Computer Methods in Applied Mechanics and Engineering最新文献

{"title":"A physics-informed 3D surrogate model for elastic fields in polycrystals","authors":"Lucas Monteiro Fernandes ,&nbsp;Samy Blusseau ,&nbsp;Philipp Rieder ,&nbsp;Matthias Neumann ,&nbsp;Volker Schmidt ,&nbsp;Henry Proudhon ,&nbsp;François Willot","doi":"10.1016/j.cma.2025.117944","DOIUrl":"10.1016/j.cma.2025.117944","url":null,"abstract":"<div><div>We develop a physics-informed neural network pipeline for solving linear elastic micromechanics in three dimensions, on a statistical volume element (SVE) of a polycrystalline material with periodic geometry. The presented approach combines a convolutional neural network containing residual connections with physics-informed non-trainable layers. The latter are introduced to enforce the strain field admissibility and the constitutive law in a way consistent with so-called fast Fourier transform (FFT) algorithms. More precisely, differential operators are discretized by finite differences in accordance with the Green operator used in FFT computations and treated as convolutions with fixed kernels. The deterministic relationship between crystalline orientations and stiffness tensors is transferred to the network by an additional non-trainable layer. A loss function dependent on the divergence of the predicted stress field allows for updating the neural network’s parameters without further supervision from ground truth data. The surrogate model is trained on untextured synthetic polycrystalline SVEs with periodic boundary conditions, realized from a stochastic 3D microstructure model based on random tessellations. Once trained, the network is able to predict the periodic part of the displacement field from the crystalline orientation field (represented as unit quaternions) of an SVE. The proposed self-supervised pipeline is compared to a similar one trained with a data-driven loss function instead. Further, the accuracy of both models is analyzed by applying them to microstructures larger than the training inputs, as well as to SVEs generated by the stochastic 3D microstructure model, utilizing various different parameters. We find that the self-supervised pipeline yields more accurate predictions than the data-driven one, at the expense of a longer training. Finally, we discuss how the trained surrogate model can be used to solve certain inverse problems on polycrystalline domains by gradient descent.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"441 ","pages":"Article 117944"},"PeriodicalIF":6.9,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143746833","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":"Neural networks meet phase-field: A hybrid fracture model","authors":"Franz Dammaß ,&nbsp;Karl A. Kalina ,&nbsp;Markus Kästner","doi":"10.1016/j.cma.2025.117937","DOIUrl":"10.1016/j.cma.2025.117937","url":null,"abstract":"<div><div>We present a hybrid phase-field model of fracture at finite deformation and its application to quasi-incompressible, hyperelastic rubber. The key idea is to combine the predictive capability of the well-established phase-field approach to fracture with a physics-augmented neural network (PANN) that serves as a flexible, high-fidelity model of the response of the bulk material. To this end, recently developed neural network approaches are developed further to better meet specific requirements of the phase-field framework. In particular, a novel architecture for a hyperelastic PANN is presented, that enables a decoupled description of the volumetric and the isochoric response based on a corresponding additive decomposition of the Helmholtz free energy. This is of particular interest when modelling fracture of soft quasi-incompressible solids with the phase-field approach, where a weakening of the incompressibility constraint in fracturing material is required. In addition, such an additive decomposition of the free energy is a prerequisite for the application of several <em>split methods</em>, i.e. decompositions of free energy into degraded and non-degraded portions, which can improve model behaviour under multiaxial stress states. For the formulation of the hybrid model, we define a pseudo-potential, in which the phase-field ansatz for fracture dissipation is combined with a polyconvex PANN model of the isochoric response. The PANN is formulated in polyconvex isochoric invariants. As a result, it can be shown that the PANN fulfils all desirable properties of hyperelastic potentials by construction. In particular, it is proven to be zero and take a global minimum for the undeformed state, which does also hold in case of deviations away from incompressibility. Moreover, a classical mixed displacement-pressure formulation of incompressibility based on the perturbed Lagrangian approach is included. Thereby, a relaxation of the incompressibility constraint in fracturing material is applied. This weakening of incompressibility is shown in to be essential in order to prevent numerical issues in the simulation, which would otherwise arise from the presence of zones showing both negligible isochoric stiffness and very high resistance against volume changes. The model is implemented in the finite element framework <em>FEniCSx</em> and studied by means of several examples. To this end, training and validation of the PANN are performed based on experimental data from the literature, and the hybrid fracture model is then verified against results of fracture experiments.