Finite Elements in Analysis and Design最新文献_第4页

Reduced-Order Modelling for Thermal–Mechanical Analysis of Power Electronic Modules 电力电子模块热力学分析的降阶建模

IF 3.5 3区工程技术 Q1 MATHEMATICS, APPLIED

Finite Elements in Analysis and Design

Pub Date : 2025-11-26 DOI: 10.1016/j.finel.2025.104488

Sheikh Hassan , Stoyan Stoyanov , Pushparajah Rajaguru , Christopher Bailey

This paper introduces a compact and time-efficient reduced-order modelling method for conducting thermal–mechanical analyses and studying material nonlinearities in power electronic modules (PEMs). Thermal–mechanical analyses in reduced-order modelling research typically follow a sequential coupling approach, where the thermal model is solved first, allowing the resulting temperature distributions to serve as loads in the mechanical system. In this study, a direct coupling method is employed for the thermomechanical analysis, enabling the simultaneous evaluation of the thermal and structural governing equations to determine thermal and directional deformation distributions, with temperature and deformations as the degrees of freedom (DOFs) of the coupled system. A novel approach, utilising the Krylov subspace-based model order reduction (MOR) process, the Newmark and Newton–Raphson algorithms within the reduced-order modelling framework, have been developed for analysing material nonlinearity in PEMs. The time domain responses, i.e., the transient ROM solutions, align remarkably well with the corresponding FOM solutions. The inelastic strains and plastic work results demonstrate strong consistency for materials having time-independent (plasticity) and time-dependent (creep and viscoplasticity) nonlinearities. Responses of the reduced-order model (ROM) in the frequency (Laplace) domain are analysed in contrast to its full-order model (FOM) to evaluate its characteristics and show suitability within the required expansion points. The MOR process provides a significantly compact ROM order of just 20

\times

20 for reduced-dimensional computation, achieving up to an 83% reduction in computational time compared to its FOM order of approximately 400,000

\times

400,000. The reduced-order modelling approach is implemented using the MATLAB coding environment.

本文介绍了一种紧凑、省时的降阶建模方法，用于电力电子模块的热力学分析和材料非线性研究。在降阶建模研究中，热-力学分析通常遵循顺序耦合方法，首先求解热模型，允许得到的温度分布作为机械系统中的载荷。在本研究中，采用直接耦合方法进行热力学分析，可以同时评估热控制方程和结构控制方程，以温度和变形作为耦合系统的自由度（DOFs），确定热和定向变形分布。利用基于Krylov子空间的模型降阶（MOR）过程，在降阶建模框架内的Newmark和Newton-Raphson算法，开发了一种新的方法来分析PEMs中的材料非线性。时域响应，即瞬态ROM解，与相应的FOM解非常一致。非弹性应变和塑性功结果表明具有时间无关（塑性）和时间相关（蠕变和粘塑性）非线性的材料具有很强的一致性。将降阶模型（ROM）在频率（拉普拉斯）域中的响应与全阶模型（FOM）进行对比分析，以评估其特性并显示其在所需扩展点内的适用性。MOR过程为降维计算提供了一个非常紧凑的ROM顺序，仅为20×20，与大约400,000×400,000的FOM顺序相比，计算时间减少了83%。在MATLAB编码环境下实现了降阶建模方法。

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引用次数: 0

3D simulation of residual stresses induced by ElectroMagnetic pulse Peening process 电磁脉冲强化过程中残余应力的三维模拟

IF 3.5 3区工程技术 Q1 MATHEMATICS, APPLIED

Finite Elements in Analysis and Design

Pub Date : 2025-11-20 DOI: 10.1016/j.finel.2025.104486

Komlavi Mawuli Senyo , Loup Plantevin , Thibaut Chaise , Eric Feulvarch , Jean-Michel Bergheau , Daniel Nélias

