International Journal for Numerical Methods in Engineering最新文献

{"title":"Energy-Dissipative Implicit-Explicit Runge-Kutta Schemes With an Optimized Stabilization Parameter for Directed Self-Assembly of Diblock Copolymer Melts","authors":"Yan Wang,&nbsp;Huiya Wang,&nbsp;Hong Zhang,&nbsp;Xu Qian","doi":"10.1002/nme.70151","DOIUrl":"https://doi.org/10.1002/nme.70151","url":null,"abstract":"<div>\u0000 \u0000 <p>We investigate high-order, energy-dissipative schemes for simulating the directed self-assembly (DSA) of diblock copolymer melts, which plays a crucial role in materials science, nanotechnology, and soft matter. The DSA process is primarily modulated through strategies such as external physical fields, substrate interfacial engineering, and geometric confinement, all of which are fundamentally described by Ohta–Kawasaki energy functionals. To preserve the intrinsic energy dissipation property of the corresponding gradient flow equations, we develop implicit-explicit Runge-Kutta (IMEXRK) schemes of up to third order and approximately fourth order, ensuring energy stability for any time step size. Under the uniform boundedness assumption of solutions, a novel criterion to justify the energy stability is established by rewriting the IMEXRK schemes in a unified matrix-vector framework. To address the time delay effect in stabilization schemes, an optimized, time-step-dependent selection of stabilization parameters is proposed, which shows significant accuracy improvement compared to a constant stabilization parameter. Numerical experiments validate the superior accuracy and stability, while simulations of directed self-assembly of diblock copolymer melts under different situations demonstrate the universality and broad applicability of the proposed schemes.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 19","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145272108","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 Family of Higher-Order Theories for Wave Propagation in One-Dimensional Structural Elements","authors":"Wiktor Waszkowiak,&nbsp;Łukasz Doliński,&nbsp;Paweł Kowalski,&nbsp;Arkadiusz Żak","doi":"10.1002/nme.70136","DOIUrl":"https://doi.org/10.1002/nme.70136","url":null,"abstract":"<p>This paper proposes a systematic framework for the development and classification of higher-order theories for modeling wave propagation in one-dimensional structural elements. Building upon and organizing the existing higher-order models, a generalized approach is introduced to construct an entire family of such theories with controllable complexity and accuracy. The methodology enables the inclusion of higher-order terms in a physically meaningful and mathematically consistent manner, going beyond the classical polynomial extension of displacement fields. The proposed theories leverage traction-free boundary conditions, leading to accurate wave representation. Preliminary considerations on their implementation in the finite element method are also discussed, laying the foundation for future work focused on advanced finite element formulations.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 19","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.70136","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145272136","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 Comprehensive Study and Insight in Co-Rotational Approach Based Geometrically Nonlinear Analysis With Planar Solid Elements","authors":"Ziyun Kan,&nbsp;Jie Deng,&nbsp;Yanting Li,&nbsp;Xueguan Song","doi":"10.1002/nme.70106","DOIUrl":"https://doi.org/10.1002/nme.70106","url":null,"abstract":"<div>\u0000 \u0000 <p>The co-rotational (CR) approach is a widely adopted and efficient strategy for geometrically nonlinear analysis. The <i>Classic Formalism</i>, which derives full variations from local element to global coordinates, has been refined over the years and is generally regarded as theoretically sound. This study presents an insight into CR planar solid elements. To isolate these issues from element-specific effects, we focus on the simplest planar solid elements: four-node quadrilaterals and three-node triangles. A comprehensive investigation is conducted to provide a unified overview and systematic comparison of commonly used local element frame construction methods. The findings indicate that the <i>Classic Formalism</i> may exacerbate unrealistic asymmetric responses in symmetric problems, particularly when the local element frame lacks precision. To address this, we propose a direct force correction formalism that introduces a correction term to directly enforce spin equilibrium. On the one hand, the derivation process eliminates the need for a second variation in computing the tangent stiffness matrix; on the other hand, the corrected equal weights act on each node of elements and are directly related to the rotation matrix, rather than a variant of the rotation matrix. As a result, this formalism may reduce the asymmetry in symmetrical cases better than <i>Classic Formalism</i>. Importantly, the proposed formalism is broadly applicable across various element types and frame construction methods.