory requirements. To solve this problem, a real-time prediction method of 1D and 2D carburizing concentration based on a Back Propagation (BP) neural network (BPNN) is proposed. First, carburizing experiments were conducted to verify the accuracy of the carburizing numerical model. Then, by establishing an accurate carburizing model, 37,800 and 177,147 1D and 2D carburizing training samples were generated using the finite element model (FEM) method, respectively. Finally, for 1D carburizing, the average relative error of the training model on the test set is 0.2911%. For 2D carburizing, the average relative error of the reconstructed BPNN model on the test set was 0.4381%, and a real-time performance evaluation was performed. The carbon concentration prediction time for each set of process parameters is only 0.12 s, nearly 175 times faster than FEM calculation, which meets the accuracy and real-time requirements for real-time prediction of carburizing carbon concentration.

FEM Modeling Strategies: Application to Mechanical and Dielectric Sensitivities of Love Wave Devices in Liquid Medium.

This paper presents an extended work on the Finite Element Method (FEM) simulation of Love Wave (LW) sensors in a liquid medium. Two models are proposed to simulate the multiphysical response of the sensor. Both are extensively described in terms of principle, composition and behavior, making their applications easily reproducible by the sensor community. The first model is a Representative Volume Element (RVE) simulating the transducer and the second focuses on the sensor's longitudinal (OXZ) cut which simulates the multiphysical responses of the device. Sensitivity of the LW device to variations in the rheological and dielectric properties of liquids is estimated and then compared to a large set of measurements issued from LW sensors presenting different technological characteristics. This integral approach allows for a deeper insight into the multiphysical behavior of the LW sensor. This article also explores the advantages and drawbacks of each model. Both are in good accordance with the measurements and could be used for various applications, for which a non-exhaustive list is proposed in the conclusion.

A semi‐analytical model for coupled THM consolidation of saturated clays improved by PVTD considering thermal contraction

AbstractPrevious studies have demonstrated that saturated normally consolidated and lightly over‐consolidated clays undergo contraction when heated due to a reduction in preconsolidation pressure. A linear constitutive model is proposed to describe the thermal contraction, with this model, governing equations are developed for the coupled thermo‐hydro‐mechanical (THM) consolidation induced by a prefabricated vertical thermo‐drain (PVTD). Corresponding semi‐analytical solutions are derived employing the Laplace transform and validated via comparison with experimental results, existing numerical model, and custom finite element method (FEM) model. Subsequently, comprehensive parametric analyses are carried out to investigate the THM coupling consolidation behaviors of the clays. Outcomes show that aside from surcharge load, generation of excess pore water pressure in soils can also be induced by thermal contraction, difference in thermal expansibility between pore water and soil grains, and thermo‐osmosis, where the influence of thermal contraction on the excess pore water pressure is the most prominent among the three factors.

Computational prediction of impact sound insulation of a full-scale timber floor applying a FEM simulation procedure

During the recent decades, simulation procedures involving the finite element method (FEM) have been developed to enable prediction of impact sound insulation of timber slabs and floors. FEM simulations have previously been applied for timber floors mainly in low frequencies despite their evident ability to operate over a wide frequency range. Additionally, the validation processes have involved calibrations and experimental modal analyses which can seldom be performed in product development tasks concerning full structures. The purpose of this research was to study the applicability of a FEM simulation procedure to predict normalised impact sound pressure levels Ln of a full-scale timber floor if material data provided by the product manufacturers is used. The floor was studied at three construction stages where the FEM simulations were performed for the bare floor and the rib slab, and the floor covering was considered in the post-processing stage in case of the full floor. The impact force excitation generated by the ISO standard tapping machine was described with the recently published procedure involving explicit dynamics analysis. To serve the purposes of this study, the FEM models were fully constructed before the measurements were carried out. According to the results, the 1/3-octave Ln of the full floor and the floor without covering was predicted with a 0 to 9 dB accuracy depending on the frequency band and the single-number quantities with a 0 to 4 dB accuracy. The single-number quantities of the bare rib slab were underestimated with the simulations by 4 to 5 dB. Probable causes for the discrepancies between the simulation and measurement results pointed mainly to the uncertain material properties but possibilities for modelling inaccuracies could not be excluded.

A hybrid boundary element-finite element approach for solving the EEG forward problem in brain modeling.