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"440 ","pages":"Article 117937"},"PeriodicalIF":6.9,"publicationDate":"2025-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143734853","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":"PIGODE: A novel model for efficient surrogate modeling in complex geometric structures","authors":"Chengyu Lu ,&nbsp;Zhaoxi Hong ,&nbsp;Xiuju Song ,&nbsp;Zhixin Liu ,&nbsp;Bingtao Hu ,&nbsp;Yixiong Feng ,&nbsp;Jianrong Tan","doi":"10.1016/j.cma.2025.117930","DOIUrl":"10.1016/j.cma.2025.117930","url":null,"abstract":"<div><div>Physics-Informed Neural Network (PINN), as a novel neural network model, is known for its strong interpretability and generalization capabilities, making it widely used in surrogate models and various engineering scenarios. While traditional PINN has achieved good results in simple geometric scenarios, there is limited research on its application to complex geometric structures. Additionally, PINN integrates boundary conditions into the loss function, requiring retraining model when boundary conditions change. To address these issues, we propose a new Physics-Informed Graph Ordinary Differential Equation (PIGODE) model for constructing surrogate models in complex geometric structures. The Peridynamic Differential Operator (PDDO) is extended to a PIGODE which is defined on graph data structure, and a PDDO-based message passing layer is developed to replace automatic differentiation (AD). This method precomputes Peridynamic weights, thereby avoiding additional computational overhead during model training. Furthermore, boundary conditions are embedded into the model input to address the need for dynamically modifying boundary conditions in surrogate models. Through comparative studies with existing PINN solvers, we validate the effectiveness of the proposed model, demonstrating its superior performance on complex geometric structures. Additionally, this model is applied to practical engineering scenarios, specifically constructing a temperature field surrogate model for the conical picks of a tunnel boring machine. The research results indicate that the proposed PIGODE model not only enhances the interpretability and efficiency of surrogate models but also extends their applicability to complex geometric structures in engineering.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"440 ","pages":"Article 117930"},"PeriodicalIF":6.9,"publicationDate":"2025-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143734852","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 new paradigm for hybrid reliability-based design optimization: From β-circle to β-cylinder","authors":"Peng Hao,&nbsp;Zehao Cui,&nbsp;Bingyi Du,&nbsp;Hao Yang,&nbsp;Yue Zhang","doi":"10.1016/j.cma.2025.117954","DOIUrl":"10.1016/j.cma.2025.117954","url":null,"abstract":"<div><div>A new paradigm for hybrid reliability-based design optimization (HRBDO) is proposed. The key innovation lies in expanding the traditional <em>β</em>-circle into a <em>β</em>-cylinder along the interval dimensions, integrating both random and interval dimensional information. Building upon this theoretical foundation, a novel interval-based dimensional expansion <em>β</em>-cylinder active learning (IBAL) method is proposed, transforming the complex double-loop reliability calculation into an efficient single-loop process. The method employs Kriging models to replace expensive physical responses. Unlike traditional sampling techniques, the IBAL method focuses exclusively on predicted means and deviations on the <em>β</em>-cylinder to guide the Kriging models of performance functions, efficiently identifying the Most Probable Point (MPP). This approach effectively addresses challenges including interval dimensions nonlinearity, multiple extreme points, and multiple MPPs. In HRBDO, the method incorporates an active constraint screening (ACS) mechanism and an MPP objective function isosurface active learning (MIAL) method to enhance computational efficiency and avoid convergence to local optima. The effectiveness of the proposed method is validated through four mathematical examples and one engineering case study.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"440 ","pages":"Article 117954"},"PeriodicalIF":6.9,"publicationDate":"2025-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143725542","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 model-constrained discontinuous Galerkin Network (DGNet) for compressible Euler equations with out-of-distribution generalization","authors":"Hai Van Nguyen ,&nbsp;Jau-Uei Chen ,&nbsp;Tan Bui-Thanh","doi":"10.1016/j.cma.2025.117912","DOIUrl":"10.1016/j.cma.2025.117912","url":null,"abstract":"<div><div>Real-time accurate solutions of large-scale complex dynamical systems are critically needed for control, optimization, uncertainty quantification, and decision-making in practical engineering and science applications, particularly in digital twin contexts. Recent research on hybrid approaches combining numerical methods and machine learning in end-to-end training has shown significant improvements over either approach alone. However, using neural networks as surrogate models generally exhibits limitations in generalizability over different settings and in capturing the evolution of solution discontinuities. In this work, we develop a model-constrained discontinuous Galerkin Network (<span>DGNet</span>) approach, a