International Journal for Numerical Methods in Engineering最新文献

{"title":"A Total-Lagrangian Material Point Method for Fast and Stable Hydromechanical Modeling of Porous Media","authors":"Weijian Liang,&nbsp;Bodhinanda Chandra,&nbsp;Jidu Yu,&nbsp;Zhen-Yu Yin,&nbsp;Jidong Zhao","doi":"10.1002/nme.70135","DOIUrl":"https://doi.org/10.1002/nme.70135","url":null,"abstract":"<div>\u0000 \u0000 <p>Modeling the incompressible fluid flow in porous media has long been a challenging task in the Material Point Method (MPM). Although widely used, conventional Updated Lagrangian MPM (ULMPM) often suffers from numerical stability and computational efficiency issues in the hydromechanical analysis of saturated porous media. To address these issues, we herein present a novel semi-implicit Total Lagrangian MPM (TLMPM). The proposed TLMPM leverages the fractional step method to decouple pore pressure from kinematic fields and employs the semi-implicit scheme to bypass the small time step constraint imposed by permeability and fluid compressibility. Unlike its UL counterpart, the TLMPM evaluates weighting functions and their gradients only once in the reference configuration, eliminating material point tracking and inherently resolving cell-crossing instabilities. Given the consistent set of active degrees of freedom throughout simulations, the proposed method greatly reduces computational costs associated with system matrix assembly for both kinematics and pore pressure and with free-surface node detection. Furthermore, this feature also facilitates the efficient Cholesky factorization, resulting in a substantial acceleration of the solver performance. The proposed approach has been validated against various benchmark tests, and our results have highlighted the remarkable performance of TLMPM, which can achieve up to 63 times speedup over conventional methods, scaling favorably with problem size, and retaining numerical stability even with low-order basis functions. These advancements position the TLMPM as a transformative tool for poroelastic analysis, with broader applicability to large-deformation problems in geomechanics, energy systems, and environmental engineering.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 19","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145224228","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 Biomimetic Moving-Mesh Topology Optimization Method","authors":"Huawei Feng,&nbsp;Huikai Zhang,&nbsp;Zhongqi Li,&nbsp;Junjie Zhou,&nbsp;Peidong Lei,&nbsp;Bin Liu","doi":"10.1002/nme.70145","DOIUrl":"https://doi.org/10.1002/nme.70145","url":null,"abstract":"<div>\u0000 \u0000 <p>Topology optimization has experienced rapid development over the past two decades and has been widely applied in fields such as aircraft structures, civil engineering, and transportation equipment. Common topology optimization methods, such as density-based methods and level set methods, focus on global variable optimization. These global optimization approaches often consume substantial computational resources and are not suitable for parallel optimization. In contrast, structures in nature evolve from a combination of numerous local optimization problems, where each cell unit adjusts on the basis of its perception of the surrounding environment, leading to the formation of biological structures. This paper proposes a novel heuristic topology optimization method, the biomimetic moving-mesh (BMM) method, inspired by biological cell growth and evolution. The BMM method uses the positions of mesh nodes as variables to simulate cellular expansion and contraction, thereby creating a new optimization approach. Compared with traditional topology optimization methods, the BMM method offers smoother meshes and is more suitable for handling large-scale parallel optimization problems.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 19","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145223802","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 F-Bar B-Spline Material Point Method for Capturing Size-Dependent Strain Localization With Finite Strain Gradient Plasticity","authors":"Ran Ma,&nbsp;Haoyu Ni,&nbsp;Panpan Cheng,&nbsp;Guodong Zhang,&nbsp;Tong Guo","doi":"10.1002/nme.70137","DOIUrl":"https://doi.org/10.1002/nme.70137","url":null,"abstract":"<p>The classical material point method (MPM) is particularly suitable for large deformation problems with surface contact, but its capability to capture size effects remains relatively limited. In order to capture the size effect widely observed in solid materials as well as to eliminate mesh dependency, we present an F-bar B-spline MPM for solving finite strain-gradient plasticity in the micromorphic approach. A multiplicative finite strain thermoplasticity model is first regularized in a micromorphic approach, where a global internal variable is introduced to take into account the size effect. An implicit B-spline MPM is developed to solve the coupled problem in a monolithic manner with consistent linearization. This implementation provides a general framework to incorporate phenomenological elasto-plasticity models while preserving the prescribed size effect in the MPM. Although B-spline basis function is effective in suppressing the volumetric-locking deformation pattern when volume-preserving plasticity model is used, severe stress oscillation may manifest when the deformation mode approaches the incompressible limit. Therefore, we propose an F-bar method for the implicit B-spline MPM to suppress the spurious stress oscillation. The exact linearization of the F-bar method and its coupling with the balance equation of micromorphic momentum are derived in closed form. Three representative numerical examples are presented to validate our implementation and demonstrate the advantages of our method. Results show that the proposed method is effective in capturing the size effect at extreme conditions with large distortion and contact, and the F-bar method suppresses the spurious stress oscillations associated with volume-preserving plastic flow. One limitation is that the convergence behavior is less satisfactory when strain-softening model is used due to the inherent limitation of the implicit MPM.