International Journal for Numerical Methods in Engineering最新文献

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On Representation of Macroscopic Crack in Periodic Fine-Scale Discrete Mechanical Models 周期精细尺度离散力学模型中宏观裂纹的表征
IF 3.3 3区 工程技术
International Journal for Numerical Methods in Engineering Pub Date : 2026-10-15 DOI: 10.1002/nme.70449
Jan Raisinger, Jan Eliáš
{"title":"On Representation of Macroscopic Crack in Periodic Fine-Scale Discrete Mechanical Models","authors":"Jan Raisinger,&nbsp;Jan Eliáš","doi":"10.1002/nme.70449","DOIUrl":"https://doi.org/10.1002/nme.70449","url":null,"abstract":"<p>The evolution of strain localization and the corresponding macroscopic response obtained in multiscale modeling of softening heterogeneous materials strongly depend on the boundary conditions imposed on the fine-scale model. For rectilinear models (e.g., squares or cubes), employing standard Periodic BCs leads to overestimation of energy dissipation and artificially ductile behavior, whenever the localization band orientation deviates from the periodic directions. Recently proposed Tessellation and Percolation-path-aligned BCs promise to address this by aligning the periodicity frame with evolving localization bands. Alternatively, spherical/circular models provide an orientation independent response by design. Unfortunately, the standard Periodic BCs do not allow development of proper localization band crossing the spherical model's boundaries. A recently proposed modification addresses this by adding a displacement jump to the spherical periodic BCs. This study evaluates the applicability of these novel BCs to a mesoscale discrete particle model of concrete. Two-dimensional square and circular models under uniaxial tension with different loading directions are analyzed, with selected approaches extended to three-dimensional cube models. Percolation-path-aligned BCs were found to suffer from several drawbacks. Uneven straining of the weakly and strongly constrained sections can trigger localization into multiple bands, and the weakly constrained section is susceptible to spurious strain localization. Tessellation BCs, on the other hand, consistently allow the development of a single localization band of predictable length, determined only by the model geometry, enabling a straightforward correction of its influence during post-processing. As a result, variations in dissipated energy with loading direction can be attributed solely to model geometry rather than to artifacts introduced by the boundary conditions. Periodic boundary conditions augmented with a displacement jump applied to a circular model yield inconsistent results. Some cases exhibit correct localization band development, but some produce crack patterns similar to those under the standard Periodic BCs. Which of these occurs is dictated by the internal heterogeneity of the model, which effectively determines whether strain localization is initiated in the boundary segment enhanced by the displacement jump.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"127 20","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.70449","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149177268","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}
引用次数: 0
A Higher-Order Multiscale Finite Element Method Based on the Ultra-Weak Mixed Formulation for 3D Solids 基于超弱混合配方的三维固体高阶多尺度有限元法
IF 3.3 3区 工程技术
International Journal for Numerical Methods in Engineering Pub Date : 2026-10-15 DOI: 10.1002/nme.70447
Witold Cecot, Waldemar Rachowicz
{"title":"A Higher-Order Multiscale Finite Element Method Based on the Ultra-Weak Mixed Formulation for 3D Solids","authors":"Witold Cecot,&nbsp;Waldemar Rachowicz","doi":"10.1002/nme.70447","DOIUrl":"https://doi.org/10.1002/nme.70447","url":null,"abstract":"<div>\u0000 <p>A new version of the multiscale finite element method (MsFEM) for elastic solid bodies, based on the mixed ultra-weak formulation is presented. The mixed formulation ensures fast stress convergence, while its ultra-weak variant facilitates the construction of conforming shape functions. Furthermore, the stability guaranteed by the discontinuous Petrov–Galerkin (DPG) methodology, combined with the high approximability inherent to MsFEM, ensures the convergence of the numerical solution. The key innovation of the proposed MsFEM modification lies in the computation of the prolongation operator between fine and coarse finite element meshes. The proposed approach, which accounts for high-order approximation, has been successfully verified on several representative numerical examples for 3D elasticity problems and can also be applied to direct FEM computations (without upscaling) for heterogeneous materials, when the multigrid method is used to solve the systems of algebraic equations for the ultra-weak mixed formulation.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"127 20","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149177269","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}
