International Journal for Numerical Methods in Engineering最新文献

{"title":"Lattice-Spring Analogy for Isotropic Elasticity","authors":"D. M. Li,&nbsp;Meng-Cheng He","doi":"10.1002/nme.70382","DOIUrl":"https://doi.org/10.1002/nme.70382","url":null,"abstract":"<div>\u0000 \u0000 <p>This study introduces an innovative Isotropic Elastic Lattice Spring Model (IELSM) that addresses the fixed Poisson's ratio constraint of classical Lattice Spring Model (LSM). By amending the total strain energy within the LSM framework, IELSM provides a theoretically self-consistent formulation for simulating isotropic elastic materials with arbitrary Poisson's ratios. The model's core innovation lies in augmenting classical axial spring frameworks with explicit additional volumetric constraints, establishing a direct and exact mapping between IELSM's parameters and macroscopic elastic constants. This enables simulation across the entire physically admissible Poisson's ratio spectrum: −1 &lt; <i>ν</i> &lt; 1 under plane stress conditions and −1 &lt; <i>ν</i> &lt; 0.5 under plane strain conditions. Eigenvalue analysis indicates that the IELSM has better numerical stability compared to the standard bilinear quadrilateral element and the constant strain triangular element. The characteristic of the numerical implementation lies in directly decomposing the additional volumetric constraints into an equivalent combination of standard mechanical components (axial, shear, and rotational springs), laying the foundation for the realization of fracture simulation based on discrete methods. Comprehensive validation through uniaxial tension, pure shear, beam bending, stress concentration around a circular hole, and stress singularity analyses for central and crucifix-shaped cracks demonstrates IELSM's accuracy, mesh convergence, and computational efficiency. The model exhibits excellent performance in stress intensity factor calculations at crack tips, validating its effectiveness for singular stress field analysis. This work bridges the gap between LSM and continuum mechanics, establishing an analog framework that maintains theoretical consistency while offering computational accuracy for the solution of elastic boundary value problems.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"127 13","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148462932","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 Hybrid-High Order Method for Fracture Modelling","authors":"Alessandra Crippa,&nbsp;Julien Coatléven,&nbsp;Daniele A. Di Pietro,&nbsp;Nicolas Guy,&nbsp;Soleiman Yousef","doi":"10.1002/nme.70374","DOIUrl":"https://doi.org/10.1002/nme.70374","url":null,"abstract":"<p>In this work we introduce a new Hybrid High-Order method for the numerical simulation of fracture propagation based on phase-field models. The proposed method: supports general meshes made of polygonal/polyhedral elements, which provides great flexibility in mesh design and adaptation; can accommodate large variations of both the displacement and damage variables thanks to the use of fully discontinuous spaces; delivers continuous (degradation-weighted) tractions at interfaces. The resolution of the corresponding algebraic problem is based on a staggered time stepping scheme which takes advantage of static condensation for each subproblem. We provide extensive numerical validation of the method on classical two-dimensional fracture propagation problems, including a comparison with a more standard finite element scheme.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"127 13","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.70374","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148386466","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":"Style-Constrained Inverse Design of Microstructures With Tailored Mechanical Properties Using Unconditional Diffusion Models","authors":"Weipeng Xu,&nbsp;Ziyuan Xie,&nbsp;Haoju Lin,&nbsp;Xinyu Wang,&nbsp;Guangjin Mou,&nbsp;Tianju Xue","doi":"10.1002/nme.70376","DOIUrl":"https://doi.org/10.1002/nme.70376","url":null,"abstract":"<p>Deep generative models, particularly denoising diffusion models, have achieved remarkable success in high-fidelity generation of architected microstructures with desired properties and styles. However, these recent methods typically rely on conditional training mechanisms that require extensive labeled data. Thus, the adaptation of these approaches to new problem settings may necessitate data regeneration and model retraining, presenting practical challenges for diverse design scenarios. In this study, we propose a new inverse design framework that integrates unconditional denoising diffusion models with differentiable programming techniques for architected microstructure design. Our approach eliminates the need for expensive labeled dataset preparation and retraining for different problem settings. By reinterpreting the noise input to the diffusion model as an optimizable design variable, we formulate the design task as an optimization problem over the noise input, enabling control over the reverse denoising trajectory to guide the generated microstructure toward the desired mechanical properties while preserving the stylistic constraints encoded in the training dataset. A unified differentiation pipeline via vector-Jacobian product concatenations is developed to enable end-to-end gradient evaluation through backpropagation. Several numerical examples are presented to showcase the effectiveness of the framework, including microstructure designs with specified homogenized properties, targeted hyperelastic responses in both two and three dimensions, and tailored elasto-plastic responses, highlighting its potential for advanced design tasks involving diverse performance and style requirements.