Computer Methods in Applied Mechanics and Engineering最新文献

{"title":"A phase field model for hydraulic fracture: Drucker–Prager driving force and a hybrid coupling strategy","authors":"Yousef Navidtehrani ,&nbsp;Covadonga Betegón ,&nbsp;Javier Vallejos ,&nbsp;Emilio Martínez-Pañeda","doi":"10.1016/j.cma.2025.118155","DOIUrl":"10.1016/j.cma.2025.118155","url":null,"abstract":"<div><div>Recent years have seen a significant interest in using phase field approaches to model hydraulic fracture, so as to optimise a process that is key to industries such as petroleum engineering, mining and geothermal energy extraction. Here, we present a novel theoretical and computational phase field framework to simulate hydraulic fracture. The framework is general and versatile, in that it allows for improved treatments of the coupling between fluid flow and the phase field, and encompasses a universal description of the fracture driving force. Among others, this allows us to bring two innovations to the phase field hydraulic fracture community: (i) a new hybrid coupling approach to handle the fracture-fluid flow interplay, offering enhanced accuracy and flexibility; and (ii) a Drucker–Prager-based strain energy decomposition, extending the simulation of hydraulic fracture to materials exhibiting asymmetric tension–compression fracture behaviour (such as shale rocks) and enabling the prediction of geomechanical phenomena such as fault reactivation and stick–slip behaviour. Four case studies are addressed to illustrate these additional modelling capabilities and bring insight into permeability coupling, cracking behaviour, and multiaxial conditions in hydraulic fracturing simulations. The codes developed are made freely available to the community and can be downloaded from <span><span>https://mechmat.web.ox.ac.uk/</span><svg><path></path></svg></span>.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"444 ","pages":"Article 118155"},"PeriodicalIF":6.9,"publicationDate":"2025-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144366629","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":"Learning elastoplasticity with implicit layers","authors":"Jeremy Bleyer","doi":"10.1016/j.cma.2025.118145","DOIUrl":"10.1016/j.cma.2025.118145","url":null,"abstract":"<div><div>We are interested in learning elastoplasticity directly from stress–strain data. Data-driven learning of plasticity is a notoriously difficult task owing to the non-smooth transition induced by the yield criterion and due to the potentially complex shape of plastic yield surfaces in a multi-dimensional space. To circumvent these issues, we present a simple machine learning architecture based on implicit layers. Such layers formulate the elastoplastic constitutive update as a convex optimization problem with learnable parameters. Parametrized classes of convex sets are proposed to describe generic plastic yield surfaces, including polyhedra, ellipsoids or spectrahedra. Examples, ranging from simple 2D domains to complex 6D shell yield surfaces demonstrate the efficiency of this implicit learning strategy. Excellent generalization is observed thanks to the embedded convex mathematical structure while requiring a low amount of learning parameters. Good performance in the low data regime and in presence of noise is also observed.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"444 ","pages":"Article 118145"},"PeriodicalIF":6.9,"publicationDate":"2025-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144366630","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":"Active learning informed proper orthogonal decomposition for reduced order modelling of heat transfer in porous medium","authors":"Pin Zhang ,&nbsp;Brian Sheil ,&nbsp;Mark Girolami","doi":"10.1016/j.cma.2025.118174","DOIUrl":"10.1016/j.cma.2025.118174","url":null,"abstract":"<div><div>Modern monitoring technologies require fast and accurate inference of the spatio-temporal responses of dynamic and complex systems. Reduced order models (ROMs) offer a cost-effective way to meet this demand, yet there are many open questions to develop a robust ROM of a complex engineering problem. This study proposes an active learning (AL) informed proper orthogonal decomposition (POD) method for developing ‘non-intrusive’ ROMs. The probability density function (PDF) of ROM errors is tailored to guide AL in the search of an optimal global energy criterion. To select an appropriate machine learning algorithms (ML) for both <em>online</em> and <em>offline</em> stages, several different ML algorithms are evaluated by constructing the same ROM for comparison. The results indicate that PDF-based AL promotes a smart sampling process at the <em>offline</em> stage, ensuring that each sample contributes effectively towards identifying the optimal global energy criterion. Random forest embedded AL shows excellent performance, exhibiting superior accuracy and data savings during intelligent sampling. For developing surrogate models and the online expansion coefficient estimators, the radial basis function network provides optimal performance in terms of accuracy and computational speed. The proposed method accurately captures spatio-temporal heat transfer in soils under various scenarios, while mitigating overfitting and over-use of POD modes, enabling the development of robust and parsimonious ROMs. The proposed framework is also generic, enabling flexible extrapolation to tackle other computationally demanding problems where accuracy and efficiency are critical.