Compression techniques such as shot peening, laser shock peening, and water jet peening are commonly employed to induce residual compressive stresses in mechanical components. These residual stresses play a crucial role in preventing the initiation and propagation of cracks. An innovative method known as the ElectroMagnetic pulse Peening (EMP) process utilizes magnetic forces to introduce residual compressive stresses in mechanical components. The EMP process shares similarities with the ElectroMagnetic Forming (EMF) process, which has been extensively studied through numerical and experimental investigations. Existing numerical studies predominantly feature axisymmetric 2D simulations, with limited availability of 3D simulations due to numerical constraints regarding computing time and resources. Since the EMP process shares similarities with EMF, similar challenges arise with respect to computational resources and time. This paper presents an innovative approach for the 3D simulation of residual stresses induced by the EMP process, based on efficient 2D axisymmetric calculations of the electromagnetic fields. The main objective of this approach is to simulate the mechanical impact of electromagnetic pulses applied by sweeping a surface, in order to analyze the stress distribution in the overlapping regions. First, the 2D model used to simulate electromagnetic phenomena is presented, and the 2D-to-3D transfer technique developed is detailed for computing residual stresses in 3D. Subsequently, the validity of this approach is established through a comparative study between 2D and 3D mechanical results for a single electromagnetic pulse. Finally, a multiple-pulse simulation is conducted to investigate the effect of overlapping treatment regions on an AA6061 aluminum alloy. The outcomes of this study are discussed in terms of the residual stresses at the subsurface.

压缩技术，如喷丸强化、激光冲击强化和水射流强化，通常用于在机械部件中产生残余压应力。这些残余应力在防止裂纹的萌生和扩展方面起着至关重要的作用。一种被称为电磁脉冲强化（EMP）工艺的创新方法利用磁力在机械部件中引入残余压应力。EMP过程与电磁成形（EMF）过程有相似之处，后者已经通过数值和实验研究得到了广泛的研究。现有的数值研究主要以轴对称二维模拟为特征，由于计算时间和资源的数值限制，三维模拟的可用性有限。由于EMP过程与EMF有相似之处，因此在计算资源和时间方面也出现了类似的挑战。本文提出了一种基于电磁场二维轴对称计算的电磁脉冲过程残余应力三维模拟方法。该方法的主要目的是模拟电磁脉冲扫面产生的机械冲击，以分析重叠区域的应力分布。首先，提出了用于电磁现象模拟的二维模型，并详细介绍了用于计算三维残余应力的二维到三维传递技术。随后，通过对单个电磁脉冲的二维和三维力学结果的对比研究，验证了该方法的有效性。最后，通过多脉冲模拟研究了重叠处理区域对AA6061铝合金的影响。本文从地下残余应力的角度对研究结果进行了讨论。

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引用次数: 0

Efficient and accurate multiscale modelling of TRIP steels: Advanced numerical strategies and experimental validation 高效和准确的TRIP钢多尺度建模：先进的数值策略和实验验证

IF 3.5 3区工程技术 Q1 MATHEMATICS, APPLIED

Finite Elements in Analysis and Design

Pub Date : 2025-11-20 DOI: 10.1016/j.finel.2025.104484

R.P. Cardoso Coelho, F.M. Andrade Pires

This work presents methodological and computational advances to a multiscale micromechanical framework for modelling transformation-induced plasticity (TRIP) steels, explicitly coupling martensitic phase transformation and multi-phase crystallographic slip within an RVE-based homogenisation setting. Building upon the framework of Cardoso Coelho et al. (2023), we introduce a series of enhancements aimed at improving computational efficiency, expanding modelling capabilities, and increasing predictive fidelity. The numerical implementation is restructured to exploit cache-optimised data access, branchless return-mapping algorithms, selective Jacobian assembly, and explicitly vectorised linear solvers, resulting in significant reductions in computational cost, particularly for martensite-dominated loading scenarios. A mixed stress–strain-driven homogenisation scheme is formulated, enabling independent control of specific stress and strain components, thus improving the representation of experimentally observed strain-controlled uniaxial tests. Model calibration and validation are performed against experimental data using a composite Bayesian optimisation strategy, showing excellent agreement with measured stress–strain responses and a consistent prediction of martensite volume fraction evolution. Additional energetic contributions are investigated to refine the description of transformation kinetics, further enhancing model accuracy. Overall, this work delivers a robust, high-performance multiscale computational framework for TRIP steels, advancing predictive modelling capabilities for phase-transforming materials and supporting more reliable virtual material design.