significant extension to our previous work (Nguyen and Bui-Thanh, 2022), for compressible Euler equations with out-of-distribution generalization. The core of <span>DGNet</span>is the synergy of several key strategies: (i) leveraging time integration schemes to capture temporal correlation and taking advantage of neural network speed for computation time reduction. This is the key to the temporal discretization-invariant property of <span>DGNet</span>; (ii) employing a model-constrained approach to ensure the learned tangent slope satisfies governing equations; (iii) utilizing a DG-inspired architecture for GNN where edges represent Riemann solver surrogate models and nodes represent volume integration correction surrogate models, enabling capturing discontinuity capability, aliasing error reduction, and mesh discretization generalizability. Such a design allows <span>DGNet</span>to learn the DG spatial discretization accurately; (iv) developing an input normalization strategy that allows surrogate models to generalize across different initial conditions, geometries, meshes, boundary conditions, and solution orders. In fact, the normalization is the key to spatial discretization-invariance for <span>DGNet</span>; and (v) incorporating a data randomization technique that not only implicitly promotes agreement between surrogate models and true numerical models up to second-order derivatives, ensuring long-term stability and prediction capacity, but also serves as a data generation engine during training, leading to enhanced generalization on unseen data. To validate the theoretical results, effectiveness, stability, and generalizability of our novel <span>DGNet</span>approach, we present comprehensive numerical results for 1D and 2D compressible Euler equation problems, including Sod Shock Tube, Lax Shock Tube, Isentropic Vortex, Forward Facing Step, Scramjet, Airfoil, Euler Benchmarks, Double Mach Reflection, and a Hypersonic Sphere Cone benchmark.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"440 ","pages":"Article 117912"},"PeriodicalIF":6.9,"publicationDate":"2025-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143715432","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 generalized non-hourglass updated Lagrangian formulation for SPH solid dynamics","authors":"Shuaihao Zhang ,&nbsp;Dong Wu ,&nbsp;Sérgio D.N. Lourenço ,&nbsp;Xiangyu Hu","doi":"10.1016/j.cma.2025.117948","DOIUrl":"10.1016/j.cma.2025.117948","url":null,"abstract":"<div><div>Hourglass modes, characterized by zigzag particle and stress distributions, are a common numerical instability encountered when simulating solid materials with updated Lagrangian smoothed particle hydrodynamics (ULSPH). While recent solutions have effectively addressed this issue in elastic materials using an essentially non-hourglass formulation, extending these solutions to plastic materials with more complex constitutive equations has proven challenging due to the need to express shear forces in the form of a velocity Laplacian. To address this, a generalized non-hourglass formulation is proposed within the ULSPH framework, suitable for both elastic and plastic materials. Specifically, a penalty force is introduced into the momentum equation to resolve the disparity between the linearly predicted and actual velocity differences of neighboring particle pairs, thereby mitigating the hourglass issue. The stability, convergence, and accuracy of the proposed method are validated through a series of classical elastic and plastic cases, with a dual-criterion time-stepping scheme to improve computational efficiency. The results show that the present method not only matches or even surpasses the performance of the recent essentially non-hourglass formulation in elastic cases but also performs well in plastic scenarios.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"440 ","pages":"Article 117948"},"PeriodicalIF":6.9,"publicationDate":"2025-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143725541","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The Shifted Boundary Method for contact problems","authors":"Kangan Li ,&nbsp;Andrea Gorgi ,&nbsp;Riccardo Rossi ,&nbsp;Guglielmo Scovazzi","doi":"10.1016/j.cma.2025.117940","DOIUrl":"10.1016/j.cma.2025.117940","url":null,"abstract":"<div><div>We propose an embedded algorithm for contact mechanics based on the Shifted Boundary Method. The contact conditions are applied on a surrogate contact surface in proximity of the true contact surface and Taylor expansions are used to change (shift) both their value and location. This approach is robust, accurate, and avoids integrating the variational formulation on cut cells and related numerical instabilities. Computational experiments in both two and three dimensions are provided to demonstrate the performance of our methodology. The proposed approach offers an advantage whenever bodies of very complex shape come into contact, especially when the shapes are not represented using standard Computer Aided Design (CAD) formats. In all these situations, body-fitted grid generation may become extremely time consuming or completely unfeasible.