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"444 ","pages":"Article 118174"},"PeriodicalIF":6.9,"publicationDate":"2025-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144366628","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":"Physics-based machine learning for fatigue lifetime prediction under non-uniform loading scenarios","authors":"Abedulgader Baktheer,&nbsp;Fadi Aldakheel","doi":"10.1016/j.cma.2025.118116","DOIUrl":"10.1016/j.cma.2025.118116","url":null,"abstract":"<div><div>Accurate lifetime prediction of structures and structural components subjected to cyclic loading is vital, especially in scenarios involving non-uniform loading histories where load sequencing critically influences structural durability. Addressing this complexity requires advanced modeling approaches capable of capturing the intricate relationship between loading sequences and fatigue lifetime. Traditional high-cycle fatigue simulations are computationally prohibitive, necessitating more efficient methods. This work highlights the potential of physics-based machine learning (<span><math><mi>ϕ</mi></math></span>ML) to predict the fatigue lifetime of materials under various loading conditions. Specifically, a feedforward neural network is designed to embed physical constraints from experimental evidence, including initial and boundary conditions, directly into its architecture to enhance prediction accuracy. It is trained using numerical simulations generated by a physically based anisotropic continuum damage fatigue model. The model is calibrated and validated against experimental fatigue data of concrete cylinder specimens tested in uniaxial compression. The simulations used for training quantify the effects of load sequences considering scenarios under two different loading ranges. The proposed approach demonstrates superior accuracy compared to purely data-driven neural networks, particularly in situations with limited training data, achieving realistic predictions of damage accumulation. To this end, a general algorithm is developed and successfully applied to predict fatigue lifetimes under complex loading scenarios with multiple loading ranges. In this approach, the <span><math><mi>ϕ</mi></math></span>ML model serves as a surrogate to capture damage evolution across load transitions. The <span><math><mi>ϕ</mi></math></span>ML based algorithm is subsequently employed to investigate the influence of multiple loading transitions on accumulated fatigue life, and its predictions align with trends observed in recent experimental studies. The presented contribution demonstrates physics-based machine learning as a promising technique for efficient and reliable fatigue life prediction in engineering structures, with possible integration into digital twin models for real-time assessment.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"444 ","pages":"Article 118116"},"PeriodicalIF":6.9,"publicationDate":"2025-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144338713","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":"Peridynamics model of viscoelasticity for shells and metasurfaces","authors":"Kundan Kumar,&nbsp;Nilesh Choudhary,&nbsp;Sajal,&nbsp;Bhushan Sah,&nbsp;Pranesh Roy","doi":"10.1016/j.cma.2025.118169","DOIUrl":"10.1016/j.cma.2025.118169","url":null,"abstract":"<div><div>This paper develops a peridynamics shell viscoelasticity theory with a view to modeling creep deformation in shells and metasurfaces. The idea here is to use Simo’s assumption on the deformation field in the three-dimensional (3D) equation of motion and viscoelastic constitutive equations and integrate the thickness information out. A derivation is presented for the elastic constitutive equations for shell. 3D viscoelastic constitutive equation is dimensionally reduced to three constitutive equations for effective membrane stress resultant, effective stress couple resultant, and effective shear stress resultant. Three evolution equations for internal variables emerge in our shell formulation which are derived from the 3D evolution equation of internal variable. If the number of internal variables is <em>p</em>, the total number of degrees of freedom at a material point on the shell is 5 + 8<em>p</em>, viz., three displacement components, two incremental rotation components, six independent components of two 2 × 2 symmetric matrices for internal variables corresponding to effective membrane stress resultant and effective stress couple resultant, and two components for vector internal variable corresponding to effective shear stress resultant. A staggered solution strategy is adopted for the equations of motion and the evolution equations of the internal variables, and the update formulae for the effective membrane stress resultant, effective stress couple resultant, effective shear stress resultant, and internal variables are derived. Linearization of the shell governing equations is carried out, and the Newton-Raphson method is used at every time step for numerical implementation. Numerical simulations are performed on solid cylindrical shell and shell with hole subjected to various loading and boundary conditions and the results are validated with finite element method solutions obtained using ANSYS®. Creep deformation of metasurfaces is also furnished which attests to the efficacy of our proposal.