这项工作为模拟相变诱发塑性（TRIP）钢的多尺度微力学框架提供了方法和计算上的进步，在基于rve的均质化设置中明确地耦合了马氏体相变和多相晶体滑移。在Cardoso Coelho等人（2023）的框架基础上，我们引入了一系列旨在提高计算效率、扩展建模能力和提高预测保真度的增强功能。数值实现进行了重组，以利用缓存优化的数据访问、无分支返回映射算法、选择性雅可比装配和明确的矢量线性求解器，从而显著降低了计算成本，特别是对于马氏体为主的加载场景。制定了混合应力-应变驱动的均质化方案，能够独立控制特定的应力和应变成分，从而改善了实验观察到的应变控制单轴试验的表现。使用复合贝叶斯优化策略对实验数据进行模型校准和验证，显示与测量的应力-应变响应和马氏体体积分数演变的一致预测非常一致。研究了额外的能量贡献，以完善转化动力学的描述，进一步提高模型的准确性。总的来说，这项工作为TRIP钢提供了一个强大的、高性能的多尺度计算框架，提高了相变材料的预测建模能力，并支持更可靠的虚拟材料设计。

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引用次数: 0

Behavior of cohesive stresses in embedded finite elements based on the strong discontinuity approach 基于强不连续方法的内嵌有限元内聚应力行为

IF 3.5 3区工程技术 Q1 MATHEMATICS, APPLIED

Finite Elements in Analysis and Design

Pub Date : 2025-11-18 DOI: 10.1016/j.finel.2025.104485

Danilo Cavalcanti , Cristian Mejia , Caio Souza , Carlos A. Mendes , Ignasi de-Pouplana , Guillermo Casas , Deane Roehl

Embedded finite element formulations have gained increased attention for modeling strong discontinuities in solid mechanics problems, as they eliminate the need for mesh conformity required by discrete fracture models. While several such formulations have been extensively studied, particularly regarding strategies to mitigate stress locking, less is understood about the causes and possible remedies to the spurious stress oscillations along cohesive discontinuities. In this work, we employ the Enhanced Assumed Strain framework to derive two of the most popular formulation types: the Kinematically Optimal Symmetric (KOS) and the Statically and Kinematically Optimal Nonsymmetric (SKON). We investigate their performance in a broad range of scenarios, including stick and slip contact conditions, in both two and three dimensions, using linear and quadratic finite elements. Our results show that the SKON formulation consistently yields smoother cohesive stress fields by enforcing local equilibrium in a strong sense. While spurious oscillations are effectively eliminated under stick conditions, small-amplitude oscillations may persist under slip conditions; however, they are significantly reduced compared to the KOS formulation. Finally, we demonstrate the application of the SKON formulation to a fault reactivation problem, confirming its capability to accurately capture stress evolution and assess fault reactivation risk.

嵌入式有限元公式在模拟固体力学问题中的强不连续面方面得到了越来越多的关注，因为它们消除了离散断裂模型所需的网格一致性。虽然已经对几种这样的公式进行了广泛的研究，特别是关于减轻应力锁定的策略，但对沿着内聚不连续的虚假应力振荡的原因和可能的补救措施了解较少。在这项工作中，我们采用增强假设应变框架来推导两种最流行的公式类型：运动最优对称（KOS）和静态和运动最优非对称（SKON）。我们研究了它们在广泛的场景下的性能，包括粘和滑接触条件，在二维和三维，使用线性和二次元有限元。我们的结果表明，SKON配方通过在强意义上强制局部平衡，始终产生更平滑的内聚应力场。虽然在粘滞条件下可以有效地消除伪振荡，但在滑移条件下可能会持续存在小振幅振荡；然而，与KOS配方相比，它们明显减少了。最后，我们演示了SKON公式在断层再激活问题中的应用，证实了其准确捕获应力演化和评估断层再激活风险的能力。

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引用次数: 0

Assessment of the Spalart–Allmaras turbulence model in a stabilized finite element framework for hypersonic turbulent flows using pressure-primitive variables 基于压力原变量的高超声速湍流稳定有限元框架下的Spalart-Allmaras湍流模型评估