This article introduces a hybrid BE-FE method for solving the EEG forward problem, leveraging the strengths of both the Boundary Element Method (BEM) and Finite Element Method (FEM). FEM accurately models complex and anisotropic tissue properties for realistic head geometries, while BEM excels in handling isotropic tissue regions and dipolar sources efficiently. The proposed hybrid method divides regions into homogeneous boundary element (BE) regions that include sources and heterogeneous anisotropic finite element (FE) regions. So, BEM models the brain, including dipole sources, and FEM models other head layers. Validation includes inhomogeneous isotropic/anisotropic three- and four-layer spherical head models, and a four-layer MRI-based realistic head model. Results for six dipole eccentricities and two orientations are computed using BEM, FEM, and hybrid BE-FE method. Statistical analysis, comparing error criteria of RDM and MAG, reveals notable improvements using the hybrid FE-BE method. In the spherical head model, the hybrid BE-FE method compared with FEM demonstrates enhancements of at least 1.05 and 38.31% in RDM and MAG criteria, respectively. Notably, in the anisotropic four-layer head model, improvements reach a maximum of 88.3% for RDM and 93.27% for MAG over FEM. Moreover, in the anisotropic four-layer realistic head model, the proposed hybrid method exhibits 55.4% improvement in RDM and 89.3% improvement in MAG compared to FEM. These findings underscore the proposed method is a promising approach for solving the realistic EEG forward problems, advancing neuroimaging techniques and enhancing understanding of brain function.

Transmission/reflection mode switchable ultra-broadband terahertz vanadium dioxide (VO2) metasurface filter for electromagnetic shielding application

In this paper, we present an ultra-broadband terahertz (THz) vanadium dioxides (VO2) metasurface (MS) filter with switchable transmission/reflection modes for electromagnetic (EM) shielding application. The MS filter is composed of a three-layer periodic composite structure, consisting of two VO2/metallic hybrid layers and a metal mesh layer, which are separated by two benzocyclobutene (BCB) dielectric layers. The transmission property of the proposed MS filter is illustrated by the numerical simulation based on the finite element method (FEM) and equivalent circuit model (ECM). When VO2 is in insulating state, the designed composite structure acts as a filter with ultra-broadband bandpass response (BPR), exhibiting that the transmission coefficient exceeds 90 % from 1.07 THz to 3.78 THz, with a relative bandwidth of 112 %. However, owing to thermal excitation, the VO2 converts from an insulating to a metallic state, the composite structure can be functioned as a filter with ultra-broadband bandstop response (BSR) with a transmission coefficient less than 6 % spanning the range of 0.1 to 4.5 THz. In addition, the physical mechanism of the designed MS filter is investigated utilizing impedance matching theory and electric field distribution analysis. Furthermore, the MS filter has good polarization insensitivity and angular stability. Finally, we quantify the shielding effectiveness (SE) in two states and evaluate the impact structural parameters of the unit-cell, resulting in a SE of more than 25 dB in reflection mode across the entire operating frequency range. Our proposed MS filter with its exquisite performance has the potential to be widely applied in EM shielding.

Estimation of inelastic heat fraction of Ti-6Al-4V alloy using inverse analysis

This work aims to determine the inelastic heat fraction of Ti-6Al-4V alloy by coupling the experimental and Finite Element Method (FEM) results by an inverse analysis approach. The inelastic heat fraction is a crucial factor in revealing information on the deformation mechanism and forms the basis of the microstructural evolution of a material. Hot compression tests on Ti-6Al-4V alloy at various temperatures and strain rates were carried out using the Gleeble thermo-mechanical simulator. An axisymmetric thermo-mechanical modelling was carried out using the FEM package i.e., ABAQUS. The work reveals that the inelastic heat fraction increases with an increase in strain rate and decreases with an increase in deformation temperature. The proposed method is capable of predicting the inelastic heat fraction of a material for a wide range of temperatures and strain rates. The FEM modelling and experimental results exhibit good agreement. The findings of this study can aid in more precise material modelling and contribute to the formation of a thermo-mechanical material database.

Surrogate numerical prediction method of TBM position via FEM simulation and machine learning

The position of the tunnel boring machine (TBM) during tunnel construction is critical and must be precisely controlled. Owing to the geological uncertainty and complexity of the interaction between the ground and the TBM, controlling the position of the TBM is challenging. Hence, a surrogate numerical method is proposed to predict the position of the TBM using the finite element method (FEM) and machine learning method. First, a refined three-dimensional FEM model was established. Different values of the property parameters of the ground and the thrust force of the TBM were input into the FEM model, generating a database that includes 1000 cases. Subsequently, the database is used to train a gradient boosting regression (GBR) model. The GBR model learns from the database and establishes the relationship between the construction parameters, ground parameters, and TBM position as a surrogate model. The surrogate model exhibited high accuracy on the test set. With a geological survey and a construction parameter monitoring system, the TBM position could be predicted quickly and precisely using a surrogate model. The construction parameters were adjusted if the TBM position did not satisfy the requirements.

