International Journal for Numerical Methods in Engineering最新文献

{"title":"Learning the Solution Operator Family in Elastic Mechanics for Response Prediction Under Various Load Scenarios","authors":"Xuliang Liu,&nbsp;Yuequan Bao","doi":"10.1002/nme.70085","DOIUrl":"https://doi.org/10.1002/nme.70085","url":null,"abstract":"<div>\u0000 \u0000 <p>Analyzing the responses of solid materials under diverse loading scenarios with different types and forms is a fundamental engineering necessity. However, a load-adaptable machine learning model that can predict such responses still needs to be explored. This study formulates the load-adaptable response prediction problem as a solution operator family regression task and develops a Load-Adaptable Physics-Informed DeepONet (LA-PIDON) to learn the solution operator family of mechanics. The proposed method utilizes the product space as the input space, composed of function spaces for force boundaries, displacement boundaries, material properties, and other mechanical factors. Distinct branch networks are established for each mechanical factor and distinct trunk networks for each corresponding response. The solution family learning task is accomplished by using shared branch networks across multiple trunk networks. The load adaptability for both concentrated and distributed forces is achieved through the integration of Gaussian Random Fields(GRFs) and Fourier polynomials to generate function spaces for the force boundary; the load adaptability for force and imposed displacement excitation is achieved by incorporating the product space of force and displacement boundaries into the input space. The numerical cases of (1) elastic plates subjected to benchmark force and imposed displacement excitations, (2) benchmark beams under pure and tensile bending, and (3) 3D elastic cubes undergoing axial tension demonstrate the method's adaptability to various load scenarios and its capacity to handle complex stress states. The proposed method has potential applications in fields that require numerous simulations for diverse load scenarios, such as reliability analysis and digital twins.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 17","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144934930","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"An Eulerian Framework for Modeling Visco-Plasticity and Isotropic and Directional Material Hardening Utilizing Neural Networks","authors":"Martin Kroon","doi":"10.1002/nme.70083","DOIUrl":"https://doi.org/10.1002/nme.70083","url":null,"abstract":"<p>A neural network is inserted into a theoretical framework for modeling the inelastic behavior of materials. The neural network replaces functional expressions for such phenomena as isotropic and directional hardening and viscoplasticity. The theoretical framework, into which the neural network is inserted, is Eulerian in the sense that all state variables are defined in the current state of the material, and the framework is independent of history variables, such as plastic strain, accumulated equivalent plastic strain, etc. The neural network-based model is compared to and trained to reproduce the uniaxial tension response of theoretical reference solutions as well as experimental results. The neural network-based model is able to reproduce the reference results with excellent precision. Also, the neural network-based model was implemented as a VUMAT in Abaqus together with one of the theoretical reference models. Deformation of a plate with a hole in it was simulated, and the outcome from the reference model and the trained neural network-based model was compared. The solutions, in terms of von Mises stress and accumulated equivalent plastic strain, were very similar. Hence, it seems like training the neural network model by use of uniaxial stress data is sufficient for being able to make accurate 3D predictions.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 17","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.70083","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144935319","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A Novel Density Correction Method for Improved Prediction of Pressure Fields in SPH","authors":"Yoon Sung Jeong,&nbsp;Phill-Seung Lee","doi":"10.1002/nme.70116","DOIUrl":"https://doi.org/10.1002/nme.70116","url":null,"abstract":"<div>\u0000 \u0000 <p>Smoothed particle hydrodynamics (SPH) has been extensively studied for several decades, yet accurate calculation of pressure fields remains a significant challenge, hindering its widespread application in practical engineering. This paper focuses on developing a novel density correction method to enhance the accuracy of hydrostatic pressure distribution in SPH, both near solid boundaries and within the fluid domain. The method incorporates two innovative concepts: an interpolation grid and supplementary particles, both aimed at refining density distributions. The proposed method is straightforward to implement, making it accessible for a wide range of applications. It proves highly effective in calculating improved hydrostatic pressure fields in high-pressure regions close to solid boundaries. Moreover, the proposed method effectively suppresses unphysical oscillations and peaks in the hydrodynamic pressure fields while alleviating unintended numerical dissipation that often occurs in long-term simulations. Additionally, the method offers greater flexibility in determining the correction interval and demonstrates excellent compatibility with various solid boundary treatments. The performance of the proposed method is validated through several numerical tests, and comparisons with other related numerical schemes are presented.