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"444 ","pages":"Article 118169"},"PeriodicalIF":6.9,"publicationDate":"2025-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144338712","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":"Multiphase SPH for surface tension: Resolving zero-surface-energy modes and achieving high Reynolds number simulations","authors":"Shuaihao Zhang ,&nbsp;Sérgio D.N. Lourenço ,&nbsp;Xiangyu Hu","doi":"10.1016/j.cma.2025.118147","DOIUrl":"10.1016/j.cma.2025.118147","url":null,"abstract":"<div><div>This study introduces a Riemann-based Smoothed Particle Hydrodynamics (SPH) framework for the stable and accurate simulation of surface tension in multiphase flows, with density and viscosity ratios as high as 1000 and 100, respectively. The methodology begins with the computation of surface stress, from which the surface tension force is derived, ensuring the conservation of momentum. For the first time, this study identifies the root cause of particle disorder at fluid–fluid interfaces, attributed to a numerical instability defined herein as <em>zero-surface-energy modes</em>. To address this, we propose a novel penalty force method, which eliminates zero-surface-energy modes and significantly enhances the overall stability of the simulation. Importantly, the penalty force correction term is designed to maintain momentum conservation. The stability and accuracy of the proposed framework are validated through several benchmark cases with analytical solutions, performed under both two-dimensional and three-dimensional conditions. Furthermore, the robustness of the method is demonstrated in a three-dimensional high-velocity droplet impact scenario, achieving stable performance at high Reynolds numbers (<span><math><mrow><mi>R</mi><mi>e</mi><mo>=</mo><mn>10000</mn></mrow></math></span>) and Weber numbers (<span><math><mrow><mi>W</mi><mi>e</mi><mo>=</mo><mn>25000</mn></mrow></math></span>). To the best of our knowledge, this represents the first successful demonstration of a mesh-free method achieving stable multiphase flow simulations under such extreme <span><math><mrow><mi>R</mi><mi>e</mi></mrow></math></span> and <span><math><mrow><mi>W</mi><mi>e</mi></mrow></math></span> conditions. A qualitative comparison with previous experimental results is also conducted, confirming the reliability of the simulation outcomes. An open-source code is provided for further in-depth study.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"444 ","pages":"Article 118147"},"PeriodicalIF":6.9,"publicationDate":"2025-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144335662","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":"FFV-PINN: A fast physics-informed neural network with simplified finite volume discretization and residual correction","authors":"Chang Wei ,&nbsp;Yuchen Fan ,&nbsp;Jian Cheng Wong ,&nbsp;Chin Chun Ooi ,&nbsp;Heyang Wang ,&nbsp;Pao-Hsiung Chiu","doi":"10.1016/j.cma.2025.118139","DOIUrl":"10.1016/j.cma.2025.118139","url":null,"abstract":"<div><div>With the growing application of deep learning techniques in computational physics, physics-informed neural networks (PINNs) have emerged as a major research focus. However, today’s PINNs encounter several limitations. Firstly, during the construction of the loss function using automatic differentiation, PINNs often neglect information from neighboring points, which hinders their ability to enforce physical constraints and diminishes their accuracy. Furthermore, issues such as instability and poor convergence persist during PINN training, limiting their applicability to complex fluid dynamics problems. To address these challenges, this paper proposes a fast physics-informed neural network framework that integrates a simplified finite volume method (FVM) and residual correction loss term, referred to as Fast Finite Volume PINN (FFV-PINN). FFV-PINN utilizes a simplified FVM discretization for the convection term, which is one of the main sources of instability, with an accompanying improvement in the dispersion and dissipation behavior. Unlike traditional FVM, which requires careful selection of an appropriate discretization scheme based on the specific physics of the problem such as the sign of the convection term and relative magnitudes of convection and diffusion, the FFV-PINN outputs can be simply and directly harnessed to approximate values on control surfaces, thereby simplifying the discretization process. Moreover, a residual correction loss term is introduced in this study that significantly accelerates convergence and improves training efficiency. To validate the performance of FFV-PINN, we solve a series of challenging problems — including flow in the two-dimensional steady and unsteady lid-driven cavity, three-dimensional steady lid-driven cavity, backward-facing step scenarios, and natural convection at previously unsurpassed Reynolds (<span><math><mrow><mi>R</mi><mi>e</mi></mrow></math></span>) number and Rayleigh (<span><math><mrow><mi>R</mi><mi>a</mi></mrow></math></span>) number, respectively — that are typically difficult for PINNs. Notably, the FFV-PINN can achieve data-free solutions for the lid-driven cavity flow at <span><math><mrow><mi>R</mi><mi>e</mi><mo>=</mo><mn>10000</mn></mrow></math></span> and natural convection at <span><math><mrow><mi>R</mi><mi>a</mi><mo>=</mo><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mn>8</mn></mrow></msup></mrow></math></span> for the first time in PINN literature, even while requiring only 680s and 231s respectively. These results further highlight the effectiveness of FFV-PINN in improving both speed and accuracy, marking another step forward in the progression of PINNs as competitive neural PDE solvers.