Advancing Structural Optimization of an Electric Motor Rotor through Mesh Morphing Techniques

The electric motor has been one of the most important inventions of the last two centuries and has become increasingly important in the last 10 years thanks to its efficiency and its ability to reduce pollution. Given this increasing importance of electrical motors, an interest in design and optimization approaches for motor components is arising. Given the different physics involved in the transformation from electrical to mechanical energy, a valuable and reliable approach has to be applied in the optimization process. In past years, Mesh Morphing based on Radial Basis Functions (RBF) has largely proved its validity in generating shape modification for Finite Element Method (FEM) models. In this work, authors will demonstrate the advantages in applying two opposite approaches for shape optimization using RBF Mesh Morphing applied to electrical motors rotors. These components need to be accurately designed in order to guarantee an adequate life duration by reducing stresses in the rotating components. The two approaches that will be described are the parameter based one, in which a set of design parameters will be varied to generate shape modification used to feed a meta-model that will be used to identify an optimal configuration, and a parameter-less approach, in which the shape modification will be driven by FEM analysis results, with the aim to reduce stress hot-spots.

Experimental assessment and numerical simulations of marine fouling effect on underwater sound absorption coatings

Underwater sound absorption coatings capable of absorbing sound energy is essential to conceal underwater vehicles. While the accumulation of marine fouling on surfaces of ship hulls, platforms, and submarines can significantly alter their acoustic properties. Currently, the precise impact that different stages of marine fouling have on underwater sound absorption coatings remains unclear. In this study, a novel lab assessment method was developed to investigate the acoustic effect of marine fouling on the underwater sound absorption coatings. Four distinct stages of marine fouling were artificial fabricated and characterized, including conditioning film, microfouling, medium macrofouling, and heavy macrofouling. These effects are quantified through comprehensive tests conducted in a water-filled impedance tube. It is found that the first two stages of marine fouling have a negligible impact on the underwater sound absorption performance within the low frequency range of 500 Hz and 2000 Hz. While a limited impact is observed in the frequency range of 2000 Hz–5000 Hz, where the sound absorption coefficient remains approximately 0.6. Conversely, in the third and fourth stages of fouling, the average sound absorption coefficient drops from 0.8 to 0.2. Further, a new acoustic finite element method (FEM) model of hard fouling was developed to predict the acoustic effect, and the numerical results show the same trend with the experimental results. These findings emphasize the importance of considering antifouling strategies during the design of underwater sound absorption coatings, with a particular focus on targeting hard fouling organisms as the primary objective.

Adjacent vertebral fractures in the lumbar and thoracic spine after balloon kyphoplasty: A finite element analysis.

The purpose of the present study was to mechanically verify after vertebral augmentation (AVA) scores using a finite element method (FEM) with accurate material constants of balloon kyphoplasty (BKP) cement. Representative cases with AVA scores of 1 (case 1), 3 (case 2), and 5 (case 3) among patients with vertebral body fractures who underwent BKP were analyzed. A FEM model consisting of 5 vertebral bodies was created, including the injured vertebral body in each case. The amount of displacement for each load (up to 4000 N) between the upper and lower vertebral bodies of each model was measured. Young modulus of the BKP cement was calculated from actual measurements using the EZ-Test EZ-S (Shimadzu Corporation, Kyoto, Japan). In all cases, the number of shell elements (209,296-299,876), solid elements (1913,029-2417,671), and nodes (387,848-487,756) were similar, indicating that FEM modeling was comparable among the cases. Young modulus of BKP cement, calculated using EZ-Test EZ-S, was 572 MPa. Fractures were detected by compressive forces of 3300 N (upper) and 3300 N (lower), 3000 N (upper) and 3100 N (lower), and 1200 N (upper) and 1200 N (lower) in cases 1, 2, and 3, respectively. The AVA scoring system was mechanically verified using the accurate material constants of BKP cement. A multicenter survey and external validation are therefore required for the clinical implementation of the AVA score.