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 17","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144935318","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A h-Adaptivity Strategy for Hybridizable Discontinuous Galerkin (HDG) Simulations of Fluid Transport Models in Tokamak Plasma","authors":"Marcello Capasso,&nbsp;Ivan Kudashev,&nbsp;Frédéric Schwander,&nbsp;Éric Serre","doi":"10.1002/nme.70107","DOIUrl":"https://doi.org/10.1002/nme.70107","url":null,"abstract":"<p>The highly anisotropic, multi-scale nature of fusion plasma simulations in tokamaks, combined with the complexity in the geometries of plasma-facing components and magnetic equilibrium, challenges numerical schemes. They therefore require the development of advanced numerical techniques to enhance computational efficiency and enable codes to simulate realistic plasma configurations relevant to tokamak operation. This paper proposes an adaptive mesh refinement strategy (<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>h</mi>\u0000 </mrow>\u0000 <annotation>$$ h $$</annotation>\u0000 </semantics></math>-adaptivity) in the SolEdge-HDG code for the resolution of 2D fluid-drift Braginskii equations using the Hybrid Discontinuous Galerkin (HDG) method. The strategy is based on an oscillation indicator implemented to detect under-resolved regions and dynamically refine the mesh, associated with an a posteriori accuracy indicator built on the local difference between the solution at order <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 </mrow>\u0000 <annotation>$$ p $$</annotation>\u0000 </semantics></math> and the post-processed one at order <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 <mo>+</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 <annotation>$$ p+1 $$</annotation>\u0000 </semantics></math> considered as reference. The method thus enables both refinement, where necessary, as well as coarsening in regions where the solution is smooth. Numerical results obtained with this method in realistic tokamak geometry and plasma conditions show significant reductions in computational resources and an improvement in code robustness while maintaining high accuracy, particularly in regions with steep gradients or near the sharp angles of the tokamak walls. This work highlights the potential of such <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>h</mi>\u0000 </mrow>\u0000 <annotation>$$ h $$</annotation>\u0000 </semantics></math>-adaptivity technique to optimize transport simulations in realistic tokamak configurations, offering a fully automated, goal-oriented mesh refinement strategy. In addition to optimizing the numerical cost of simulation, this strategy offers all users a fully automated means of designing a mesh in any tokamak geometry.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 17","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.70107","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144934846","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Featured Cover","authors":"Zhuo Deng,&nbsp;Shi-Xuan Liu,&nbsp;Song Cen,&nbsp;Ming Sun,&nbsp;Yan Shang","doi":"10.1002/nme.70122","DOIUrl":"https://doi.org/10.1002/nme.70122","url":null,"abstract":"<p>The cover image is based on the article <i>Corotational Unsymmetric Membrane Element Formulation for Geometric Nonlinear Analysis of Flexoelectric Solids Within the Consistent Couple Stress Theory</i> by Yan Shang et al., https://doi.org/10.1002/nme.70045.\u0000\u0000 <figure>\u0000 <div><picture>\u0000 <source></source></picture><p></p>\u0000 </div>\u0000 </figure></p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 11","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.70122","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144915293","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Topology Optimization of Load-Bearable Phononic Crystals","authors":"Wei-Zhi Luo,&nbsp;Chao Wang,&nbsp;Mu He,&nbsp;Liang Xia","doi":"10.1002/nme.70114","DOIUrl":"https://doi.org/10.1002/nme.70114","url":null,"abstract":"<div>\u0000 \u0000 <p>Phononic crystals are artificially engineered metamaterials that exhibit outstanding performance in vibro-isolation. While their optimization for vibro-isolation applications has been widely studied, the integration of load-bearing functionality requires further research. Our work presents a topology optimization framework for load-bearing phononic crystals that maximizes band-gaps under modulus constraints. Two-scale asymptotic homogenization theory is considered to calculate the effective modulus under a static or dynamic regime. Additionally, a material interpolation model with independent penalty factors is employed to analyze its influence on the optimized configuration. Numerical results confirm the effectiveness of the proposed optimization framework and reveal the significant impact of load-bearing constraints on vibro-isolation performance. This work enriches the theoretical foundation and methodological framework for multifunctional phononic crystals that combine load-bearing and vibro-isolation performance.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 16","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144897587","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Physics-Informed Neural Networks for Solving Parameterized Dual-Domain Darcy–Brinkman Flows in Gradient Porous Mediums","authors":"Haoyun Xing,&nbsp;Guice Yao,&nbsp;Hang Yuan,&nbsp;Jin Zhao,&nbsp;Dongsheng Wen","doi":"10.1002/nme.70110","DOIUrl":"https://doi.org/10.1002/nme.70110","url":null,"abstract":"<div>\u0000 \u0000 <p>The ability to solve parameterized partial differential equations is pivotal to improving engineering design efficiency, and with the advancement of machine learning technologies, physics-informed neural networks (PINNs) provide a promising avenue. In this work, a coupled dual-domain Darcy–Brinkman flow model for gradient porous media is established. Building upon this, the trunk-branch (TB)-net PINN framework, which is capable of dealing with multi-physical field issues, is utilized to conduct predictions for a specific porosity configuration scenario, and the performance of different data collocation strategies is examined. Following this, explorations for parameterized flows are implemented, demonstrating remarkable accuracy in two randomly chosen conditions. This is the first known application of PINNs-like methods to handle such complex parameterized dual-domain Darcy–Brinkman flows, yielding invaluable experience pertinent to engineering design and efficiency optimization.