引用次数: 0
Surrogate Computational Homogenization Enhanced by Partition-of-Unity RBF Interpolation With Decision Trees 基于决策树的统一分割RBF插值增强代理计算均匀性
IF 3.3 3区 工程技术
International Journal for Numerical Methods in Engineering Pub Date : 2026-10-14 DOI: 10.1002/nme.70442
Yosuke Yamanaka, Norio Hirayama, Kenjiro Terada
{"title":"Surrogate Computational Homogenization Enhanced by Partition-of-Unity RBF Interpolation With Decision Trees","authors":"Yosuke Yamanaka,&nbsp;Norio Hirayama,&nbsp;Kenjiro Terada","doi":"10.1002/nme.70442","DOIUrl":"https://doi.org/10.1002/nme.70442","url":null,"abstract":"<p>This study enhances a framework of surrogate computational homogenization (SCH) using decision tree-based partition-of-unity radial basis function (PU-RBF) interpolation for three-dimensional finite-deformation two-scale analysis. The method addresses the scalability limitation of global RBF interpolation for large numerical material test (NMT) datasets by partitioning the strain space into overlapping subdomains with a binary-tree strategy and training local RBF interpolants blended by smooth partition-of-unity weights. This local-global construction reduces training cost while preserving a continuously differentiable stress response, enabling consistent tangent evaluation in implicit finite element solvers. For hyperelastic composite unit-cell problems, the SCH model is trained with datasets exceeding <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 <msup>\u0000 <mrow>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>5</mn>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$$ 1{0}^5 $$</annotation>\u0000 </semantics></math> samples, reconstructs database responses with high fidelity, and reproduces <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mrow>\u0000 <mtext>FE</mtext>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$$ {mathrm{FE}}^2 $$</annotation>\u0000 </semantics></math>-level trends in both macroscopic and localization analyses with improved computational efficiency. Because it is nonintrusive at the constitutive-update level, the surrogate is straightforward to integrate into standard CAE workflows. The present model is interpolation-based and therefore intended for deformation states covered by the training data.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"127 20","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.70442","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149177098","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}
引用次数: 0
A Level Set Method on Particle Flow Maps 粒子流图的水平集方法
IF 3.3 3区 工程技术
International Journal for Numerical Methods in Engineering Pub Date : 2026-10-13 DOI: 10.1002/nme.70441
Jinjin He, Taiyuan Zhang, Zhiqi Li, Junwei Zhou, Duowen Chen, Bo Zhu
{"title":"A Level Set Method on Particle Flow Maps","authors":"Jinjin He,&nbsp;Taiyuan Zhang,&nbsp;Zhiqi Li,&nbsp;Junwei Zhou,&nbsp;Duowen Chen,&nbsp;Bo Zhu","doi":"10.1002/nme.70441","DOIUrl":"https://doi.org/10.1002/nme.70441","url":null,"abstract":"<p>Accurate interface tracking is central to numerical simulations involving moving boundaries, including multiphase flows, free-surface dynamics, phase-change problems, and other interface-driven processes in computational mechanics. Although, level set methods provide a flexible implicit representation of evolving interfaces, their grid-based advection and reinitialization procedures often introduce numerical diffusion, volume loss, and degradation of thin or highly curved structures. This paper introduces a particle flow map level set (PFM-LS) method that addresses these limitations by transporting interface geometry through particle-carried bidirectional flow maps. In contrast to particle level set methods that use particles mainly as corrective markers, PFM-LS uses particles as primary carriers of level-set values, gradients, and Hessians within a narrow band around the interface. The method combines long-range flow-map transport, high-order particle-grid reconstruction, adaptive particle control, and a hybrid particle-grid redistancing scheme to preserve both signed-distance consistency and sub-grid geometric features. Numerical benchmarks in two and three dimensions, including topology-change tests, chamfer and Hausdorff shape-error metrics, and coupling to an incompressible free-surface flow solver, show that PFM-LS achieves strong volume preservation, high shape fidelity, and near fourth-order convergence, outperforming a broad range of existing level set and reference-map-based methods.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"127 20","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.70441","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149176991","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}
引用次数: 0
Hybrid Carrera Unified Formulation Plate Elements for Nearly Incompressible Hyperelastic Plates 几乎不可压缩超弹性板的混合Carrera统一公式板单元