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"127 13","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.70376","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148358095","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 3D Acoustic Diodes in Waveguides","authors":"Kazunori Fukada,&nbsp;Nari Nakayama,&nbsp;Naoyuki Ishida,&nbsp;Kozo Furuta,&nbsp;Kazuhiro Izui,&nbsp;Shinji Nishiwaki","doi":"10.1002/nme.70375","DOIUrl":"https://doi.org/10.1002/nme.70375","url":null,"abstract":"<div>\u0000 \u0000 <p>An acoustic diode is a structure that exhibits opposing functions, allowing sound waves of a specific frequency to propagate in one direction while blocking them in the opposite direction. This paper proposes a topology optimization method for the design of high-performance acoustic diodes. In such an acoustic diode design scheme, a coupled acoustic-structural status should be analyzed. Sound propagation is governed by the Helmholtz equation in air and the elastic equation in a structure, and the interaction at the boundary between air and the structure must also be considered during the analysis. However, it is cumbersome to switch the governing equations during optimization according to the shape and topological changes of the design domain. To mitigate this problem, a topology optimization method using a two-phase material model, which represents the ratio of the air phase to the solid phase (elastic body) as a normalized density, has been proposed. However, the conventional density approach using such a two-phase material model tends to generate grayscale regions to achieve the high diode performance. Furthermore, even when the binarization from the obtained grayscales is performed using a filtering scheme, the binarized structure does not yield the desired diode performance. Therefore, this paper formulates a two-phase material model based on a new physical property interpolation, in which the power of the design variable is applied to the RAMP method, and develops an optimization algorithm based on this formulation. The proposed method is then applied to the structural design of an acoustic diode, confirming the obtained structures with clear boundaries and desired performance.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"127 13","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148358293","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 Data-Driven Multiscale Scheme for Anisotropic Finite Strain Magneto-Elasticity","authors":"Heinrich T. Roth,&nbsp;Philipp Gebhart,&nbsp;Karl A. Kalina,&nbsp;Thomas Wallmersperger,&nbsp;Markus Kästner","doi":"10.1002/nme.70367","DOIUrl":"https://doi.org/10.1002/nme.70367","url":null,"abstract":"<p>In this work, we develop a neural network-based, data-driven, decoupled multiscale scheme for the modeling of structured magnetically soft magnetorheological elastomers (MREs). On the microscale, sampled magneto-mechanical loading paths are imposed on a representative volume element containing spherical particles and an elastomer matrix, and the resulting boundary value problem is solved using a mixed finite element formulation. The computed microscale responses are homogenized to construct a database for the training and testing of a macroscopic physics-augmented neural network model. The proposed model automatically detects the material's preferred direction during training and enforces key physical principles, including objectivity, material symmetry, thermodynamic consistency, and the normalization of free energy, stress, and magnetization. Within the range of the training data, the model enables accurate predictions of magnetization, mechanical stress, and total stress. For larger magnetic fields, the model yields plausible results. Finally, we apply the model to investigate the magnetostrictive behavior of a macroscopic spherical MRE sample, which exhibits contraction along the magnetic field direction when aligned with the material's preferred direction.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"127 12","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.70367","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148324689","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":"Numerical Model of the Plastic Failure Behavior of Projectile Impacting Semi-Infinite Metal Target Plate","authors":"Sen Cao,&nbsp;Jitang Fan,&nbsp;Jiacong Pan","doi":"10.1002/nme.70372","DOIUrl":"https://doi.org/10.1002/nme.70372","url":null,"abstract":"<div>\u0000 \u0000 <p>Plastic failure of the projectile is a key phenomenon in high-velocity impact events, which leads to shear sharpening for penetration and, in another way, induces the decrease of kinetic energy for protection. Thus, studying the plastic failure of the projectile is full of interest for impact engineering. The transient impact process involves complex physical origins, and this topic has a challenge in science and technology. In this work, a new physics-based numerical model of flat-ended projectile impacting