International Journal for Numerical Methods in Engineering最新文献

{"title":"A Sequential Quadratic Numerical Optimization Technique to Compute Critical Flutter Speeds","authors":"Alfredo R. de Faria","doi":"10.1002/nme.70426","DOIUrl":"https://doi.org/10.1002/nme.70426","url":null,"abstract":"<p>A stable sequential quadratic numerical optimization technique is proposed to compute critical flutter speeds without resorting to complex algebra. The solution of the traditional eigenproblem stated in the frequency domain, and whose complex conjugate eigenvalues provide insights on the stability of the dynamic aeroelastic response, is avoided altogether. Instead, the technique relies on evaluation of the determinant of the dynamic matrix, which is certainly real (noncomplex). Since computation of the determinant of large, although banded (or sparse), nonsymmetric matrices is a computationally expensive routine, the procedure relies on a sequential quadratic polynomial approximation to the determinant in terms of natural frequency and free stream velocity, both properly scaled. The optimization technique is shown to be robust and to quickly converge when applied to beams and plates under supersonic flows modeled by piston theory. Two additional contributions of the paper are a method to scale the free stream velocity (essential for convergence) based on the stencil of the aeroelastic beam problem and a parallel algorithm to compute the determinant of the dynamic matrix (essential for fast computer processing).</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"127 17","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.70426","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148942489","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":"Robust Inverse Identification of Heterogeneous Hyperelastic Materials Under Large Deformation via Residual-Adaptive Physics-Informed Neural Networks","authors":"Jing-Ang Zhu,&nbsp;Wenjing Lu,&nbsp;Han Li,&nbsp;Zishun Liu","doi":"10.1002/nme.70427","DOIUrl":"https://doi.org/10.1002/nme.70427","url":null,"abstract":"<div>\u0000 \u0000 <p>Characterizing heterogeneous inclusions in hyperelastic materials is critical for diverse fields ranging from soft robotics to medical diagnostics. However, this inverse problem remains challenging as traditional engineering approaches struggle to resolve sharp material interface and strong nonlinearity, while data-driven approaches typically require prior geometric assumptions or accurate stress measurements. To address these limitations, we propose a robust framework based on physics-informed neural networks equipped with residual-based adaptive refinement (AR-PINN). By dynamically appending collocation points according to governing-equation residuals, our method autonomously resolves both the complex inclusion topologies and the relative shear modulus distributions using only sparse Green–Lagrange strain measurements, requiring no prior knowledge regarding the shape or size of inclusions. Extensive numerical studies demonstrate accurate identification and remarkable robustness under large nonlinear deformation, including uniaxial stretching up to <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>λ</mi>\u0000 <mo>=</mo>\u0000 <mn>3.0</mn>\u0000 </mrow>\u0000 <annotation>$$ lambda =3.0 $$</annotation>\u0000 </semantics></math>, as well as resistance to measurement noise levels up to 30%. These results firmly establish AR-PINN as a data-efficient, assumption-free, and practical tool for nondestructive characterization and inverse design of heterogeneous soft materials in experimental settings.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"127 17","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148942377","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":"Stress-Constrained Topology Optimization of Sweep-Frequency Harmonic Vibration Problems Using a B-Spline-Parameterized Topology Description Function Method","authors":"Xuan Wang,&nbsp;Kailin Zheng,&nbsp;Kai Long,&nbsp;Yi Min Xie","doi":"10.1002/nme.70428","DOIUrl":"https://doi.org/10.1002/nme.70428","url":null,"abstract":"<div>\u0000 \u0000 <p>This paper presents a novel B-spline-parameterized topology description function (TDF) method to tackle the challenging problem of stress-constrained topology optimization under sweep-frequency harmonic excitations. The proposed method employs B-spline coefficients as design variables, enabling a smooth and implicit representation of evolving topologies. A two-layer aggregation strategy with a dynamically adjusted correction coefficient is introduced to condense the spatial-frequency peak stress into a single, smooth, and differentiable global stress constraint. A rigorous error analysis of the introduced two-layer aggregation strategy is provided. The sensitivities of the global spatial-frequency stress constraint and the volume objective with respect to the B-spline coefficients are derived in detail. Furthermore, the model reduction technique based on the modified Gram-Schmidt orthonormalization is introduced to reduce the cost of repeated harmonic-response analyses at multiple frequencies. Finally, three numerical examples, including an L-shaped beam, a U-shaped beam, and a corbel structure, are investigated to validate the proposed approach. The results show that the developed method effectively controls local stress concentrations under sweep-frequency harmonic vibrations, providing a robust tool for designing lightweight structures subjected to variable-frequency dynamic loads.