IF 3.5 3区工程技术 Q1 MATHEMATICS, APPLIED

Finite Elements in Analysis and Design

Pub Date : 2025-11-08 DOI: 10.1016/j.finel.2025.104473

Rahul Verma , David Codoni , Craig Johansen , A. Korobenko

This study evaluates the performance of the Spalart–Allmaras (SA) turbulence model within a finite element framework. The streamline upwind Petrov–Galerkin (SUPG) method is employed as a stabilization technique to provide numerical stability. The proposed formulation solves the three-dimensional Navier–Stokes (N-S) equations expressed in primitive variables. The robustness and accuracy of the stabilized framework, incorporating the one-equation SA turbulence model, are assessed across a wide range of Mach numbers using benchmark test cases. The results demonstrate the effectiveness of the present approach in modeling high-speed turbulent flows, including separated boundary layers and shock wave interactions.

本研究在有限元框架内评估了Spalart-Allmaras （SA）湍流模型的性能。采用流线迎风彼得罗夫-伽辽金（SUPG）方法作为稳定技术来提供数值稳定性。该公式求解了以原始变量表示的三维Navier-Stokes （N-S）方程。结合单方程SA湍流模型的稳定框架的鲁棒性和准确性，使用基准测试用例在广泛的马赫数范围内进行了评估。结果证明了该方法在模拟高速湍流流动时的有效性，包括分离边界层和激波相互作用。

引用次数: 0

The adaptive thermo-mechanical-electro-magnetic enriched finite element method for statics analysis of functionally graded magneto-electro-elastic structures 功能梯度磁电弹性结构静力分析的自适应热-机-电磁富集有限元法

IF 3.5 3区工程技术 Q1 MATHEMATICS, APPLIED

Finite Elements in Analysis and Design

Pub Date : 2025-11-08 DOI: 10.1016/j.finel.2025.104476

Liming Zhou , Guangyu Liang , Jiye Wang , Panpan Zhu

In this paper, the thermo-mechanical-electro-magnetic enriched finite element method (TMEM-EFEM) is proposed to analyze static models of magneto-electro-elastic smart structures. An improvement over the traditional finite element method (FEM) is that the displacement, electric and magnetic fields are fitted by interpolation covering functions. The support domain of the node is constructed by a series of triangular elements. Although the concept of support domain is used, the proposed method does not require high computational cost to solve the extent of the support domain. The feasibility of TMEM-EFEM is demonstrated by a series of numerical examples. The proposed method is proven to be efficient under coarse and distorted meshes. Besides, the adaptive mesh refinement (AMR) technology is used to locally refine functionally graded magneto-electro-elastic smart structures in interested areas under a coarse mesh. The generalized strain energy criterion is used in the AMR technology. Through a series of numerical examples, the high accuracy of the proposed method under the AMR partitioning scheme is demonstrated. The results show that the values of displacement u_z, electric potential Φ and magnetic potential Ψ decrease with the increase of exponential factors. The computational efficiency of TMEM-EFEM is significantly higher than that of FEM, which verifies the correctness and effectiveness of this method.

本文提出了热-机-电磁富集有限元法（TMEM-EFEM）来分析磁-电弹性智能结构的静态模型。对传统有限元法的改进是利用插值覆盖函数拟合位移场、电场场和磁场。节点的支持域由一系列三角形元素构成。虽然采用了支撑域的概念，但该方法求解支撑域范围的计算成本不高。通过一系列数值算例验证了该方法的可行性。在粗糙和变形网格下，该方法是有效的。此外，采用自适应网格细化（AMR）技术在粗网格下对感兴趣区域的功能梯度磁电弹性智能结构进行局部细化。AMR技术采用广义应变能准则。通过一系列的数值算例，证明了该方法在AMR划分方案下具有较高的精度。结果表明：位移uz、电势Φ和磁势Ψ随指数因子的增大而减小；TMEM-EFEM的计算效率明显高于FEM，验证了该方法的正确性和有效性。

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引用次数: 0

PGD-based local surrogate models via overlapping domain decomposition: A computational comparison 基于重叠域分解的pgd局部代理模型：计算比较

