Computer Methods in Applied Mechanics and Engineering最新文献

{"title":"Reducing parameter tuning in topology optimization of flow problems using a Darcy and Forchheimer penalization","authors":"M.J.B. Theulings ,&nbsp;L. Noël ,&nbsp;M. Langelaar ,&nbsp;R. Maas","doi":"10.1016/j.cma.2025.118027","DOIUrl":"10.1016/j.cma.2025.118027","url":null,"abstract":"<div><div>In density-based topology optimization of flow problems, flow in the solid domain is generally inhibited using a penalization approach. Setting an appropriate maximum magnitude for the penalization traditionally requires manual tuning to find an acceptable compromise between flow solution accuracy and design convergence. In this work, three penalization approaches are examined, the Darcy (D), the Darcy with Forchheimer (DF), and the newly proposed Darcy with filtered Forchheimer (DFF) approach. Parameter tuning is reduced by analytically deriving an appropriate penalization magnitude for accuracy of the flow solution. The Forchheimer penalization is found to be required to reliably predict the accuracy of the flow solution. The state-of-the-art D and DF approaches are improved by developing the novel DFF approach, based on a spatial average of the velocity magnitude. In comparison, the parameter selection in the DFF approach is more reliable, as convergence of the flow solution and objective convexity are more predictable. Moreover, a continuation approach on the maximum penalization magnitude is derived by numerical inspection of the convexity of the pressure drop response. Using two-dimensional optimization benchmarks, the DFF approach reliably finds accurate flow solutions and is less prone to converge to inferior local optima.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"443 ","pages":"Article 118027"},"PeriodicalIF":6.9,"publicationDate":"2025-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144116417","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":"Parallel constrained Bayesian optimization via batched Thompson sampling with enhanced active learning process for reliability-based design optimization","authors":"Thu Van Huynh ,&nbsp;Sawekchai Tangaramvong ,&nbsp;Wei Gao","doi":"10.1016/j.cma.2025.118066","DOIUrl":"10.1016/j.cma.2025.118066","url":null,"abstract":"<div><div>This paper proposes an effective and robust decoupled approach for addressing reliability-based design optimization (RBDO) problems. The method iteratively performs a parallel constrained Bayesian optimization (PCBO) with deterministic parameters based on the most probable point (MPP) underpinning limit-state functions (LSFs) sequentially updated through an enhanced active learning-based reliability evaluation process. During the deterministic optimization process, the PCBO integrates with a trust region approach that considers a collection of simultaneous local optimization runs, each guided by an independent Gaussian process (GP) model. The trust region approach leverages a well-established selection strategy in reinforcement learning, known as the multi-armed bandit, to allocate samples across local trust regions and decide which local optimization runs to continue. In particular, batched Thompson sampling is adopted as an acquisition function to determine the optimal design by selecting a batch of candidate points from local trust regions via sampling from the posterior of the independent GP models, with the batch evaluations executed in parallel. In the reliability analysis, the GP model estimates, from the optimal design offered by the PCBO, the spectrum of LSFs under random parameters, and hence allows an efficient failure probability estimation through a cross-entropy (CE) method with Gaussian mixture (GM) clustering without direct performance function evaluations. By leveraging information from the GM clustering, an enhanced active learning mechanism is developed to strategically refine the GP model by generating multiple informative points in the clustered regions with the largest uncertainty and high-reliability sensitivity, thus improving the accuracy of failure probability predictions. Eventually, an invertible cross-entropy (iCE) method is proposed to decouple the reliability analysis from the optimization process, enabling the update of the new MPP assigned for the PCBO to identify the new optimal design. The proposed method significantly alleviates computational costs for both deterministic design optimization and reliability analysis and quickly converges to the optimal RBDO design. Three numerical examples are provided to illustrate the efficiency and robustness of the proposed approach in addressing the RBDO problem.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"443 ","pages":"Article 118066"},"PeriodicalIF":6.9,"publicationDate":"2025-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144106731","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 unit cell based multilevel substructuring method for fast vibration response calculations of finite metamaterial structures","authors":"Fei Qu ,&nbsp;Lucas Van Belle ,&nbsp;Wim Desmet ,&nbsp;Elke Deckers","doi":"10.1016/j.cma.2025.118069","DOIUrl":"10.1016/j.cma.2025.118069","url":null,"abstract":"<div><div>Locally resonant metamaterial structures have gained significant attention across multiple engineering disciplines due to their ability to exhibit vibration stop bands not found in regular materials. These structures are composed of an assembly of unit cells, which are often discretized