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"444 ","pages":"Article 118139"},"PeriodicalIF":6.9,"publicationDate":"2025-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144330532","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":"Homogenization in hyperelasticity using Empirically Corrected Cluster Cubature (E3C) hyper-reduction","authors":"Stephan Wulfinghoff","doi":"10.1016/j.cma.2025.118137","DOIUrl":"10.1016/j.cma.2025.118137","url":null,"abstract":"<div><div>Computational homogenization methods open the possibility to simulate engineering structures on two scales simultaneously and to accurately describe complex macroscopic material behavior. Their intrinsically high computational cost can be alleviated through model order reduction methods in combination with hyper-reduction. The recently proposed E3C hyper-reduction method is applied to plane-strain hyperelasticity in this work. It is found that errors in the order of 1% are obtained for reinforced composites with phase contrasts of 10–100 and for porous microstructures with compressible and nearly incompressible material behavior using 10–30 integration points, depending on the application.</div><div>A second topic of the paper is concerned with the remedy of objectivity issues in geometrically nonlinear Galerkin projection applications and the related macroscopic tangent. The resulting simulation tool is provided online and enables the solution of simple two-dimensional two-scale boundary value problems with CPU times in the order of seconds to minutes with training efforts also typically in the minute range.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"444 ","pages":"Article 118137"},"PeriodicalIF":6.9,"publicationDate":"2025-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144321935","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":"Development and validation of an offline multiscale topology optimization framework using interpolated constraint functions","authors":"Brent Bielefeldt ,&nbsp;Richard Beblo ,&nbsp;Kevin Lawson ,&nbsp;Edward Meixner ,&nbsp;Robert Lowe","doi":"10.1016/j.cma.2025.118120","DOIUrl":"10.1016/j.cma.2025.118120","url":null,"abstract":"<div><div>Multiscale structural design is an emerging field within the aerospace community driven by the need for innovative structural concepts capable of fulfilling ever-expanding performance requirements. However, exploring novel material systems or architectures at the preliminary design stage can be inefficient due to potential changes in objectives, boundary conditions, and constraints. Such changes often necessitate a complete redesign at both the material and system levels, and can thus rapidly become intractable. To address this challenge, this paper presents a novel computational framework that seeks to reduce the barrier to entry for multiscale structural design by optimizing the structure sequentially across length scales. Specifically, a precomputed database of potential material-level responses is developed and subsequently passed to a system-level optimization process via a series of constraints. This database can be reused if the system-level problem changes, making it more suitable for the preliminary design stage. An optimized solution to a benchmark structural design problem is presented in the context of both the predicted mechanics of the problem as well as a solution obtained using a traditional structural design tool. A simplified design is then generated and compared against both an experimentally characterized 3D printed structure as well as high-fidelity finite element models, where it is shown that the proposed framework is capable of generating high-performance solutions.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"444 ","pages":"Article 118120"},"PeriodicalIF":6.9,"publicationDate":"2025-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144321937","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":"AK-UL: An active learning kriging method based on uniform sampling and local refinement for efficient reliability analysis with small failure probability","authors":"Yong Pang ,&nbsp;Xiwang He ,&nbsp;Pengwei Liang ,&nbsp;Xueguan Song ,&nbsp;Ziyun Kan","doi":"10.1016/j.cma.2025.118163","DOIUrl":"10.1016/j.cma.2025.118163","url":null,"abstract":"<div><div>This paper introduces a novel active learning kriging-based reliability analysis method that uses uniform sampling and local refinement, termed AK-UL, with a focus on problems involving small failure probabilities. Traditional methods, such as AK-MCS, struggle to identify failure regions efficiently because of the irregular distribution of candidate points and the high computational cost of generating many samples. The AK-UL method overcomes these challenges by introducing a uniform sampling employed in active learning, which is separated from the random samples used for failure probability calculation. This separation ensures a more uniform distribution of training data around the limit state function, thereby enhancing the efficiency of failure region identification. Additionally, a small uniform sample set dramatically reduces the computational cost of the evaluation by the surrogate model in a small failure probability problem. Additionally, a local search process is incorporated to refine candidate points, guiding them closer to the limit state function along the gradient direction of the performance function and overcoming the sparse problem of the small uniform set that is not able to infill the design space. Numerical examples and an engineering case study demonstrate that AK-UL reduces the computational time and improves the accuracy compared with traditional methods. The results highlight that AK-UL is particularly effective for complex reliability analysis problems with small failure probabilities, offering significant computational cost savings while maintaining high accuracy.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"444 ","pages":"Article 118163"},"PeriodicalIF":6.9,"publicationDate":"2025-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144321934","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}