IF 3.5 3区工程技术 Q1 MATHEMATICS, APPLIED

Finite Elements in Analysis and Design

Pub Date : 2025-11-07 DOI: 10.1016/j.finel.2025.104475

Marco Discacciati , Ben J. Evans , Matteo Giacomini

An efficient strategy to construct physics-based local surrogate models for parametric linear elliptic problems is presented. The method relies on proper generalized decomposition (PGD) to reduce the dimensionality of the problem and on an overlapping domain decomposition (DD) strategy to decouple the spatial degrees of freedom. In the offline phase, the local surrogate model is computed in a non-intrusive way, exploiting the linearity of the operator and imposing arbitrary Dirichlet conditions, independently at each node of the interface, by means of the traces of the finite element functions employed for the discretization inside the subdomain. This leads to parametric subproblems with reduced dimensionality, significantly decreasing the complexity of the involved computations and achieving speed-ups up to 100 times with respect to a previously proposed DD-PGD algorithm that required clustering the interface nodes. A fully algebraic alternating Schwarz method is then formulated to couple the subdomains in the online phase, leveraging the real-time (less than half a second) evaluation capabilities of the computed local surrogate models, that do not require the solution of any additional low-dimensional problems. A computational comparison of different PGD-based local surrogate models is presented using a set of numerical benchmarks to showcase the superior performance of the proposed methodology, both in the offline and in the online phase.

提出了一种构造参数线性椭圆问题的基于物理的局部代理模型的有效方法。该方法采用适当的广义分解（PGD）来降低问题的维数，采用重叠域分解（DD）策略来解耦空间自由度。在离线阶段，局部代理模型以非侵入式的方式计算，利用算子的线性，并通过用于子域中离散化的有限元函数的轨迹，在界面的每个节点独立地施加任意的狄利克雷条件。这导致了维度降低的参数子问题，显著降低了所涉及计算的复杂性，并且相对于先前提出的需要聚集接口节点的DD-PGD算法实现了高达100倍的加速。然后制定了一个完全代数交替Schwarz方法来耦合在线阶段的子域，利用计算的局部代理模型的实时（不到半秒）评估能力，不需要解决任何额外的低维问题。使用一组数值基准对不同的基于pgd的局部代理模型进行了计算比较，以展示所提出的方法在离线和在线阶段的优越性能。

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引用次数: 0

A generic tomography-based conforming finite elements model 基于层析成像的通用有限元模型

IF 3.5 3区工程技术 Q1 MATHEMATICS, APPLIED

Finite Elements in Analysis and Design

Pub Date : 2025-11-05 DOI: 10.1016/j.finel.2025.104472

Chandrashekhar M. Pilgar , Jean-Luc Bouvard , Teddy Fixy , Daniel Pino-Munoz

This study presents a novel, automated pipeline to transform Micro-computed tomography (

μ

CT) images into conformal Finite element analysis (FEA) models with high-quality tetrahedral elements. The proposed methodology uses image separation techniques and levelset methods to isolate distinct material components while avoiding overlaps and voids. A graph-based algorithm further optimizes the separation by grouping components into minimal non-overlapping level sets, enhancing computational efficiency and ensuring geometric fidelity. Subsequent mesh adaptation and remeshing procedures produce conformal meshes that accurately represent complex geometries and boundaries. The framework is validated through three case studies: woven composites, polycrystals, and dental implants, demonstrating its applicability across diverse material systems. This approach provides a robust solution for bridging tomographic imaging and high fidelity simulations, enabling more precise predictions of mechanical behavior and material performance.

本研究提出了一种新的自动化流水线，将微计算机断层扫描（μCT）图像转换为具有高质量四面体单元的共形有限元分析（FEA）模型。所提出的方法使用图像分离技术和水平集方法来隔离不同的材料成分，同时避免重叠和空隙。基于图的算法通过将组件分组到最小的不重叠水平集来进一步优化分离，提高了计算效率并保证了几何保真度。随后的网格适应和网格重新划分程序产生的保形网格，准确地表示复杂的几何形状和边界。该框架通过三个案例研究进行了验证：编织复合材料、多晶体和牙科植入物，证明了它在不同材料系统中的适用性。这种方法为层析成像和高保真模拟提供了一个强大的解决方案，可以更精确地预测机械行为和材料性能。

