Computer Methods in Applied Mechanics and Engineering最新文献

{"title":"A consistent phase-field-regularised partition of unity method for fracture analysis","authors":"Farshid Fathi,&nbsp;René de Borst,&nbsp;Giacomo Torelli","doi":"10.1016/j.cma.2025.118267","DOIUrl":"10.1016/j.cma.2025.118267","url":null,"abstract":"<div><div>Recent advancements in phase-field models have significantly reshaped the landscape of fracture mechanics, which was dominated by the partition of unity method in the early 21st century. In this study, we aim to leverage the advantages of the two approaches by adopting a novel phase-field-regularised partition of unity method to improve computational efficiency, robustness and physical consistency. Specifically, we establish a connection between early phase-field models and the partition of unity method for cohesive fracture. To this end, we replace the standard discontinuous Heaviside enrichment in the partition of unity method with a regularised and continuous Heaviside function, leveraging the phase-field approximation of the Dirac-<span><math><mi>δ</mi></math></span> function. The proposed formulation effectively resolves ill-conditioning issues in the traditional partition of unity method while retaining the key advantages of discrete fracture representations, offering a distinct contrast to traditional phase-field approaches for smeared crack models. These advantages include eliminating the need for extremely fine meshes and providing an unambiguous and physically consistent representation of the displacement jump across a crack. Furthermore, by integrating Non-Uniform Rational B-Splines (NURBS) for spatial discretisation, the approach enhances solution accuracy compared to standard finite element formulations. Compatibility enforcement is also modified to accommodate the crack diffused by the phase-field approximation. Through numerical examples, including stationary and propagating cracks, mesh refinement studies, and sensitivity analyses of the phase-field length scale, we establish an optimal prescription for the internal length scale based solely on the element size. The examples compare the results obtained via the presented formulations with exact solutions and other numerical techniques, demonstrating the accuracy, conditioning stability, and computational efficiency of the methodology. The proposed methodology thus presents a robust alternative to conventional fracture models, combining key advantages offered by discrete and smeared approaches.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"446 ","pages":"Article 118267"},"PeriodicalIF":7.3,"publicationDate":"2025-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144739201","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"TAEN: a model-constrained Tikhonov autoencoder network for forward and inverse problems","authors":"Hai Van Nguyen ,&nbsp;Tan Bui-Thanh ,&nbsp;Clint Dawson","doi":"10.1016/j.cma.2025.118245","DOIUrl":"10.1016/j.cma.2025.118245","url":null,"abstract":"<div><div>Efficient real-time solvers for forward and inverse problems are essential in engineering and science applications. Machine learning surrogate models have emerged as promising alternatives to traditional methods, offering substantially reduced computational time. Nevertheless, these models typically demand extensive training datasets to achieve robust generalization across diverse scenarios. While physics-based approaches can partially mitigate this data dependency and ensure physics-interpretable solutions, addressing scarce data regimes remains a challenge. Both purely data-driven and physics-based machine learning approaches demonstrate severe overfitting issues when trained with insufficient data. <em>We propose a novel model-constrained Tikhonov autoencoder neural network framework, called <span>TAEN</span>, capable of learning both forward and inverse surrogate models using a single arbitrary observational sample</em>. We develop comprehensive theoretical foundations including forward and inverse inference error bounds for the proposed approach for linear cases. For comparative analysis, we derive equivalent formulations for pure data-driven and model-constrained approach counterparts. At the heart of our approach is a data randomization strategy with theoretical justification, which functions as a generative mechanism for exploring the training data space, enabling effective training of both forward and inverse surrogate models even with a single observation, while regularizing the learning process. We validate our approach through extensive numerical experiments on two challenging inverse problems: 2D heat conductivity inversion and initial condition reconstruction for time-dependent 2D Navier–Stokes equations. Results demonstrate that <span>TAEN</span> achieves accuracy comparable to traditional Tikhonov solvers and numerical forward solvers for both inverse and forward problems, respectively, while delivering orders of magnitude computational speedups.