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 19","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.70137","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145223801","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":"The Complex Variable Dimension Coupling Method for 3D Inhomogeneous Transient Heat Conduction Problems","authors":"Wenna He,&nbsp;Heng Cheng","doi":"10.1002/nme.70149","DOIUrl":"https://doi.org/10.1002/nme.70149","url":null,"abstract":"<div>\u0000 \u0000 <p>Based on the dimensional splitting method (DSM) and an improved complex variable element-free Galerkin (ICVEFG) method, the complex variable dimension coupling method (CVDCM) is proposed to analyze 3D inhomogeneous transient heat conduction problems. The original 3D governing equation is split into a collection of 2D forms by the dimensional splitting method (DSM), and the discrete equation of the 2D problem is derived via the ICVEFG method. The splitting direction is then treated by using the finite element method (FEM), while the time-dependent term in the governing equation is handled by the finite difference method (FDM). Finally, the numerical solution formula is obtained. To verify the accuracy of the CVDCM, the ratio of the <i>L</i>₂ norm to the true value is used as the relative error. The convergence of the proposed method is demonstrated by increasing the number of nodes and meshes. Five numerical examples of transient inhomogeneous heat conduction problems with spatially varying material properties (density, specific heat capacity, and thermal conductivity) are solved using the CVDCM; the results show that the proposed method achieves good convergence and achieves higher accuracy compared to the dimension coupling method (DCM) and the improved element-free Galerkin (IEFG) method in five examples.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 19","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145196277","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":"Lippmann–Schwinger Spectrum, Composite Materials Eigenstates and Their Role in Computational Homogenization","authors":"C. Bellis,&nbsp;H. Moulinec","doi":"10.1002/nme.70130","DOIUrl":"https://doi.org/10.1002/nme.70130","url":null,"abstract":"<div>\u0000 \u0000 <p>Focusing on the homogenization of periodic composite materials, this study investigates computational methods based on volume integral equations. Such formulations are revisited from the standpoint of the preconditioning of the original cell problem by the introduction of a comparison material. This allows for to recovery of simple convergence criteria for iterative steepest-descent and fixed-point schemes for composites with general non-linear behaviour. In the case of linear materials, the preconditioned volume integral formulation coincides with the well-known Lippmann–Schwinger equation. The spectral properties of the featured linear integral operator, which is bounded and self-adjoint, are investigated to shed light on the behaviour of conventional computational homogenization methods. The so-called Lippmann–Schwinger spectrum is analyzed, with its bounds governing the convergence rate of iterative solution methods. The associated eigenvectors, which constitute the eigenstates of the composite material considered, are also described in detail to understand their role in constructing the solution to the cell problem and ultimately in computing the effective properties. Formulated in the continuous setting, this analysis is followed by the investigation of a discrete representation of the integral operator considered. A number of examples on synthetic microstructures are finally considered in the conductivity setting to illustrate the obtained theoretical results and highlight the role of the spectral properties in the operation of computational homogenization methods. This paves the way for the development of reduced models and more efficient computations.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 19","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145196452","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 Study on Time-Dependent Two Parameter Singularly Perturbed Problems via Trigonometric Quintic B-Splines on an Exponentially Graded Mesh","authors":"Sangeetha C,&nbsp;Aswin V S,&nbsp;Ashish Awasthi","doi":"10.1002/nme.70146","DOIUrl":"https://doi.org/10.1002/nme.70146","url":null,"abstract":"<div>\u0000 \u0000 <p>This paper presents a fresh perspective on solving two-parameter singularly perturbed parabolic convection-diffusion-reaction equations with Dirichlet boundary conditions. The methodology integrates the Crank–Nicolson (CN) scheme for discretizing temporal derivatives and applies the Trigonometric Quintic B-splines (TQBS) approach to approximate both the state variable and its spatial derivatives on an exponentially graded mesh. Through a meticulous convergence analysis, the study establishes a parameter-uniform convergence of fourth order in space and second order in time. To verify the theoretical claims and evaluate the method's efficacy, four test examples are solved using the numerical algorithm, offering tangible evidence of the parameter-uniform convergence of the proposed numerical scheme. Additionally, the paper includes a graphical comparison of the proposed method with Shishkin meshes, providing empirical evidence of its efficacy and parameter-uniform convergence.