引用次数: 0

One-way coupled staggered implementation of gradient-enhanced damage models coupled to thermoplasticity 热塑性梯度增强损伤模型的单向耦合交错实现

IF 3.5 3区工程技术 Q1 MATHEMATICS, APPLIED

Finite Elements in Analysis and Design

Pub Date : 2025-10-31 DOI: 10.1016/j.finel.2025.104471

Johannes Friedlein, Paul Steinmann, Julia Mergheim

Gradient-enhancement of the damage variable for the regularisation of coupled plasticity-damage constitutive models leads to a coupled system of equations. This is mostly solved monolithically due to the strong coupling and often implemented by a thermomechanical substitution approach into commercial finite element solvers. Therewith the analogy between implicit gradient theory and heat equation is utilised. This avoids the implementation of a separate element formulation and is compatible with many existing finite element solvers. However, for some commercial solvers only a staggered thermomechanical approach is available. Therefore, a method is introduced to use a staggered solver for gradient-enhanced damage formulations. The strong coupling is thereby only approximated, but the size and symmetry of the subsystems can be preserved. Moreover, the staggered approach leads to a modular implementation, which enables to stack multiple subsystems without permanently occupying the thermal solver by a single monolithic coupling. This easily extendable multi-purpose use of the thermal solver is demonstrated by a three-field problem solving coupled thermo-plasticity-gradient-damage. The staggered and monolithic approach are compared and investigated by numerical examples.

为了正则化耦合塑性-损伤本构模型，损伤变量的梯度增强导致了一个耦合方程组。由于强耦合，这主要是整体解决的，并且通常通过热机械替代方法实现到商业有限元求解器中。利用隐式梯度理论与热方程的类比。这避免了单独的单元公式的实现，并与许多现有的有限元求解器兼容。然而，对于一些商业解决方案，只有交错的热机械方法是可用的。因此，引入了一种使用交错求解器求解梯度增强损伤公式的方法。因此，强耦合只是近似的，但子系统的大小和对称性可以保持。此外，交错方法导致模块化实现，这使得可以堆叠多个子系统，而无需通过单个单片耦合永久占用热求解器。通过求解耦合热塑性-梯度-损伤的三场问题，证明了热求解器的这种易于扩展的多用途用途。通过数值算例对交错法和整体法进行了比较和研究。

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引用次数: 0

Temperature response bounds analysis for heat conduction problems with spatial uncertainties 空间不确定性热传导问题的温度响应界分析

IF 3.5 3区工程技术 Q1 MATHEMATICS, APPLIED

Finite Elements in Analysis and Design

Pub Date : 2025-10-30 DOI: 10.1016/j.finel.2025.104474

Weiwei Chen , Wanyi Tian , Bingyu Ni , Rong Wang , Qun Wang , Shouhua Yi

Spatial uncertainties in heat conduction problems, such as uncertain heat sources and boundary condition parameters, significantly influence the temperature response within the control domain. Constructing reliable probabilistic random fields for these uncertainties is often infeasible due to the scarcity of experimental data, particularly in the early design stages. To address this challenge, this paper develops a temperature response bounds analysis method based on the concept of the interval field, enabling the uncertainty analysis of structural temperature responses under limited sample data conditions. For one-dimensional heat conduction problems, analytical formulations of temperature response bounds are derived under three typical boundary conditions. For multi-dimensional problems, a semi-analytical formulation is proposed by integrating the interval field approach with the interval finite element method. The effectiveness and efficiency of the proposed approach are demonstrated through three numerical examples, highlighting its potential for practical engineering applications under data-scarce conditions.

热传导问题中的空间不确定性，如热源和边界条件参数的不确定性，会显著影响控制域中的温度响应。由于实验数据的缺乏，特别是在早期设计阶段，为这些不确定性构建可靠的概率随机场往往是不可行的。针对这一挑战，本文提出了基于区间场概念的温度响应界分析方法，实现了有限样本数据条件下结构温度响应的不确定性分析。对于一维热传导问题，导出了三种典型边界条件下温度响应边界的解析表达式。对于多维问题，将区间域法与区间有限元法相结合，提出了一种半解析式。通过三个数值算例证明了该方法的有效性和效率，突出了其在数据稀缺条件下的实际工程应用潜力。

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引用次数: 0