IF 3.3 3区 工程技术
International Journal for Numerical Methods in Engineering Pub Date : 2026-10-13 DOI: 10.1002/nme.70443
Xueyan Hu, Erasmo Carrera, Alfonso Pagani, Weiqiu Chen
{"title":"Hybrid Carrera Unified Formulation Plate Elements for Nearly Incompressible Hyperelastic Plates","authors":"Xueyan Hu,&nbsp;Erasmo Carrera,&nbsp;Alfonso Pagani,&nbsp;Weiqiu Chen","doi":"10.1002/nme.70443","DOIUrl":"https://doi.org/10.1002/nme.70443","url":null,"abstract":"<div>\u0000 \u0000 <p>Incompressible hyperelastic plates are widely used as fundamental structures in soft robotics and flexible devices, yet their nonlinear analysis remains challenging due to volumetric and shear locking. This work develops a family of locking-free hybrid carrera unified formulation (CUF) plate elements based on a mixed <i>u–p</i> variational setting. By exploiting the features of CUF, various structural theories with different displacement–pressure approximate orders are constructed to balance computational accuracy and efficiency, and the mixed interpolation of tensorial components (MITC) technique is incorporated to ensure locking-free performance for low-order in-plane discretizations in the thin-plate limit. Several benchmark and representative numerical examples, covering different through-the-thickness descriptions of the primary unknowns and mesh densities, demonstrate that the proposed hybrid CUF elements eliminate locking and accurately capture pressure variations with significantly fewer degrees of freedom than conventional three-dimensional solid models.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"127 20","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149176992","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}
引用次数: 0
Non-Central Wishart Random Matrices in Structural Dynamics: A Modal-Basis Approach 结构动力学中的非中心Wishart随机矩阵:一种模态基方法
IF 3.3 3区 工程技术
International Journal for Numerical Methods in Engineering Pub Date : 2026-10-13 DOI: 10.1002/nme.70446
Alan Das Mannoosseril, Sondipon Adhikari, H. Murat Panayirci
{"title":"Non-Central Wishart Random Matrices in Structural Dynamics: A Modal-Basis Approach","authors":"Alan Das Mannoosseril,&nbsp;Sondipon Adhikari,&nbsp;H. Murat Panayirci","doi":"10.1002/nme.70446","DOIUrl":"https://doi.org/10.1002/nme.70446","url":null,"abstract":"<p>This article develops a non-parametric stochastic computational model for linear structural dynamics based on a reduced non-central Wishart (NCW) random matrix formulation. The objective is to represent uncertainty in the mass and stiffness matrices while preserving the matrix properties required for modal and frequency-domain analysis. Although the non-central Wishart distribution provides a more flexible random matrix representation than the central Wishart (CW) model, its direct identification in physical finite-element coordinates is limited by the storage and computational cost associated with full matrix-covariance information. To address this limitation, a reduced modal-basis calibration of the non-central Wishart random matrix model is proposed. The method uses a reference parametric ensemble to identify variance information in the reduced system matrices and provides a direct sampling procedure for forward uncertainty propagation. The formulation is demonstrated using the forced vibration response of a clamped aluminum plate with spatially correlated uncertainty in material and thickness properties. A parametric random-field ensemble provides the reference matrix statistics and frequency-response uncertainty bands and the proposed model is compared with a central Wishart baseline through driving-point and cross frequency response functions. The response statistics indicate that, for the plate problem considered, the dominant contribution to the frequency-response uncertainty can be represented by the mode-indexed diagonal covariance content of the reduced system matrices. The proposed formulation therefore provides a computationally tractable non-central Wishart model for forward uncertainty propagation, while identifying the treatment of off-diagonal inter-modal covariance as a key direction for future development.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"127 20","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.70446","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149176990","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}
引用次数: 0
Topology Optimization of Transient Two-Phase Flows via Phase-Field-Based Penalty Interpolation Model 基于相场惩罚插值模型的瞬态两相流拓扑优化
IF 3.3 3区 工程技术
International Journal for Numerical Methods in Engineering Pub Date : 2026-10-13 DOI: 10.1002/nme.70435
Yulong Ji, Xin Zhang, Jingjie He, Fei Long, Peng Zhang