into large finite element models due to their sub-wavelength nature and intricate design. Moreover, due to the contribution of local dynamics of resonator modes, the overall modal density of the entire structure is proportional to the number of unit cells multiplying the number of resonator modes. Therefore, high-fidelity frequency response analyses of such large-scale structures with high modal density are typically computationally expensive, making them impractical for structural design. In order to efficiently solve these models, the multilevel substructuring method is often used for a high level of dimensional reduction while balancing the errors associated with truncated component mode synthesis. However, accurate and efficient modeling of complex dynamics of metamaterial structures containing a large number unit cells still poses challenges for conventional multilevel substructuring method. Three main issues arise in this context: (i) Block Gaussian elimination becomes inefficient for large models; (ii) Ignoring mass coupling and load information during the reduction weakens accuracy, especially around the critical stop-band frequencies; (iii) Existing error estimation is not directly applicable to frequency response analyses. This work overcomes these challenges by introducing a multilevel assembly strategy, an improved interface reduction and a heuristic truncation criterion. Doing so, these advancements facilitate efficient and accurate frequency response analyses for assemblies with many unit cells, thereby enabling the practical design of locally resonant metamaterial structures in various engineering applications.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"443 ","pages":"Article 118069"},"PeriodicalIF":6.9,"publicationDate":"2025-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144098757","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":"Deep mechanics prior - for the multiscale finite element method","authors":"Senlin Huo,&nbsp;Yong Zhao,&nbsp;Bingxiao Du,&nbsp;Zeyu Zhang,&nbsp;Yaqi Cao,&nbsp;Yiyu Du","doi":"10.1016/j.cma.2025.118073","DOIUrl":"10.1016/j.cma.2025.118073","url":null,"abstract":"<div><div>The Multiscale Finite Element Method (MsFEM) decomposes the problem of solving partial differential equations with multiscale characteristics into two subproblems at two discrete resolution levels, i.e., the macroscopic one on a coarse mesh and the microscopic one on a fine mesh. The microscopic subproblems are used for constructing the Equivalent Stiffness Matrices (ESMs) of the coarse elements, and the calculation of them is the most time-consuming part in the MsFEM. Using a pure data-driven model that is independent of mechanical knowledge to directly predict ESMs, even with a pretty high-precision model, the outputs may still lack basic physical rationality. The core challenge lies in the strict assurance of the basic physical characteristics of the predicted ESMs, that is, the Rigid Displacement Properties (RDPs), which require the ESM to produce zero-strain energy under rigid body displacement. In terms of the mechanical essence, this requirement is closely correlated with the physical meaning of the eigenvectors and eigenvalues of the ESMs. Based on the above deep mechanics prior knowledge, a surrogate model based on Deep Learning (DL) and orthogonal decomposition techniques is developed. The inputs of the DL neural networks are the geometry parameters of the coarse element, while the outputs are eigenvectors and eigenvalues of the ESM. The dimensions of the outputs are reduced by directly specifying a specific number of zero eigenvalues and eigenvectors. The RDPs are embedded in the reconstruction calculation of the ESMs based on the outputs in a structured manner, assuring the physical reasonability of the predictions. Numerical examples demonstrate the performance of the proposed method.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"443 ","pages":"Article 118073"},"PeriodicalIF":6.9,"publicationDate":"2025-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144098802","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 physics-consistent material behavior from dynamic displacements","authors":"Zhichao Han ,&nbsp;Mohit Pundir ,&nbsp;Olga Fink ,&nbsp;David S. Kammer","doi":"10.1016/j.cma.2025.118040","DOIUrl":"10.1016/j.cma.2025.118040","url":null,"abstract":"<div><div>Accurately modeling the mechanical behavior of materials is crucial for numerous engineering applications. The quality of these models depends directly on the accuracy of the constitutive law that defines the stress–strain relation. However, discovering these constitutive material laws remains a significant challenge, in particular when only material deformation data is available. To address this challenge, unsupervised machine learning methods have been proposed to learn the constitutive law from deformation data. Nonetheless, existing approaches have several limitations: they either fail to ensure that the learned constitutive relations are consistent with physical principles, or they rely on boundary force data for training which are unavailable in many in-situ scenarios. Here, we introduce a machine learning approach to learn physics-consistent constitutive relations solely from material deformation without boundary force information. This is achieved by considering a dynamic formulation rather than static equilibrium data and applying an input convex neural network (ICNN). We validate the effectiveness of the proposed method on a diverse range of hyperelastic material laws. We demonstrate that it is robust to a significant level of noise and that it converges to the ground truth with increasing data resolution. We also show that the model can be effectively trained using a displacement field from a subdomain of the test specimen and that the learned constitutive relation from one material sample is transferable to other samples with different geometries. The developed methodology provides an effective tool for discovering constitutive relations. It is, due to its design based on dynamics, particularly suited for applications to strain-rate-dependent materials and situations where constitutive laws need to be inferred from <em>in-situ</em> measurements without access to global force data.