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"440 ","pages":"Article 117940"},"PeriodicalIF":6.9,"publicationDate":"2025-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143715430","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":"Teaching artificial intelligence to perform rapid, resolution-invariant grain growth modeling via Fourier Neural Operator","authors":"Iman Peivaste ,&nbsp;Ahmed Makradi ,&nbsp;Salim Belouettar","doi":"10.1016/j.cma.2025.117945","DOIUrl":"10.1016/j.cma.2025.117945","url":null,"abstract":"<div><div>Microstructural evolution, particularly grain growth, plays a critical role in shaping the physical, optical, and electronic properties of materials. Traditional phase-field modeling accurately simulates these phenomena but is computationally intensive, especially for large systems and fine spatial resolutions. While machine learning approaches have been employed to accelerate simulations, they often struggle with resolution dependence and generalization across different grain scales. This study introduces a novel approach utilizing Fourier Neural Operator (FNO) to achieve resolution-invariant modeling of microstructure evolution in multi-grain systems. FNO operates in the Fourier space and can inherently handle varying resolutions by learning mappings between function spaces. By integrating FNO with the phase-field method, we developed a surrogate model that significantly reduces computational costs while maintaining high accuracy across different spatial scales. We generated a comprehensive dataset from phase-field simulations using the Fan–Chen model, capturing grain evolution over time. Data preparation involved creating input–output pairs with a time shift, allowing the model to predict future microstructures based on current and past states. The FNO-based neural network was trained using sequences of microstructures and demonstrated remarkable accuracy in predicting long-term evolution, even for unseen configurations and higher-resolution grids not encountered during training.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"440 ","pages":"Article 117945"},"PeriodicalIF":6.9,"publicationDate":"2025-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143705337","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":"SK-PINN: Accelerated physics-informed deep learning by smoothing kernel gradients","authors":"Cunliang Pan ,&nbsp;Chengxuan Li ,&nbsp;Yu Liu ,&nbsp;Yonggang Zheng ,&nbsp;Hongfei Ye","doi":"10.1016/j.cma.2025.117956","DOIUrl":"10.1016/j.cma.2025.117956","url":null,"abstract":"<div><div>The automatic differentiation (AD) in the vanilla physics-informed neural networks (PINNs) is the computational bottleneck for the high-efficiency analysis. The concept of derivative discretization in smoothed particle hydrodynamics (SPH) can provide an accelerated training method for PINNs. In this paper, smoothing kernel physics-informed neural networks (SK-PINNs) are established, which solve differential equations using smoothing kernel discretization. It is a robust framework capable of solving problems in the computational mechanics of complex domains. When the number of collocation points gradually increases, the training speed of SK-PINNs significantly surpasses that of vanilla PINNs. In cases involving large collocation point sets or higher-order problems, SK-PINN training can be up to tens of times faster than vanilla PINN. Additionally, analysis using neural tangent kernel (NTK) theory shows that the convergence rates of SK-PINNs are consistent with those of vanilla PINNs. The superior performance of SK-PINNs is demonstrated through various examples, including regular and complex domains, as well as forward and inverse problems in fluid dynamics and solid mechanics.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"440 ","pages":"Article 117956"},"PeriodicalIF":6.9,"publicationDate":"2025-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143715429","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":"Information entropy regularization method for structural identification with large-scale damaged parameters","authors":"Yifei Wang,&nbsp;Xiaojun Wang,&nbsp;Geyong Cao","doi":"10.1016/j.cma.2025.117947","DOIUrl":"10.1016/j.cma.2025.117947","url":null,"abstract":"<div><div>With the advancement of structural health monitoring technology, the increasing precision in modeling, scalability of model parameters, and complexity of external environments have introduced significant challenges to damage identification. Notably, the ill-posed nature of large-scale parameter identification from refined models has become a critical technical challenge. Regularization methods are widely employed to mitigate ill-posedness and control the complexity of identification problems. Traditional regularization methods often penalize imbalances in damage parameters, leading to errors and suboptimal convergence, failing to accurately reflect actual damage conditions. To address these challenges, an information entropy regularization term is introduced to capture the distribution of structural damage location and severity. By integrating regularization term with an adjoint sensitivity optimization algorithm, a refined iterative approach is developed to manage large-scale damage parameter identification from detailed finite element models. Numerical analyses on a 2D stress plate and a 3D wing, along with experimental validation on impact damage of clamped plates, demonstrate the accuracy and effectiveness of the proposed method.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"440 ","pages":"Article 117947"},"PeriodicalIF":6.9,"publicationDate":"2025-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143705339","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}