On the influence of local deformation on structural dynamic models of bolted lap joints

The acoustic and structural dynamic behavior of technical products—often referred to as Noise, Vibration, and Harshness (NVH)—is an important criterion in customers’ purchasing decisions. Therefore, NVH optimization is a crucial goal of the development process. NVH is influenced by dynamic excitations, caused by time-varying forces e.g. in gears or electric machines, as well as the transfer path of sound from the location of excitation to a receiver such as a driver’s ear and the sound perception. The behavior of the transfer path is determined by amplification or isolation of structure-borne and airborne sound between the location of the excitation and the location of the receiver. As a result, eigenfrequencies and damping in the transfer path form crucial structural dynamic properties.Within jointed structures, friction between the surfaces of lap joints are the most dominant influencing factor on the transfer path’s damping. In order to increase the efficiency of NVH optimization in the development process, methods of virtual product development have become an established tool. Especially finite element method (FEM) and elastic multi-body simulation (eMBS) have allowed to numerically evaluate the structural dynamic behavior of technical products before manufacturing physical prototypes. While numerous methods for modeling jointed structures exist in FEM and eMBS environments, the choice of suitable eMBS models of joints remains challenging today. This is because the frictional behavior between the jointed partners in higher frequencies is largely influenced by the deformation of the joint surface. However, the deformation of the jointed parts is simplified in eMBS models compared to quasi-continuous FEM models. Accordingly, the choice of a suitable spatial discretization of eMBS joint models is a key factor in the model quality of eMBS models. Thus, this work proposes a modeling guideline for eMBS models of jointed structures based on the deformation of the structure using the criterion of rigidness. The method is demonstrated on an eMBS model of the academic Brake Reuß beam, which consists of two beam elements jointed with three screws in an overlap lap joint. Good agreement between eMBS simulation and measurement with an error of 1 dB is achieved using the proposed modeling method.

Theoretical modeling and experimental investigation of in-phase resonant MEMS mirrors with cascaded structures

This paper proposes an efficient nonlinear one-dimensional (1D) compact mass-damper-spring model to predict the dynamic response of electrostatic resonant micro-electro-mechanical system (MEMS) mirrors with cascaded structures. The time-dependent damping moment due to viscous shear and pressure drag is computed using semi-empirical analytical equations for comb-drive structures and device frames. Nonlinear electrostatic force induced by the comb drives is efficiently acquired based on the hybrid method. The optimized device is fabricated using MEMS fabrication processes based on a 4-inch silicon-on-insulator wafer. The proposed compact model with the measured key parameters from the fabricated device shows excellent capability to accurately predict nonlinear dynamic responses of the fabricated device, including parametric excitation and hysteretic frequency response, with an average error of less than 5%. In particular, our 1D model is three orders of magnitude faster than the conventional finite element method model (0.8 s versus 1 h), enabling efficient system-level optimization of the critical design parameters. Based on the parametric study, electrode gap distance and torsion spring width are found to be two critical design parameters and dimensional analysis is conducted for design optimization with scan angle enhancing from 16.8° to 24° compared with the first design.

Magnetic focusing sensor and its characterizations of defect non-destructive testing for ferromagnetic steel plate

The fast development in precision manufacturing and product quality inspection of ferromagnetic material desperately demands that the defect determining the performance, service life and reliability of the mechanical part should be accurately sensed, detected and evaluated. However, conventional defect detection methods and related magnetic induction sensors are usually characterized with low accuracy in small defect detection, which makes the non-destructive testing (NDT) for ferromagnetic material full of challenges. Thus, a new magnetic focusing sensor is proposed and designed for the precision defect detection of ferromagnetic steel plate here. First, the theoretical principle analysis of the magnetic focusing sensor is introduced, and the preliminary finite element modeling (FEM) is conducted to demonstrate the feasibility of the magnetic focusing sensor in tiny defect inspection. Then, both the static and coupling dynamic characterizations of the magnetic focusing sensor are investigated using the FEM method. The optimal structural parameters of the magnetic focusing (MF) sensor in static conditions are summarized. Furthermore, the effects of the dynamic movement of the MF sensor on the multi-physical fields of the magnetization field, electric field, electromagnetic attraction force field and thermal field are all revealed. Finally, experiments regarding the performance evaluation and comparison between the MF sensor and other two magnetic flux leakage (MFL) sensors are conducted, and the prominent capabilities of accurate and precise defect detection for the MF sensor is demonstrated through the defect detection with different sizes. The effectiveness and feasibility of the MF sensor in detecting tiny defects on ferromagnetic object, as well as its great potential for practical application is therefore validated. Additionally, the main conclusions, advantages of the MF sensor are summarized and the future work is discussed.