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"443 ","pages":"Article 118040"},"PeriodicalIF":6.9,"publicationDate":"2025-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144098755","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 cohesive-zone model for simulation of mixed-mode interfacial and bulk fracture in heterogeneous materials with directional energy decomposition","authors":"Pei-Liang Bian ,&nbsp;Qinghui Liu ,&nbsp;Heng Zhang ,&nbsp;Hai Qing ,&nbsp;Siegfried Schmauder ,&nbsp;Tiantang Yu","doi":"10.1016/j.cma.2025.118062","DOIUrl":"10.1016/j.cma.2025.118062","url":null,"abstract":"<div><div>Interfacial debonding, a critical failure mechanism in heterogeneous materials, is often characterized by mixed-mode fracture. This study develops a numerical framework to simulate bulk and interfacial fractures in composite materials. A phase-field cohesive zone model, incorporating a directional energy decomposition scheme and a modified toughness method, is employed to capture complex fracture behaviors. A level-set method explicitly defines interface positions, while an adaptive mesh refinement strategy enhances computational efficiency. Numerical examples validate the model’s accuracy and efficiency in predicting mixed-mode crack propagation and interfacial debonding. This work provides a robust and efficient approach to simulate complex fracture phenomena in heterogeneous materials, especially for the mixed-mode fracture.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"443 ","pages":"Article 118062"},"PeriodicalIF":6.9,"publicationDate":"2025-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144098754","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":"Mesh-based super-resolution of fluid flows with multiscale graph neural networks","authors":"Shivam Barwey ,&nbsp;Pinaki Pal ,&nbsp;Saumil Patel ,&nbsp;Riccardo Balin ,&nbsp;Bethany Lusch ,&nbsp;Venkatram Vishwanath ,&nbsp;Romit Maulik ,&nbsp;Ramesh Balakrishnan","doi":"10.1016/j.cma.2025.118072","DOIUrl":"10.1016/j.cma.2025.118072","url":null,"abstract":"<div><div>A graph neural network (GNN) approach is introduced in this work which enables mesh-based three-dimensional super-resolution of fluid flows. In this framework, the GNN is designed to operate not on the full mesh-based field at once, but on localized meshes of elements (or cells) directly. To facilitate mesh-based GNN representations in a manner similar to spectral (or finite) element discretizations, a baseline GNN layer (termed a message passing layer, which updates local node properties) is modified to account for synchronization of coincident graph nodes, rendering compatibility with commonly used element-based mesh connectivities. The architecture is multiscale in nature, and is comprised of a combination of coarse-scale and fine-scale message passing layer sequences (termed processors) separated by a graph unpooling layer. The coarse-scale processor embeds a query element (alongside a set number of neighboring coarse elements) into a single latent graph representation using coarse-scale synchronized message passing over the element neighborhood, and the fine-scale processor leverages additional message passing operations on this latent graph to correct for interpolation errors. Demonstration studies are performed using hexahedral mesh-based data from Taylor–Green Vortex and backward-facing step flow simulations at Reynolds numbers of 1600 and 3200. Through analysis of both global and local errors, the results ultimately show how the GNN is able to produce accurate super-resolved fields compared to targets in both coarse-scale and multiscale model configurations. Reconstruction errors for fixed architectures were found to increase in proportion to the Reynolds number. Geometry extrapolation studies on a separate cavity flow configuration show promising cross-mesh capabilities of the super-resolution strategy.