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"127 17","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148942442","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 Stabilization-Free Virtual Element Method for 2D Thermo-Mechanical Contact Problems","authors":"Zhen-Kun Cao,&nbsp;Bing-Bing Xu,&nbsp;Miao Cui,&nbsp;De-Chuan Sun","doi":"10.1002/nme.70424","DOIUrl":"https://doi.org/10.1002/nme.70424","url":null,"abstract":"<div>\u0000 \u0000 <p>The virtual element method (VEM) has gained increasing attention in recent years due to its flexibility with respect to element shapes. The applications of VEM to thermo-mechanical contact problems remains largely unexplored. In this work, the stabilization-free virtual element method (SFVEM) is applied to two dimensional thermo-mechanical contact problems for the first time. Compared with the conventional VEM, the SFVEM modifies the virtual element space to enable the calculation of the higher-order <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mrow>\u0000 <mi>L</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 </msub>\u0000 </mrow>\u0000 <annotation>$$ {L}_2 $$</annotation>\u0000 </semantics></math> projection of the gradient, thereby eliminating the need for stabilization terms in the stiffness matrix. This feature significantly simplifies the implementation and analysis of nonlinear thermo-mechanical contact problems and avoids the influence of artificial stabilization parameters on the numerical results. To accurately capture the coupled thermo-mechanical interactions at contact interfaces (governed by heat conduction and mechanical pressure), a node-to-segment discretization strategy is employed to handle non-conforming meshes. A staggered solution strategy is further employed to solve the resulting nonlinear coupled system. Several numerical examples are presented to demonstrate the accuracy and convergence of the proposed method in thermal contact problems. The results confirm that the stabilization-free VEM achieves high accuracy in both temperature and stress fields, provides a computational framework for the simulation of complex thermal contact problems without the use of traditional stabilization techniques.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"127 17","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148942107","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":"ML-Accelerated Framework for Fatigue Life-Timescale Homogenization and Cyclic Damage Evolution Under Physics Constraints","authors":"Elsayed S. Elsayed,&nbsp;Abedulgader Baktheer,&nbsp;Fadi Aldakheel","doi":"10.1002/nme.70394","DOIUrl":"https://doi.org/10.1002/nme.70394","url":null,"abstract":"<p>Predicting structural lifetime under complex loading remains a major challenge in computational mechanics, especially for high cycle fatigue in large scale systems such as aircraft, bridges, and wind turbines. This difficulty arises from the need to capture fatigue damage accumulation, crack initiation, crack growth across scales, and life prediction, making direct simulation over millions of load cycles computationally infeasible. To overcome this limitation, the presented work introduces a physics-based machine learning (<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>ϕ</mi>\u0000 <mtext>ML</mtext>\u0000 </mrow>\u0000 <annotation>$$ phi mathrm{ML} $$</annotation>\u0000 </semantics></math>) framework to accelerate fatigue life-timescale homogenization and cyclic damage evolution. The first model predicts damage evolution over the full cyclic loading history, while the second operates at the lifetime scale by estimating accumulated damage over blocks of load cycles through the development of macro- and micromechanically motivated degradation mechanisms. Both models are built on double feed-forward neural networks and are guided by physical constraints, including energy balance, damage evolution, and degradation laws, thereby ensuring physically consistent, interpretable, and generalizable predictions for unseen materials and loading conditions. Validation studies of the proposed framework demonstrate that the models accurately reproduce nonlinear damage evolution under diverse loading histories and material parameters. Most importantly, the lifetime-scale model directly predicts damage over large blocks of load cycles, thereby eliminating the need for costly cycle-by-cycle simulations. Quantitative comparisons show computational speed-ups of up to approximately <b>2700 times</b>\u0000compared with conventional incremental fatigue analyses, while maintaining excellent agreement with reference solutions. As a result, this acceleration makes large-scale high-cycle fatigue simulations computationally feasible under physics constrains, providing a pathway toward scalable, reliable, and interpretable lifetime assessment of structural components subjected to cyclic loading.