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"446 ","pages":"Article 118245"},"PeriodicalIF":7.3,"publicationDate":"2025-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144739200","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Center manifold reduction of geometrically nonlinear beams: From 3D to 1D models","authors":"Shilei Han ,&nbsp;Mingwu Li ,&nbsp;Qiang Tian ,&nbsp;Olivier A. Bauchau","doi":"10.1016/j.cma.2025.118242","DOIUrl":"10.1016/j.cma.2025.118242","url":null,"abstract":"&lt;div&gt;&lt;div&gt;This paper presents a novel center manifold-based approach for reducing the geometrically nonlinear three-dimensional continuum description of beam structures to efficient one-dimensional models. The beam considered is composed of hyperelastic material and features uniform cross-sectional geometry and material properties along its axial line. While Mielke previously proved that Saint-Venant’s solution resides within a twelve-dimensional center manifold, its construction for nonlinear dimensional-reduction of beams remains unexplored. This study presents the first explicit construction of the center manifold by approximating the warping field, sectional strains, and one-dimensional equilibrium equations as polynomials of the six stress resultant components, enabling dimensional reduction for beams undergoing geometrically nonlinear deformations. The method begins by decomposing beam kinematics into rigid-section motion and a warping field. A finite element semi-discretization of the cross-section is employed, and Hamilton’s variational principle yields equilibrium equations as nonlinear ordinary differential equations along the beam’s axial coordinate, enabling center manifold reduction. A critical challenge arises from the kinematic decomposition, requiring two interdependent mappings: sectional strains and warping field as nonlinear functions of stress resultants. Unlike conventional center manifold methods, which use a single set of invariance equations, this approach demands two distinct, coupled invariance equations. Additionally, the non-uniqueness of the kinematic decomposition leads to inherently singular cohomological equations, differing from traditional center manifold reduction. To address these challenges, four key advancements are proposed: &lt;em&gt;(1)&lt;/em&gt; Two coupled set of invariance equations are established: one ensures sectional strains and warping fields satisfy three-dimensional equilibrium, and the other ensures the composed mapping for stress resultants reduces to the identity mapping. &lt;em&gt;(2)&lt;/em&gt; The left- and right-null spaces of the cohomological equations, arising from non-unique kinematic decomposition, are rigorously identified, ensuring solution existence. &lt;em&gt;(3)&lt;/em&gt; Uniqueness of compliance and warping matrices is established via energetic analysis of the system’s Hamiltonian, guaranteeing symmetry in higher-order compliance matrices. &lt;em&gt;(4)&lt;/em&gt; Distributed functions of loads are reformulated as differential equations, transforming inhomogeneous systems into augmented homogeneous ones for dimensional reduction. Finally, the reduced-order one-dimensional beam model is solved using a mixed finite element formulation to enforce complementary-energy-based nonlinear constitutive laws derived from the center manifold reduction. Numerical examples validate the accuracy and computational efficiency of the proposed method, demonstrating its capability to capture geometric nonlinearities in beams with complex cross","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"446 ","pages":"Article 118242"},"PeriodicalIF":7.3,"publicationDate":"2025-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144739126","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Generative learning of densities on manifolds","authors":"Dimitris G. Giovanis ,&nbsp;Ellis Crabtree ,&nbsp;Roger G. Ghanem ,&nbsp;Ioannis G. Kevrekidis","doi":"10.1016/j.cma.2025.118266","DOIUrl":"10.1016/j.cma.2025.118266","url":null,"abstract":"<div><div>A generative modeling framework is proposed that combines diffusion models and manifold learning to efficiently sample data densities on manifolds. The approach utilizes Diffusion Maps to uncover possible low-dimensional underlying (latent) spaces in the high-dimensional data (ambient) space. Two approaches for sampling from the latent data density are described. The first is a score-based diffusion model, which is trained to map a standard normal distribution to the latent data distribution using a neural network. The second one involves solving an Itô stochastic differential equation in the latent space. Additional realizations of the data are generated by lifting the samples back to the ambient space using <em>Double Diffusion Maps</em>, a recently introduced technique typically employed in studying dynamical system reduction; here the focus lies in sampling densities rather than system dynamics. The proposed approaches enable sampling high dimensional data densities restricted to low-dimensional, <em>a priori unknown</em> manifolds. The efficacy of the proposed framework is demonstrated through a benchmark problem and a material with multiscale structure.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"446 ","pages":"Article 118266"},"PeriodicalIF":7.3,"publicationDate":"2025-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144724405","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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 extended ordinary state-based peridynamics model for addressing contact problems during crack propagation","authors":"JinMeng Yang ,&nbsp;ZhenZhong Shen ,&nbsp;Federico Dalla Barba ,&nbsp;LanHao Zhao","doi":"10.1016/j.cma.2025.118271","DOIUrl":"10.1016/j.cma.2025.118271","url":null,"abstract":"<div><div>A novel nonlocal peridynamics contact model, which guarantees conservation of angular momentum, is proposed for addressing the contact problems during crack propagation. The algorithms for normal vector computation, contact initiation conditions, and contact type evaluation are described in detail. The numerical examples, including two plates with a vertical contact surface, and the specimen containing one or two pre-existing fissures are successfully studied to validate the proposed contact model. The numerical results reveal that the proposed contact model properly captures the contact behavior during crack propagation. Furthermore, it improves the accuracy of numerical simulations of fracture in materials containing defects.