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 19","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145196279","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":"Modeling the Fluid-Structure Interactions of a Hairy Yarn in Air-Jet Weaving: A Multiscale Approach","authors":"Axel Bral,&nbsp;Lode Daelemans,&nbsp;Joris Degroote","doi":"10.1002/nme.70142","DOIUrl":"https://doi.org/10.1002/nme.70142","url":null,"abstract":"<div>\u0000 \u0000 <p>The interaction between air jets and hairy yarns is an important aspect in textile machinery. Currently, there is a need for high-fidelity two-way coupled Fluid-Structure Interaction (FSI) simulations of a hairy yarn subjected to high-speed air flows in textile processing, as these models are vital to understand yarn dynamics in, for example, air-jet weaving looms. Therefore, this work develops a fully three-dimensional two-way coupled FSI framework for modeling the yarn dynamics in air-jet weaving. The framework combines an adapted version of the Actuator Line Method (ALM) for the flow with beam elements for the structural representation of the yarn. This enables computationally efficient simulations at the machine scale without the need for resolving fiber-level details. Instead, these properties—derived in earlier work using microscale simulations—are homogenized into aerodynamic force coefficients and structural material parameters, resulting in a multiscale modeling approach. The framework is first validated on the launch of a nylon monofilament yarn, demonstrating its ability to predict yarn velocity and transversal oscillations while reducing the computational cost compared to existing overset mesh methods. In a second step, the method is applied to a hairy staple-fiber yarn, marking the first high-fidelity FSI simulation of such a system. The results confirm the potential of this approach for characterizing hairy yarn behavior in air-jet weaving without tuning of coefficients.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 18","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145146515","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 Stabilized Bipenalty Formulation Using a Predictor-Corrector Scheme for Explicit Contact-Impact Analysis","authors":"Yun-Jae Kwon,&nbsp;Jin-Gyun Kim,&nbsp;Sang Soon Cho,&nbsp;José A. González","doi":"10.1002/nme.70119","DOIUrl":"https://doi.org/10.1002/nme.70119","url":null,"abstract":"<div>\u0000 \u0000 <p>This work presents a novel stabilized bipenalty formulation for explicit contact-impact analysis, aiming to enhance traditional bipenalty methods and resolve issues associated with a large mass penalty parameter. To address this challenge, two key contributions are introduced. First, a new formulation integrates the bipenalty method with a predictor-corrector scheme, enabling a more accurate penetration estimation by dividing the computational process into prediction and correction phases. This separation ensures that the mass penalty affects only the contact forces, thereby eliminating undesirable mass effects on internal forces when a large mass penalty parameter is used. Second, new criteria tailored to the predictor-corrector scheme are proposed for two types of contact problems: the flexible-rigid case and the flexible-flexible case. Unlike traditional bipenalty methods, which rely on stability conditions for explicit time integrators, the proposed criteria focus on enforcing the kinematic constraints. As a result, any predicted penetration is eliminated during the correction phase, leading to zero penalty energy. Stability analysis confirms that the computation of the gap within the correction phase maintains stability. Contact impact examples are performed in 1D, 2D, and 3D and demonstrate that the proposed method provides improved stability and superior performance compared to the penalty and traditional bipenalty methods for various contact scenarios, including extremely large penalty parameter cases.