semi-infinite metal target plate at a high velocity is proposed. The plastic deformation and failure of the projectile and the resultant mass loss, the pit-opening performance of the target plate as well as the energy distribution are theoretically calculated, and thus the impact response of both the projectile and target plate is revealed. With timing, the length, upsetting deformation and failure-induced mass loss of the projectile, the pit-opening depth of the target plate and the projectile-target contact force are quantitatively given. Correspondingly, the panoramic view of plastic failure behavior is quantitatively drawn. The numerical results show that the failure-induced mass loss of the projectile increases with the increase of initial impact velocity of the projectile that significantly dissipates the kinetic energy accompanying the plastic deformation of the projectile and pit-opening of the target plate. This numerical model is based on the intrinsic physical mechanisms and offers an effective computational method for quantitatively analyzing the high-velocity impact events.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"127 12","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148324073","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 Virtual Heat Flux Method for Simple and Accurate Neumann Thermal Boundary Imposition in the Material Point Method","authors":"Jidu Yu,&nbsp;Jidong Zhao","doi":"10.1002/nme.70371","DOIUrl":"https://doi.org/10.1002/nme.70371","url":null,"abstract":"<p>In the material point method (MPM), accurate enforcement of thermal boundary conditions, particularly convective heat flux boundaries, is crucial for the reliable simulation of thermally coupled multiphysics processes, such as natural heat-convection phenomena on Earth. However, the MPM typically employs a fixed, regular background mesh, whereas material boundaries are often complex and evolve over time. As a result, the boundaries do not generally align with the mesh, making boundary tracking and the consistent application of boundary conditions challenging. This study introduces a virtual heat flux method (VHFM) that enables the simple and accurate imposition of nonconforming heat flux boundary conditions in the MPM. The core idea is to construct a virtual flux field that satisfies the prescribed boundary conditions and converts boundary integrals into volume integrals. This approach eliminates the need for explicit boundary tracking while maintaining ease of implementation and computational efficiency. A unified formulation of the virtual flux field is further developed, allowing the method to be readily extended to general Neumann boundary conditions. Through a series of numerical experiments, the proposed method is shown to achieve high accuracy and convergence across a wide range of nonconforming boundary configurations, including curved, moving, and evolving boundaries. The VHFM provides a potential way for Neumann thermal boundary imposition in thermo-mechanical and other multiphysics MPM frameworks.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"127 12","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.70371","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148324041","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":"Online Adaptive Model Reduction of the Discontinuous Galerkin Method for Unsteady Flows","authors":"Jian Yu,&nbsp;Penghao Guo,&nbsp;Rundong Wang,&nbsp;Jan S. Hesthaven","doi":"10.1002/nme.70373","DOIUrl":"https://doi.org/10.1002/nme.70373","url":null,"abstract":"<div>\u0000 \u0000 <p>An online adaptive reduced order model (ROM) of the discontinuous Galerkin (DG) method is developed for predicting unsteady scale-resolved flow simulation. The least-squares Petrov-Galerkin (LSPG) projection is chosen as the baseline ROM framework, along with typical hyperreduction techniques for acceleration. Since LSPG requires multiplication operations of the Jacobian and the basis, a Jacobian-free approach is proposed for forming the low-dimensional ROM system, to keep consistent with the Jacobian-free strategy of the original implicit DG method. Then, a comprehensive online adaptation algorithm of the LSPG model is developed by updating the basis and sampling elements with snapshots generated by the full-order DG solver in an efficient way. The key idea for the adaptation is to update the ROM with the most recent flow information to predict the unseen features. Given a set of parameters, the proposed algorithm firstly runs the full-order DG solver for a short period, secondly generates the initial basis and reduced mesh, and finally runs the adaptive ROM for future-state predictions, which enables the model to possess predictive capability. Several benchmark cases have been conducted for verification and comparison to static ROMs. The chosen cases involve typical challenges, that is, transportation and discontinuity, for static ROMs, including the isentropic vortex convection, the Sod shock tube, the Kelvin-Helmholtz instability, and the two-dimensional Riemann problem. The results demonstrate that the adaptive ROM is able to effectively address the above challenges encountered by its static counterpart from a predictive perspective while achieving reasonable acceleration.