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"446 ","pages":"Article 118271"},"PeriodicalIF":7.3,"publicationDate":"2025-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144724404","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Control of the accuracy and improvement of the convergence rate of a LATIN-based multiscale strategy for frictional contact problems","authors":"Donald Zeka ,&nbsp;Pierre-Alain Guidault ,&nbsp;David Néron ,&nbsp;Martin Guiton","doi":"10.1016/j.cma.2025.118268","DOIUrl":"10.1016/j.cma.2025.118268","url":null,"abstract":"<div><div>This paper deals with the control and improvement of the convergence of the interface contact quantities in the framework of a multiscale strategy for the resolution of time-dependent frictional contact problems. The considered strategy is the multiscale mixed domain decomposition method based on the LATIN non-incremental solver, whose specificity is that it generates successive approximations of the solution over the entire space-time domain. In order to highlight this characteristic of the method, in a previous paper [1], the robustness of the strategy was pointed out, but also how challenging it is to control the accurate convergence of microquantities at the interfaces and how the convergence rate of microquantities depends on the parameters of search directions used in the LATIN, in a manner similar to the influence of augmentation parameters in augmented Lagrangian approaches combined with an Uzawa-like solver. The objective of this work is to propose, first of all, a dedicated convergence indicator in order to stop the iterative process of the resolution strategy for ensuring converged contact quantities with a reasonable level of accuracy. Such a convergence indicator is crucial for the second part of the paper, where a strategy is introduced for the on-the-fly updating of search directions along the LATIN iterations based on the contact status in space and time to improve the convergence rate of the interface quantities. The robustness of the convergence indicator and the updating strategy is tested on several 2D frictional contact problems with multiple contact interfaces and different time-evolving contact conditions (open/closed and stick/slip transitions), allowing for accurate control and improved convergence rate of local microquantities, especially when a high level of accuracy is required.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"446 ","pages":"Article 118268"},"PeriodicalIF":7.3,"publicationDate":"2025-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144739125","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Adaptive phase-field smoothed total Lagrangian material point method for fracture analysis of soft materials involving large deformation","authors":"Shun Zhang ,&nbsp;Weilong Yang ,&nbsp;Wei Sun ,&nbsp;Yisong Qiu ,&nbsp;Hongfei Ye ,&nbsp;Liang Zhang ,&nbsp;Yonggang Zheng","doi":"10.1016/j.cma.2025.118250","DOIUrl":"10.1016/j.cma.2025.118250","url":null,"abstract":"<div><div>An adaptive phase-field smoothed total Lagrangian material point method (APS-TLMPM) is proposed in this paper to analyze the fracture behavior of nearly incompressible materials. The total Lagrangian material point method (TLMPM) combining with the phase-field model (PFM) is developed to describe the fracture behavior and solve the governing equations. Moreover, a hybrid <strong>F</strong>-bar method is developed to effectively alleviate volumetric locking caused by the nearly incompressible nature of soft materials. The physically meaningful and numerically induced volumetric changes are distinguished based on the pressure field to mitigate the inconsistency between the incompressibility constraint and the diffusive crack model. To efficiently solve the phase-field governing equations, an adaptive mesh refinement (AMR) algorithm is developed to refine the background grid and particles near the crack tip. Meanwhile, a unified formulation for constructing interpolation functions is established based on corrected smoothed kernel functions to efficiently handle transition grid with hanging nodes generated by the AMR. Finally, the accuracy and effectiveness of the proposed method for simulating the fracture of nearly incompressible materials are demonstrated through several representative numerical examples and comparisons with experimental results.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"446 ","pages":"Article 118250"},"PeriodicalIF":7.3,"publicationDate":"2025-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144720949","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Adaptive Strategy Management: A new framework for large-scale structural optimization design","authors":"Siamak Talatahari ,&nbsp;Behnaz Nouhi ,&nbsp;Amin Beheshti ,&nbsp;Fang Chen ,&nbsp;Amir H. Gandomi","doi":"10.1016/j.cma.2025.118256","DOIUrl":"10.1016/j.cma.2025.118256","url":null,"abstract":"<div><div>This study introduces the Adaptive Strategy Management (ASM) framework designed to enhance the efficiency of computationally expensive optimization processes by dynamically switching between multiple solution-generation strategies. The ASM framework integrates three core steps: filtering, switching, and updating, which allow it to adaptively decide which solutions to evaluate based on real-time performance feedback. Several ASM-based variants are proposed, each implementing different filtering and switching mechanisms, such as generated-based selection, proximity-based filtering, and strategy switching guided by the current or global best solutions. Chaos Game Optimization (CGO) is selected as the core optimizer, with its updated equations modified to improve performance without incurring additional computational costs alongside strategy-level innovations. Extensive evaluations on medium-, large- and very large-scale structural problems demonstrate that the developed methods consistently outperform other approaches. Notably, the ASM-Close Global Best method, which combines proximity filtering with global best knowledge, achieved superior results across all performance intervals, showcasing robust convergence and high-quality solutions. These findings underscore the potential of Adaptive Strategy Management in improving large-scale optimization performance and open new directions for future research, including other strategy selections, broader applications across metaheuristics, and extensions to multi-objective and constrained optimization problems.