Early detection of deep-seated smouldering fires in wood waste storage using ERT

Incidents of waste and biofuel fires are common at all stages of the waste recycling chain and have grave implications for business, employees, firefighters, society, and environment. An early detection of waste and biofuel fires in the smouldering stage could save precious lives, resources, and our environment. Existing fire detection methodologies e.g. handheld temperature sensors, IR cameras, gas sensors, and video and satellite-based monitoring techniques have inherent limitations to efficiently detect smouldering fires. An attempt was made to explore the potential of electrical resistivity tomography (ERT) as an alternate tool to address the problem. In the experiments an externally powered resistive wire was employed to initiate the smouldering fire inside the test material (wood pellets, wood shavings, wood fines). Time series of ERT that followed the initiation and development of smouldering were recorded using an automated monitoring instrument setup. The actual geometry of the experimental sample container and electrode setup was integrated in the 3D finite element method (FEM) model grid to perform inverse numerical modelling (inversion) and to develop resistivity tomographic images. The study shows a sharp increase in ratio of resistivity (R/Ro ≥ 50 %) in the test material in the region of smouldering hotspot and demonstrates the potential use of ERT technique for the detection of smouldering hotspots in silos and pile storage of organic material such as wood-based fuels, wood waste, coal, municipal solid waste (MSW), recyclables etc. More research is however required for enabling the use of this technique at the practical scale for different storage conditions.

Model-Based Design of Variable Stiffness Soft Gripper Actuated by Smart Hydrogels.

Soft grippers have shown their ability to grasp fragile and irregularly shaped objects, but they often require external mechanisms for actuation, limiting their use in large-scale situations. Their limited capacity to handle loads and deformations also restricts their customized grasping capabilities. To address these issues, a model-based soft gripper with adaptable stiffness was proposed. The proposed actuator comprises a silicone chamber with separate units containing hydrogel spheres. These spheres exhibit temperature-triggered swelling and shrinking behaviors. In addition, variable stiffness strips embedded in the units are introduced as the stiffness variation method. The validated finite element method model was used as the model-based design approach to describe the hydrogel behaviors and explore the affected factors on the bending performance. The results demonstrate that the actuator can be programmed to respond in a desired way, and the stiffness variation method enhances bending stiffness significantly. Specifically, a direct correlation exists between the bending angle and hydrogel sphere layers, with a maximum of 128° achieved. In addition, incorporating gap configurations into the chamber membrane results in a maximum threefold increase in the bending angle. Besides, the membrane type minimally impacts the bending angle from 21.3° to 24.6°. In addition, the embedded variable stiffness strips substantially increase stiffness, resulting in a 30-fold rise in bending stiffness. In conclusion, the novel soft gripper actuator enables substantial bending and stiffness control through active actuation, showcasing the potential for enhancing soft gripper performance in complex and multiscale grasping scenarios.

Rolling contact fatigue analysis of the soft zone for the main bearing in a tunnel boring machine

A hierarchical finite element modeling method is proposed to study the problem of fatigue spalling easily due to low hardness in the soft zone for the main bearing of a tunnel boring machine. Quasi-static analyses of the main bearing are performed based on the global symmetric model and verified by relative displacement tests of the rings. The invariant contact pressure is replaced by the rolling contact of the rollers in the local sub-model. The contact load is used as an input to solve the stress field, and then the effects of soft zone and hardened depth on the contact characteristics and fatigue lifetime of the sub-model are investigated. The results show there are stress peaks at the junction of the hardened and soft zones. The effect of hardened depth on the stress distribution and fatigue lifetime is relatively small. However, the optimum hardened depth is influenced by the contact load and the permissible stress of the material. The minimum lifetime of the raceway during rolling occurs in the soft zone. This paper achieves a fast and effective rolling contact fatigue analysis of the main bearing, which provides a theoretical basis for optimizing the main bearing design.

A comparative study of J–A and Preisach improved models for core loss calculation under DC bias

Power transformer is widely used in the power system with the rapid development of the power converters connected to the grid. When a transformer operates under DC bias conditions, its iron core loss increases significantly, causing local overheating and threatening the proper operation of the transformer. However, there are persistent difficulties in accurately assessing the core loss when the induction waveform is influenced by a DC bias. This paper first proposes improvements to the J–A and Preisach models to evaluate the core loss of the iron core under DC bias. Additionally, we incorporate the hysteresis models into the finite element method (FEM) by modifying the fundamental constitutive equations in the FEM model in order to perform a precise core loss/distribution calculation. To verify the accuracy of prediction, a transformer prototype with a laminated core is developed. The improved J–A-FEM and Preisach-FEM models were directly compared in terms of calculation accuracy, numerical implementation, and computational burden.