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"127 12","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148324040","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":"Upscaling the Strength Domain of Heterogeneous Cohesive-Frictional Materials via a General FFT-Based Limit Analysis Approach","authors":"Elodie Donval,&nbsp;Matti Schneider","doi":"10.1002/nme.70370","DOIUrl":"https://doi.org/10.1002/nme.70370","url":null,"abstract":"<p>Limit analysis and yield design provide a well-defined mathematical framework for upscaling the strength properties of heterogeneous materials. These techniques can be incorporated into an FFT-based computational micromechanics framework to evaluate the strength of heterogeneous materials, based on images of their microstructure. However, the currently existing approaches are limited to rather specific forms of strength criteria, and their convergence for cohesive frictional materials was questioned. In the present contribution, we abstract and reformulate an existing kinematic upper-bound approach that relies on an Augmented Lagrangian and on Uzawa's algorithm, and link it to the traditional and damped ADMM. We show that the strength constraint may be enforced by means of an orthogonal projection operator, and provide the closed-form formulation of the projector for two cases: the Drucker-Prager and the Mohr-Coulomb strength criteria. We also discuss the link between the choice of the discretization and the bounding status of the solution. Finally, building upon the ADMM reformulation of the problem, we ascertain the sublinear convergence of the FFT-based strength homogenization method for a large class of convex strength criteria, which includes cohesive-frictional materials, provided that a projector is available, either analytically or algorithmically. A first set of numerical studies, performed on a toy example, highlights the role of the solver parameters and the discretization on the effectiveness and accuracy of the approach. The obtained FFT-based strength homogenization results are compared to state-of-the-art Finite-Element Limit-Analysis for validation and to discuss the bounding status of the solution. Then, computational experiments performed on industrial scale, potentially porous microstructures, show that FFT-based strength homogenization enables the analysis of the macroscopic strength anisotropy induced by the local geometric anisotropy of the microstructure using reasonable computational resources.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"127 12","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.70370","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148269299","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 Multiscale Mixed Three-Field Finite Element Formulation Coupled With Phase Field Fracture for Incompressible Rubber-Like Materials","authors":"Prajwal Kammardi Arunachala,&nbsp;Sina Abrari Vajari,&nbsp;Wenyuan Xue,&nbsp;Christian Linder","doi":"10.1002/nme.70345","DOIUrl":"https://doi.org/10.1002/nme.70345","url":null,"abstract":"<div>\u0000 \u0000 <p>Rubber-like materials possess remarkable properties such as high stretchability, low modulus, and impressive toughness, making them ideal for applications across various emerging domains. Given their growing relevance, understanding the fracture behavior of these materials is crucial for designing applications against failure. Although numerous models have been developed to simulate fracture propagation in these materials, few accurately account for their incompressible nature, which often leads to numerical challenges. This study introduces a multiscale polymer model integrated with the phase field approach, specifically designed to capture the fracture behavior in incompressible rubber-like materials using mixed finite elements. At the microscale, the entropic chain behavior is modeled using non-Gaussian statistics while also accounting for an internal energy due to molecular bond distortions. The non-affine microsphere network model, adapted for damaged systems, is employed to bridge the microscale deformations with those at the macroscale. Furthermore, the phase field approach is utilized at the macroscale to model damage, which is primarily assumed to be caused by the rupture of chain segments. This is coupled with a three-field mixed formulation, and augmented Lagrangian iterations are performed to strongly enforce the incompressibility constraint. The major advantage of this proposed formulation lies in the fact that it does not lead to an increase in the global system size. The numerical implementation of the proposed model using a monolithic scheme is detailed, and three-dimensional simulations are performed to validate the model's performance. The predictions are compared with experimental data to evaluate the potential and reliability of the framework in accurately predicting the fracture behavior of rubber-like materials. Furthermore, the volumetric deformation contours are visualized to demonstrate the effectiveness of the proposed model in strictly enforcing the incompressibility constraint. Moreover, the effect of the phase field regularization parameter on the predicted fracture behavior in specimens having geometric features of different sizes is investigated.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"127 11","pages":""},"PeriodicalIF":2.9,"publicationDate":"2026-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148174222","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}