{"title":"Topology Optimization of Transient Two-Phase Flows via Phase-Field-Based Penalty Interpolation Model","authors":"Yulong Ji,&nbsp;Xin Zhang,&nbsp;Jingjie He,&nbsp;Fei Long,&nbsp;Peng Zhang","doi":"10.1002/nme.70435","DOIUrl":"https://doi.org/10.1002/nme.70435","url":null,"abstract":"<div>\u0000 \u0000 <p>Based on the characteristics of transient two-phase flows, a novel phase-field-based penalty interpolation model is proposed in this study. The governing equations are established by coupling the Cahn–Hilliard phase-field model with the Navier–Stokes–Brinkman equations. The numerical solution of the flow fields is computed using the streamline-upwind Petrov–Galerkin stabilization method combined with the penalty finite element method, while the phase field is solved using the convex splitting method. Several engineering numerical cases are carried out in two-dimensional computational rectangular domains to verify the applicability and stability of the proposed model, with flow conditions corresponding to relatively low Reynolds numbers. The topological structures of the proposed model adhere to the characteristics of transient two-phase flows. Moreover, the process of sensitivity analysis is significantly simplified. This study provides a novel approach to transient two-phase flow topology optimization and offers an optimization design framework for relevant engineering problems.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"127 20","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149176993","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}
引用次数: 0
A Nonlinear Extension of Parametric Model Embedding for Dimensionality Reduction in Parametric Shape Design 参数化形状设计降维中参数化模型嵌入的非线性扩展
IF 3.3 3区 工程技术
International Journal for Numerical Methods in Engineering Pub Date : 2026-10-12 DOI: 10.1002/nme.70437
Andrea Serani, Giorgio Palma, Matteo Diez
{"title":"A Nonlinear Extension of Parametric Model Embedding for Dimensionality Reduction in Parametric Shape Design","authors":"Andrea Serani,&nbsp;Giorgio Palma,&nbsp;Matteo Diez","doi":"10.1002/nme.70437","DOIUrl":"https://doi.org/10.1002/nme.70437","url":null,"abstract":"<p>Dimensionality reduction is essential in simulation-based shape design, where high-dimensional parameterizations hinder optimization, surrogate modeling, and systematic design-space exploration. Parametric Model Embedding (PME) addresses this issue by constructing reduced variables from geometric information while preserving an explicit backmapping to the original design parameters. However, PME is intrinsically linear and may become inefficient when the sampled design space is governed by nonlinear geometric variability. This paper introduces a nonlinear extension of PME, denoted NLPME. The proposed framework preserves the defining principle of PME—geometry-driven latent variables and parameter-mediated reconstruction—while replacing the linear reduced subspace with a nonlinear latent representation. Geometry is not reconstructed directly from the latent variables; instead, the latent representation is decoded into admissible design parameters, and the corresponding geometry is recovered through a forward parametric map. The method is assessed on a bio-inspired autonomous underwater glider with a 32-dimensional parametric shape description and a CAD-based geometry-generation process. NLPME reaches a 5% reconstruction-error threshold with <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>N</mi>\u0000 <mo>=</mo>\u0000 <mn>5</mn>\u0000 </mrow>\u0000 <annotation>$$ N=5 $$</annotation>\u0000 </semantics></math> latent variables, compared with <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>N</mi>\u0000 <mo>=</mo>\u0000 <mn>8</mn>\u0000 </mrow>\u0000 <annotation>$$ N=8 $$</annotation>\u0000 </semantics></math> for linear PME, and a 1% threshold with <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>N</mi>\u0000 <mo>=</mo>\u0000 <mn>9</mn>\u0000 </mrow>\u0000 <annotation>$$ N=9 $$</annotation>\u0000 </semantics></math>, compared with <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>N</mi>\u0000 <mo>=</mo>\u0000 <mn>15</mn>\u0000 </mrow>\u0000 <annotation>$$ N=15 $$</annotation>\u0000 </semantics></math> for PME. Comparison with a deep autoencoder shows that most of the nonlinear compression gain can be retained while preserving an explicit backmapping to the original design variables. The results establish NLPME as a compact, admissible, and engineering-compatible nonlinear reduced representation for parametric shape design spaces.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"127 20","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.70437","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149177372","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}
引用次数: 0
A Three-Dimensional Orthotropic Peridynamic Framework for Laser Powder Bed Fusion Simulation 激光粉末床熔合模拟的三维正交各向异性动力学框架
IF 3.3 3区 工程技术
International Journal for Numerical Methods in Engineering Pub Date : 2026-10-05 DOI: 10.1002/nme.70438
Qi-Qing Liu, Francesco Scabbia, Ugo Galvanetto, Mirco Zaccariotto