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"443 ","pages":"Article 118072"},"PeriodicalIF":6.9,"publicationDate":"2025-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144098756","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":"Point cloud neural operator for parametric PDEs on complex and variable geometries","authors":"Chenyu Zeng ,&nbsp;Yanshu Zhang ,&nbsp;Jiayi Zhou ,&nbsp;Yuhan Wang ,&nbsp;Zilin Wang ,&nbsp;Yuhao Liu ,&nbsp;Lei Wu ,&nbsp;Daniel Zhengyu Huang","doi":"10.1016/j.cma.2025.118022","DOIUrl":"10.1016/j.cma.2025.118022","url":null,"abstract":"<div><div>Surrogate models are critical for accelerating computationally expensive simulations in science and engineering, particularly for solving parametric partial differential equations (PDEs). Developing practical surrogate models poses significant challenges, particularly in handling geometrically complex and variable domains, which are often discretized as point clouds. In this work, we systematically investigate the formulation of neural operators — maps between infinite-dimensional function spaces — on point clouds to better handle complex and variable geometries while mitigating discretization effects. We introduce the Point Cloud Neural Operator (PCNO), designed to efficiently approximate solution maps of parametric PDEs on such domains. We evaluate the performance of PCNO on a range of pedagogical PDE problems, focusing on aspects such as boundary layers, adaptively meshed point clouds, and variable domains with topological variations. Its practicality is further demonstrated through three-dimensional applications, such as predicting pressure loads on various vehicle types and simulating the inflation process of intricate parachute structures.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"443 ","pages":"Article 118022"},"PeriodicalIF":6.9,"publicationDate":"2025-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144098800","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 modeling for electromechanical fracture in flexoelectric materials using multi-patch isogeometric analysis","authors":"Haozhi Li ,&nbsp;Tiantang Yu ,&nbsp;Zhaowei Liu ,&nbsp;Jiaping Sun ,&nbsp;Leilei Chen","doi":"10.1016/j.cma.2025.118070","DOIUrl":"10.1016/j.cma.2025.118070","url":null,"abstract":"<div><div>The fracture of flexoelectric materials involves strain gradients, which pose challenges for theoretical and numerical analysis. The phase-field model (PFM) is highly effective for simulating crack propagation. However, PFM within the finite element method (FEM) framework faces certain challenges in simulating the fracture behavior of flexoelectric materials since the conventional FEM can only provide <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>0</mn></mrow></msup></math></span> continuity. In this study, an adaptive PFM within multi-patch isogeometric analysis using polynomial splines over hierarchical T-meshes (PHT-splines) is proposed to simulate electromechanical fracture in flexoelectric materials. The PHT-splines functions feature higher-order continuity and can effectively discretize the strain gradient. All computational models are accurately modeled using multiple PHT-splines patches. The continuity of field variables such as displacement, electric potential, and phase field at the coupling edge is ensured using Nitsche’s method. To effectively compute the crack-driving force, the generalized Miehe decomposition method is employed. To alleviate the computational burden, a mesh refinement adaptive scheme based on user-defined thresholds for the phase field is used. The proposed method’s accuracy, reliability, and robustness are demonstrated using several fracture simulations.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"443 ","pages":"Article 118070"},"PeriodicalIF":6.9,"publicationDate":"2025-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144098801","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":"Quantum computer formulation of the FKP-operator eigenvalue problem for probabilistic learning on manifolds","authors":"Christian Soize ,&nbsp;Loïc Joubert-Doriol ,&nbsp;Artur F. Izmaylov","doi":"10.1016/j.cma.2025.118080","DOIUrl":"10.1016/j.cma.2025.118080","url":null,"abstract":"<div><div>We present a quantum computing formulation to address a challenging problem in the development of probabilistic learning on manifolds (PLoM). It involves solving the spectral problem of the high-dimensional Fokker–Planck (FKP) operator, which remains beyond the reach of classical computing. Our ultimate goal is to develop an efficient approach for practical computations on quantum computers. For now, we focus on an adapted formulation tailored to quantum computing. The methodological aspects covered in this work include the construction of the FKP equation, where the invariant probability measure is derived from a training dataset, and the formulation of the eigenvalue problem for the FKP operator. The eigen equation is transformed into a Schrödinger equation with a potential <span><math><mi>V</mi></math></span>, a non-algebraic function that is neither simple nor a polynomial representation. To address this, we propose a methodology for constructing a multivariate polynomial approximation of <span><math><mi>V</mi></math></span>, leveraging polynomial chaos expansion within the Gaussian Sobolev space. This approach preserves the algebraic properties of the potential and adapts it for quantum algorithms. The quantum computing formulation employs a finite basis representation, incorporating second quantization with creation and annihilation operators. Explicit formulas for the Laplacian and potential are derived and mapped onto qubits using Pauli matrix expressions. Additionally, we outline the design of quantum circuits and the implementation of measurements to construct and observe specific quantum states. Information is extracted through quantum measurements, with eigenstates constructed and overlap measurements evaluated using universal quantum gates.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"443 ","pages":"Article 118080"},"PeriodicalIF":6.9,"publicationDate":"2025-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144098759","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}