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"127 17","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.70394","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148942282","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":"Phase Field Modeling Considering Interfacial Effect for Investigating Corrosion-Induced Damage in Confined Realistic Multiphase Structures","authors":"Xuan-Lam Nguyen,&nbsp;Ba-Thanh Vu,&nbsp;Dac-Duc Nguyen","doi":"10.1002/nme.70411","DOIUrl":"https://doi.org/10.1002/nme.70411","url":null,"abstract":"<div>\u0000 \u0000 <p>Rebar corrosion is one of the primary causes of deterioration and reduction in the resistance of reinforced concrete (RC) structures. Previous studies employing phase field modeling for corrosion-related problems commonly idealize concrete as a brittle, homogeneous material and unconfined structures. Moreover, the phase field methods adopted in these studies do not satisfy the strain-tensor orthogonal condition, which has been demonstrated to be essential for accurately modeling the damage in brittle or quasi-brittle materials. To address these research gaps, the present paper provides the following main contributions: (i) a phase field method with interfacial effect, which satisfies the strain tensor orthogonal condition, is employed; (ii) the influences of the distribution and number of inclusions or/and pores, as well as the concrete cover thickness, on damage evolution in both unconfined structure and confined structure are investigated; and (iii) damage in realistic RC structures with randomly distribution and shape of aggregates induced by corrosion expansion of two rebars is numerically simulated. The results illustrate crack propagation paths and corrosion-induced rust expansion displacement values at both the crack initiation state and the fully cracked propagation state of the structure. Through the representative numerical examples, an overall insight into corrosion behavior in typical multiphase structures is provided. The obtained results contribute to rational rebar layout and strengthening strategies for practical RC structures, thereby mitigating the rapid failure of structures caused by rebar corrosion.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"127 17","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148942199","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":"High-Order Accurate Taylor Correction-Based Backward Differentiation Formulas With Spatial Transferable Neural Networks for Moving Interface Problems","authors":"Tao Cheng,&nbsp;Lili Ju,&nbsp;Zhonghua Qiao,&nbsp;Xiaoping Zhang","doi":"10.1002/nme.70423","DOIUrl":"https://doi.org/10.1002/nme.70423","url":null,"abstract":"<div>\u0000 \u0000 <p>Parabolic partial differential equations with moving interfaces arise in a wide range of applications, including materials science, fluid dynamics, and environmental engineering. The primary challenge in their numerical simulation lies in the evolving position of the interface, which introduces temporal discontinuities and necessitates modifications to standard numerical methods. To address this issue, we propose in this paper a class of Taylor correction-based backward differentiation formula (BDF-TC) schemes, specifically designed for the time discretization of moving interface problems. For spatial approximation, we employ the so-called transferable neural network (TransNet), a special class of two-layer fully connected neural networks in which the hidden-layer parameters are predetermined and fixed according to a uniform neuron distribution. In particular, at each time step, two TransNets are constructed to approximate the solutions in the subdomains on both sides of the interface and are connected through the interface conditions. The resulting fully discrete system can then be solved efficiently using linear least-squares techniques, without resorting to stochastic optimization algorithms. Finally, we present numerical experiments and comparisons in both two and three dimensions to demonstrate the accuracy, stability, and efficiency of the proposed method.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"127 17","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148942109","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":"Machine-Learning Enhanced Parametric Reynolds-Averaged Navier-Stokes Equations at the Full- and Reduced-Order Levels","authors":"Davide Oberto,&nbsp;Maria Strazzullo,&nbsp;Stefano Berrone","doi":"10.1002/nme.70415","DOIUrl":"https://doi.org/10.1002/nme.70415","url":null,"abstract":"<p>In this contribution, we focus on the Reynolds-averaged Navier-Stokes (RANS) models and their exploitation to build reliable reduced-order models to further accelerate predictions for real-time applications and many-query scenarios. Specifically, we investigate how machine learning can be employed to enhance the predictive capabilities of the model, both at the full-order model (FOM) and reduced-order model (ROM) levels. We explore a novel integration of these two areas. We generate the FOM snapshots, essential for ROM construction, using a data-driven RANS model: the <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mrow>\u0000 <mi>ν</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>t</mi>\u0000 </mrow>\u0000 </msub>\u0000 </mrow>\u0000 <annotation>$$ {nu}_t $$</annotation>\u0000 </semantics></math>-Vector Basis Neural Network. This is the first time that this machine-learning procedure covers a large parametric variation, and we propose tailored training strategies to increase the accuracy of the FOM model. At the ROM level, we compare the results obtained by standard proper orthogonal decomposition (POD) in an intrusive Galerkin setting (PODG) and POD neural network approach (PODNN). The numerical validation is conducted on a classic turbulent square-duct flow benchmark, with the bulk Reynolds number as the sole varying parameter. Our investigation reveals that the PODG method proves to be unstable and inaccurate for turbulent flow prediction, while PODNN demonstrates superior performance in terms of accuracy and computational efficiency.