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 16","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144897584","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Solving Fractional Differential Equations Using Differential Transform Method and Fermat Collocation Method: Formulation Convergence and Error Analysis","authors":"A. S. Mohamed","doi":"10.1002/nme.70099","DOIUrl":"https://doi.org/10.1002/nme.70099","url":null,"abstract":"<div>\u0000 \u0000 <p>This paper shows how to solve fractional differential equations (FDEs) with two methods: the differential transform method (DTM) and the Fermat collocation method (FCM). Provides a comprehensive overview of the formulation and features of both algorithms. The first method turns the differential equation and its boundary conditions into a series using a step-by-step process, then obtains the exact solution. The second method converts the equation into a set of simpler equations for the coefficients. We used Fermat polynomials (FPs) as the basis functions and evaluated the coefficients using matrix techniques. The paper also looks at how well these methods work and what kind of errors to expect. An analysis of the convergence behavior and the associated computational complexity is also presented in the paper. We solved many test problems using our methods and compared the errors with those obtained from other methods. The results of this comparison highlight the superior accuracy and effectiveness of the proposed techniques over alternative methods.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 16","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144897585","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A Correction to ‘A Generalized Single-Step Multi-Stage Time Integration Formulation and Novel Designs With Improved Stability and Accuracy’","authors":"Yazhou Wang,&nbsp;Nikolaus A. Adams,&nbsp;Kumar K. Tamma","doi":"10.1002/nme.70112","DOIUrl":"https://doi.org/10.1002/nme.70112","url":null,"abstract":"<p>In this note, we describe a correction to the generalized single-step multi-stage time integration framework published in IJNME(2025)126:e7658. The correction does not change any numerical analysis or conclusions in the paper. However, it is necessary, as the numerical implementation might be misunderstood.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 16","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.70112","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144897586","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Finite Element Analysis of Particle Size Effects on Piezoelectric Nanogenerator Performance","authors":"Fatma Benbrahim,&nbsp;Slim Naifar,&nbsp;Mohamed Dhia Ayadi,&nbsp;Olfa Kanoun","doi":"10.1002/nme.70095","DOIUrl":"https://doi.org/10.1002/nme.70095","url":null,"abstract":"&lt;p&gt;This study presents a multiscale finite element investigation into how particle dimensions influence the performance of piezoelectric nanogenerators (PENGs) based on PDMS/&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mtext&gt;BaTiO&lt;/mtext&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;3&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ {mathrm{BaTiO}}_3 $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; nanocomposites. Using COMSOL Multiphysics, we developed a comprehensive computational framework to analyze the effects of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mtext&gt;BaTiO&lt;/mtext&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;3&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ {mathrm{BaTiO}}_3 $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; particle size (50 nm, 100 nm, 2 &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;μ&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ upmu $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;m and 5 &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;μ&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ upmu $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;m) and loading concentration (10%, 15%, 20%, and 25%) on energy harvesting efficiency. Our model integrates an advanced stochastic algorithm for particle distribution and employs representative volume element (RVE) analysis to accurately capture the material's heterogeneous microstructure. The model's validity was established through rigorous comparison with theoretical predictions of resonance frequencies and experimental power density measurements, demonstrating excellent agreement across multiple operating conditions. Our findings reveal that nanoscale &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mtext&gt;BaTiO&lt;/mtext&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;3&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ {mathrm{BaTiO}}_3 $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; particles (50–100 nm) generate substantially higher power densities compared to their microscale counterparts (2–5 &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;μ&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 ","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 16","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.70095","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144894458","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}