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 18","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145146287","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":"On the Robustness of Dirichlet–Neumann Coupling Schemes for Fluid-Structure-Interaction Problems With Nearly-Closed Fluid Domains","authors":"A. Aissa-Berraies,&nbsp;F. A. Auricchio,&nbsp;G. J. van Zwieten,&nbsp;E. H. van Brummelen","doi":"10.1002/nme.70139","DOIUrl":"https://doi.org/10.1002/nme.70139","url":null,"abstract":"<p>The partitioned approach for fluid-structure interaction (FSI) simulations involves solving the structural and flow field problems sequentially. This approach allows separate settings for the fluid and solid subsystems, ensuring modularity and leveraging advanced commercial and open-source software capabilities to offer increased flexibility for diverse FSI applications. Most partitioned FSI schemes apply the Dirichlet–Neumann partitioning of the interface conditions. The Dirichlet–Neumann coupling scheme has proven adequate in a wide range of applications. However, this coupling scheme is sensitive to the added-mass effect and is susceptible to the incompressibility dilemma, that is, it completely fails for FSI problems in which the fluid is incompressible and furnished with Dirichlet boundary conditions on the part of its boundary complementary to the interface. In the present paper, we demonstrate that if the fluid is incompressible and the fluid domain is nearly- closed, in the sense that the fluid domain is furnished with Dirichlet conditions except for a permeable part of the boundary where a Robin-type condition holds, then the Dirichlet–Neumann partitioned approach is sensitive to the flow resistance at the permeable part and, in particular, convergence of the partitioned approach deteriorates as the flow resistance increases. The Dirichlet–Neumann partitioned approach then becomes arbitrarily unstable in the limit of vanishing permeability, that is, if the flow resistance passes to infinity. Based on a simple model problem, we establish that in the nearly closed case, the convergence rate of the Dirichlet–Neumann partitioned method depends on a so-called <i>added-damping effect</i>. The presented analysis provides insights that can be leveraged to improve the robustness and efficiency of partitioned approaches for FSI problems involving contact, such as valve opening/closing applications. In addition, the results elucidate the incompressibility dilemma as a formal limit of the added-damping effect passing to infinity, and the corresponding challenges related to FSI problems with nearly closed fluid-domain configurations. Based on numerical experiments, we consider the generalization of the results of the simple model problem to more complex, nearly closed FSI problems.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 18","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.70139","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145110943","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 Posteriori Error Estimates and h-Adaptive Algorithms for Accuracy Control of a Second-Order Generalized/eXtended FEM for 3-D Linear Elastic Fracture Mechanics Problems","authors":"Murilo H. C. Bento,&nbsp;Sergio P. B. Proença,&nbsp;C. Armando Duarte","doi":"10.1002/nme.70141","DOIUrl":"https://doi.org/10.1002/nme.70141","url":null,"abstract":"<p>The Generalized/eXtended Finite Element Method (G/XFEM) augments standard FEM approximation spaces with functions tailored to represent well specific behaviors of a problem, such as those introduced by cracks in linear elastic fracture mechanics (LEFM). The method allows mesh generation to be made independently of crack surfaces and achieves optimal first- and second-order convergence rates, while keeping the condition number of its global matrices under control. Regarding second-order G/XFEM formulations, it has been shown that when only singular enrichment functions able to represent the <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msqrt>\u0000 <mrow>\u0000 <mi>r</mi>\u0000 </mrow>\u0000 </msqrt>\u0000 </mrow>\u0000 <annotation>$$ sqrt{r} $$</annotation>\u0000 </semantics></math> singularity are adopted, the convergence rate is still bounded by the second-highest crack singularity. In this case, mesh refinement around crack fronts is a strategy to recover optimal convergence. In this work, this is addressed by h-adaptive mesh refinement algorithms. To this end, first, a Zienkiewicz and Zhu block-diagonal (ZZ-BD) error estimator is proposed for three-dimensional (3-D) LEFM problems. For that, the most challenging part is the definition of good recovery enrichment functions that are able to represent the crack singularity. These functions are proposed in this work based on the derivatives of enrichment functions commonly adopted in the G/XFEM context. It is shown that the use of these new singular recovery enrichment functions in the recovery process of the ZZ-BD error estimator leads to estimated discretization errors that are very close to the exact discretization errors. Also, the performance of the error estimator becomes much better than if one adopts recovery enrichment functions commonly used in 2-D. Finally, with a good error estimator able to also quantify the distribution of discretization errors over the domain and along crack fronts, adaptive algorithms are developed. Herein, h-adaptive techniques are proposed to recover optimal second-order convergence for G/XFEM and enhance its usability in such a way that final discretizations meeting a user's pre-specified tolerance on the discretization error are delivered on the fly by the adaptive procedure. 3-D LEFM numerical experiments with increasing levels of complexity are used to assess the ZZ-BD effectivity as well as to show that the proposed h-adaptive algorithms can, at a reasonable computational cost, deliver accurate discretizations at optimal convergence rates.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 18","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.70141","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145111079","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}