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"127 17","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.70415","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148942200","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":"PINNA: Physics-Informed Neural Networks Architecture for Implicit Governing Physics With Interpretability","authors":"Zhengtao Yao,&nbsp;Philippe Hawi,&nbsp;Venkat Aitharaju,&nbsp;Jay Mahishi,&nbsp;Roger Ghanem","doi":"10.1002/nme.70399","DOIUrl":"https://doi.org/10.1002/nme.70399","url":null,"abstract":"&lt;div&gt;\u0000 \u0000 &lt;p&gt;Modern engineering simulations frequently operate in regimes where &lt;i&gt;explicit&lt;/i&gt; governing equations are incomplete or experiments are prohibitively expensive. To remain accurate and trustworthy under such constraints, we propose the &lt;b&gt;Physics-Informed Neural Network Architecture (PINNA)&lt;/b&gt;, a deep-learning surrogate that fuses data with domain knowledge &lt;i&gt;inside&lt;/i&gt; the network. Concretely, a fully connected &lt;i&gt;encoder&lt;/i&gt; &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;g&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;ϕ&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ {g}_{phi } $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; embeds raw inputs (e.g., material descriptors, loads, or operating conditions) into a latent space, while an &lt;i&gt;intermediate-physics head&lt;/i&gt; is &lt;i&gt;explicitly supervised&lt;/i&gt; to predict expert-selected quantities with clear physical meaning, such as strain-energy densities or chemically relevant indicators. These intermediate predictions are &lt;i&gt;residual-concatenated&lt;/i&gt; with the original inputs and passed to a &lt;i&gt;task decoder&lt;/i&gt; &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;h&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;θ&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ {h}_{theta } $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, enabling the network to learn and correct mismatches between approximate physics and observed responses. This architecture achieves (i) higher &lt;b&gt;accuracy&lt;/b&gt; and sample efficiency than purely data-driven baselines, (ii) negligible &lt;b&gt;computational overhead&lt;/b&gt; at inference time, and (iii) intrinsic &lt;b&gt;interpretability&lt;/b&gt;, as intermediate predictions expose physically meaningful internal representations. We further introduce a scalable extension, Generalized PINNA (&lt;b&gt;G-PINNA&lt;/b&gt;), which stacks multiple physics heads to accommodate multiscale and multi-physics constraints within the same residual-concatenation framework. PINNA is validated across three fundamentally different benchmarks: two composite-material problems involving nonlinear stress-strain behavior and multistage failure, and a large-scale 1-D laminar combustion problem governed by stiff chemical kinetics, thermal transport, and reduced fluid mechanics. In the composite benchmarks, PINNA reduces test errors by up to an order of magnitude relative to Fourier Neural Operators and DeepONets while using fewer parameters. In the combustion benchmark, PINNA accurately predicts both interpretable intermediate chemical indicators and high-dimensional flame quantities, including scalar metrics and full","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"127 17","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148942106","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 Pressure-Projection Stabilized Hybrid ES-FEM/FEM Formulation for Phase-Field Fracture of Nearly Incompressible Elastomers","authors":"Shuyu Chen,&nbsp;Fucheng Tian,&nbsp;Kunpeng Cui","doi":"10.1002/nme.70418","DOIUrl":"https://doi.org/10.1002/nme.70418","url":null,"abstract":"<div>\u0000 \u0000 <p>Modeling phase-field fracture in nearly incompressible elastomers is challenging due to volumetric locking and mesh distortion under finite strains. Conventional displacement-based FEM often exhibits locking-induced over-stiff responses and severe mesh distortion, leading to inaccurate stress fields and loss of convergence. To address these issues, we propose a pressure-projection stabilized hybrid ES-FEM/FEM framework for large-deformation phase-field fracture. The mixed displacement–pressure field is approximated by equal-order interpolation within an edge-based smoothed finite element (ES-FEM) formulation equipped with pressure projection, which alleviates volumetric locking and enhances stability under large deformations through strain smoothing. The phase-field variable is solved using standard FEM on the same mesh, maintaining computational efficiency comparable to classical implementations. The resulting framework is naturally compatible with adaptive mesh refinement, rendering it well suited for resolving the highly localized gradients inherent to phase-field formulations. Benchmark tests and comparisons with experimental observations demonstrate improved convergence, accurate load–displacement responses, and physically consistent crack paths in soft, nearly incompressible elastomers.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"127 17","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148942160","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}