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"446 ","pages":"Article 118256"},"PeriodicalIF":7.3,"publicationDate":"2025-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144720950","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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 phase-field length scale insensitive micropolar fatigue model","authors":"Ayyappan Unnikrishna Pillai,&nbsp;Mohammad Masiur Rahaman","doi":"10.1016/j.cma.2025.118259","DOIUrl":"10.1016/j.cma.2025.118259","url":null,"abstract":"<div><div>This article proposes a novel micropolar phase-field model for size-dependent fatigue failure in solids under mechanical loading. To develop the proposed model that can capture experimentally observed size effects in brittle materials, we employ micropolar theory in a phase-field length scale-insensitive framework and address the limitations of classical phase-field fatigue models. A key advantage of the proposed model is its ability to eliminate artificial nonlocal effects introduced by the phase field length scale while preserving the physical size effects dictated by the material microstructure. In the proposed model, we introduce micro-rotation as an additional kinematic variable and derive the governing partial differential equations by invoking the principle of virtual power. The constitutive relations are established in accordance with thermodynamic laws, enabling the incorporation of dissipative effects whenever required. To make the proposed model insensitive to the phase-field length scale and thus eliminate artificial nonlocal effects, we incorporate a fatigue-related parameter that defines the fatigue threshold energy as a function of the material fracture strength. We demonstrate the efficacy of the proposed model through numerical simulations on a set of benchmark two- and three-dimensional problems that include three-point bending tests, single-edge notched plates, etc., and provide a qualitative experimental validation against the results available in the literature. The numerical results show a significant influence of the micropolar parameters on fatigue behavior, emphasizing the necessity of the proposed formulation for materials that exhibit pronounced nonlocal effects. We demonstrate the insensitivity of the proposed model to the phase-field length scale using plots of consistent crack growth versus the number of cycles for different values of the phase-field length scale. For the numerical implementation of the proposed model, we use an open-source finite element library called Gridap, available in Julia, a recently developed high-performance programming language. The availability of open-source codes ensures transparency, reproducibility, and ease of verification, setting a high standard for open-source computational tools in scientific research. The numerical findings validate the robustness of the proposed model, establishing its suitability for accurately simulating size-dependent fatigue behavior in materials.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"446 ","pages":"Article 118259"},"PeriodicalIF":7.3,"publicationDate":"2025-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144720948","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Inverse design of structures with accurately programmable nonlinear mechanical responses by topology optimization","authors":"Jiashuo Xu,&nbsp;Mi Xiao,&nbsp;Liang Gao","doi":"10.1016/j.cma.2025.118243","DOIUrl":"10.1016/j.cma.2025.118243","url":null,"abstract":"<div><div>Structures with programmable nonlinear responses have promising applications in the design of medical stents, soft robotics, wearable and flexible electronic devices, and so on. However, it is exceptionally difficult to precisely tune the nonlinear mechanical responses in terms of structural inverse design from target properties to configurations. This paper proposes an inverse design method based on topology optimization, which is targeted at the customized design of structures featuring target nonlinear mechanical responses. In this method, a tangent stiffness constraint is introduced, which significantly improves the programmable accuracy of nonlinear mechanical responses. To track the nonlinear mechanical behavior of structures, the modified generalized displacement control method is used to solve the nonlinear finite element equations. A strain energy interpolation scheme is employed to address numerical instability during nonlinear topology optimization. Moreover, numerical tensile and compression test models, along with periodic boundary conditions, are employed to characterize the macroscopic nonlinear mechanical behavior of microstructures. Numerical examples of macrostructures and microstructures in terms of stiffening, softening, constant force, and bistable mechanical behaviors are provided. The results indicate that the proposed method is accurate and robust, and has wide applicability in realizing programmable nonlinear mechanical responses.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"446 ","pages":"Article 118243"},"PeriodicalIF":6.9,"publicationDate":"2025-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144714485","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}