{"title":"A Three-Dimensional Orthotropic Peridynamic Framework for Laser Powder Bed Fusion Simulation","authors":"Qi-Qing Liu,&nbsp;Francesco Scabbia,&nbsp;Ugo Galvanetto,&nbsp;Mirco Zaccariotto","doi":"10.1002/nme.70438","DOIUrl":"https://doi.org/10.1002/nme.70438","url":null,"abstract":"<div>\u0000 \u0000 <p>This paper presents a novel three-dimensional (3D) Peridynamic (PD) framework for simulating the Laser Powder Bed Fusion (L-PBF) process. An orthotropic heat-conduction PD model is proposed to efficiently account for Marangoni-enhanced heat transport, and it is coupled with a phase-change formulation to capture solid–liquid interface evolution. A Gaussian-exponential volumetric heat source is further incorporated to represent laser energy deposition, yielding a unified 3D PD computational framework for L-PBF simulation. The orthotropic heat conduction and phase-change models are validated against a series of 3D test cases, followed by single-track L-PBF simulations of 316 L stainless steel to demonstrate the overall capability of the PD-based L-PBF framework. Comparisons with finite-element solutions show excellent agreement in thermal fields for single- and two-material systems, while solidification case for orthotropic materials demonstrates accurate interface tracking. Experimental validation further confirms that the PD-based framework accurately reproduces the melt pool geometry of 316 L stainless steel, even without requiring explicit fluid-dynamics coupling. This capability thereby provides a solid basis for future fully coupled thermomechanical PD modeling in additive manufacturing.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"127 19","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149099664","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}
引用次数: 0
A Unified Block-Modal Framework for Inverse Source Problems in Heat and Mass Transfer 热质传递反源问题的统一块模态框架
IF 3.3 3区 工程技术
International Journal for Numerical Methods in Engineering Pub Date : 2026-10-05 DOI: 10.1002/nme.70440
André J. P. de Oliveira, Diego C. Knupp, Lucas L. S. Costa, Luiz A. S. Abreu, Mousa J. Huntul, Antônio J. Silva Neto
{"title":"A Unified Block-Modal Framework for Inverse Source Problems in Heat and Mass Transfer","authors":"André J. P. de Oliveira,&nbsp;Diego C. Knupp,&nbsp;Lucas L. S. Costa,&nbsp;Luiz A. S. Abreu,&nbsp;Mousa J. Huntul,&nbsp;Antônio J. Silva Neto","doi":"10.1002/nme.70440","DOIUrl":"https://doi.org/10.1002/nme.70440","url":null,"abstract":"<p>This work presents a unified block–modal framework for inverse source identification in linear diffusive problems arising in heat and mass transfer. Starting from a general parabolic model with mixed boundary operators, the Classical Integral Transform Technique is employed to project the dynamics onto an orthonormal eigenbasis, yielding a family of decoupled convolution-type ordinary differential equations in time. The transformed source in each mode is represented by a parametric temporal expansion, so that the inverse problem becomes a block-diagonal linear least-squares estimation problem. The Tikhonov regularization is incorporated either with a single global parameter or with mode-wise parameters, with automatic parameter selection by generalized cross-validation, the L-curve, quasi-optimality, and the Bazán fixed-point criterion, while the truncation order of the inverse series is determined by an efficient implementation of the discrepancy principle based on cumulative reconstructions in the transformed space. The methodology is assessed on one- and two-dimensional heat conduction benchmarks with smooth and discontinuous space–time sources under different boundary conditions, using noisy synthetic temperature data. The results show that the relative performance of the mode-wise and global regularization strategies depends on both the dimensionality of the problem and the adopted parameter-choice rule: mode-wise GCV provides the best overall performance in the one-dimensional benchmarks, whereas global regularization becomes advantageous in the two-dimensional problem. Spatial and temporal data-enrichment analyses further show that higher-order spectral information can be recovered as the amount of measurement information increases. Direct comparisons with another CITT-based least-squares formulation and with an adjoint conjugate-gradient method show that the proposed block-modal organization preserves comparable reconstruction accuracy while substantially reducing the computational cost. The spectral analysis clarifies the interplay between modal energy content, regularization strategy, and optimal truncation, and supports the computational efficiency and scalability of the proposed framework for inverse source problems in heat and mass transfer.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"127 19","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.70440","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149099665","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}
引用次数: 0
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