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 19","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145272135","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 Novel Improved Collocation Approach to Solve Good Boussinesq Equation Describing Propagation of Shallow Water Waves","authors":"Emre Kırlı","doi":"10.1002/nme.70152","DOIUrl":"https://doi.org/10.1002/nme.70152","url":null,"abstract":"<div>\u0000 \u0000 <p>The present work is about obtaining a high-order accurate numerical approach to approximate the solution of the good Boussinesq equation (GBeq). In present approach, the quintic B-spline collocation procedure equipped with new approximations for the second-order and the fourth-order spatial derivatives is employed to discretize the spatial variables and Crank–Nicolson scheme is used to obtain temporal integration of the GBeq. The proposed approach achieves sixth-order accuracy and second-order accuracy in spatial and temporal directions, respectively. By von-Neumann stability analysis, the unconditionally stability of the suggested approach is proved. The efficiency and applicability of the computational approach is verified by examining the sample problems including motion of single solitary, interaction of two solitons and birth of solitons. The <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mrow>\u0000 <mi>L</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>∞</mi>\u0000 </mrow>\u0000 </msub>\u0000 </mrow>\u0000 <annotation>$$ {L}_{infty } $$</annotation>\u0000 </semantics></math> error norm is computed and compared with the existing studies in the literature. The comparisons demonstrate that the suggested approach is superior to some existing techniques in terms of accuracy. Also, the rate of convergence and invariant constant are numerically computed and seen to match with their theoretical values.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 19","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145272137","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 Deep Learning Constitutive Model for Anisotropic and Pressure-Dependent Behavior of Short Fiber-Reinforced Polymers","authors":"Aamir Dean,&nbsp;Vinayak B. Naik,&nbsp;Betim Bahtiri,&nbsp;Elsadig Mahdi,&nbsp;Pavan K. A. V. Kumar","doi":"10.1002/nme.70144","DOIUrl":"https://doi.org/10.1002/nme.70144","url":null,"abstract":"<p>Short fiber-reinforced polymers (SFRPs) exhibit complex anisotropic, nonlinear, and pressure-dependent behavior due to their heterogeneous microstructures. Conventional constitutive models, while accurate, require extensive parameter calibration and may lack generalization capability under varied loading conditions. In this study, a physics-informed deep learning (PIDL) constitutive framework is proposed that integrates the governing physical laws with the flexibility of neural networks. The model employs long short-term memory (LSTM) networks to capture path-dependent behaviors and utilizes scalar invariants consistent with transverse isotropy to ensure thermodynamic consistency, objectivity, and material symmetry. The neural network is trained using synthetic data generated from a validated continuum-mechanical model for SFRPs, including elasto-plastic behavior and anisotropy. To validate the PIDL model, an open-hole tensile (OHT) test is simulated, and the predicted stresses are compared against those obtained from the classical constitutive model. While the initial PIDL model showed limitations under complex multiaxial stress states, a retraining strategy using randomly generated loading paths significantly improved its predictive accuracy. This study demonstrates the potential of physics-informed machine learning for developing generalizable and efficient data-driven constitutive models for complex composite materials.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 19","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.70144","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145272056","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":"Smoothed Particle Hydrodynamics Enhanced With Unstructured Finite-Volume Method for Low-Speed Flows With Moving Boundaries","authors":"Tianrun Gao,&nbsp;Mingduo Yuan,&nbsp;Lin Fu","doi":"10.1002/nme.70150","DOIUrl":"https://doi.org/10.1002/nme.70150","url":null,"abstract":"<div>\u0000 \u0000 <p>In this study, the conventional smoothed particle hydrodynamics is enhanced by coupling it with an unstructured finite-volume scheme for solving flows near the moving boundary, particularly in wall-bounded turbulence, capable of both robustly capturing free surface flows and accurately resolving flows near the wall. A mesh domain is deployed encompassing the moving object, and the corresponding flow field is resolved using an unstructured arbitrary Lagrangian-Eulerian finite-volume scheme. Beyond the mesh domain, the flows are resolved using the particle-based smoothed particle hydrodynamics scheme. Under the turbulence circumstance, the large-eddy simulation model is incorporated into the governing equations, and the wall-modeled large-eddy simulation based on the reduced-order wall model is adopted when the flows near the wall boundary are under-resolved. Regarding the coupling between finite-volume and smoothed particle hydrodynamics domains, the smoothed particle hydrodynamics particles are divided into activated and non-activated particles, and the field values of non-activated particles are interpolated from the finite-volume domain; for the finite-volume domain, the interface points, serving as flux inputs into the finite-volume domain, are deployed on the finite-volume domain boundary, where the field values of the interface points are interpolated from the activated smoothed particle hydrodynamics particles. A set of two-dimensional and three-dimensional cases with low and high Reynolds numbers is simulated using the present method, which presents good accuracy and efficiency and is particularly suitable for simulating turbulent flows. Overall, the proposed method can serve as a remarkable enhancement to the conventional smoothed particle hydrodynamics scheme to reliably predict low-speed wall-bounded flows with moving boundaries.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 19","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145272059","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 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}