Computer Methods in Applied Mechanics and Engineering最新文献

{"title":"Accurate, scalable, and efficient Bayesian optimal experimental design with derivative-informed neural operators","authors":"Jinwoo Go,&nbsp;Peng Chen","doi":"10.1016/j.cma.2025.117845","DOIUrl":"10.1016/j.cma.2025.117845","url":null,"abstract":"<div><div>We consider optimal experimental design (OED) problems in selecting the most informative observation sensors to estimate model parameters in a Bayesian framework. Such problems are computationally prohibitive when the parameter-to-observable (PtO) map is expensive to evaluate, the parameters are high-dimensional, and the optimization for sensor selection is combinatorial and high-dimensional. To address these challenges, we develop an accurate, scalable, and efficient computational framework based on derivative-informed neural operators (DINO). We propose to use derivative-informed dimension reduction to reduce the parameter dimensions, based on which we train DINO with derivative information as an accurate and efficient surrogate for the PtO map and its derivative. Moreover, we derive DINO-enabled efficient formulations in computing the maximum a posteriori (MAP) point, the eigenvalues of approximate posterior covariance, and three commonly used optimality criteria for the OED problems. Furthermore, we provide detailed error analysis for the approximations of the MAP point, the eigenvalues, and the optimality criteria. We also propose a modified swapping greedy algorithm for the sensor selection optimization and demonstrate that the proposed computational framework is scalable to preserve the accuracy for increasing parameter dimensions and achieves high computational efficiency, with an over 1000<span><math><mo>×</mo></math></span> speedup accounting for both offline construction and online evaluation costs, compared to high-fidelity Bayesian OED solutions for a three-dimensional nonlinear convection–diffusion–reaction example with tens of thousands of parameters at the same resolution.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"438 ","pages":"Article 117845"},"PeriodicalIF":6.9,"publicationDate":"2025-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143474958","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":"The rationality of using dynamic relaxation method for failure simulation in peridynamics","authors":"Xiaohua Huang ,&nbsp;Ting Hu ,&nbsp;Yanli Jin ,&nbsp;Shuang Li ,&nbsp;Dong Yang ,&nbsp;Zhi Zheng","doi":"10.1016/j.cma.2025.117847","DOIUrl":"10.1016/j.cma.2025.117847","url":null,"abstract":"<div><div>In peridynamics, a large amount of research related to material failure has applied the dynamic relaxation (DR) method under static or quasi-static loading conditions. However, as a pseudo-dynamic method that converts static problems into dynamic problems by introducing fictitious inertia and damping terms, the intermediate attenuation process of the DR method is not realistic. Whether it is truly suitable for simulating the irreversible mechanical behavior of material failure, which closely depends on the real process and has significant dynamic effects in the later stage of failure, is still a debatable issue. This article first derives the prerequisite for applying the DR method to solve static or quasi-static problems, which is to ensure that the load and system stiffness remain constant during the solving process. However, material damage will inevitably weaken the stiffness of the system and break this prerequisite. In view of this, using explicit dynamic algorithm for failure simulation is worthy of being reconsidered. Secondly, the DR method is used to simulate the failure of <em><span>l</span></em>-shaped concrete specimen, and it is found that selecting different fictitious damping coefficients may lead to different crack propagation paths, resulting in uncertainty in the simulation results. It is also found that due to the use of fictitious damping in the DR method to suppress the acceleration effect in the accelerated failure stage, the dynamic effect of the system is not fully utilized, which leads to distortion of simulation results. At last, a two-stage joint algorithm is proposed suitable for material failure problems under static or quasi-static loading conditions. The DR method is only applied to the continuous deformation stage of materials without any damage, while the explicit dynamic algorithm is applied to the crack initiation and propagation stage after damage occurs. The numerical examples illustrate the effectiveness of the joint algorithm.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"438 ","pages":"Article 117847"},"PeriodicalIF":6.9,"publicationDate":"2025-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143479185","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":"Univariate conditional variational autoencoder for morphogenic pattern design in frontal polymerization-based manufacturing","authors":"Qibang Liu ,&nbsp;Pengfei Cai ,&nbsp;Diab Abueidda ,&nbsp;Sagar Vyas ,&nbsp;Seid Koric ,&nbsp;Rafael Gomez-Bombarelli ,&nbsp;Philippe Geubelle","doi":"10.1016/j.cma.2025.117848","DOIUrl":"10.1016/j.cma.2025.117848","url":null,"abstract":"<div><div>Under some initial and boundary conditions, the rapid reaction-thermal diffusion process taking place during frontal polymerization (FP) destabilizes the planar mode of front propagation, leading to spatially varying, complex hierarchical patterns in thermoset polymeric materials. Although modern reaction–diffusion models can predict the patterns resulting from unstable FP, the inverse design of patterns, which aims to retrieve process conditions that produce a desired pattern, remains an open challenge due to the non-unique and non-intuitive mapping between process conditions and manufactured patterns. In this work, we propose a probabilistic generative model named univariate conditional variational autoencoder (UcVAE) for the inverse design of hierarchical patterns in FP-based manufacturing. Unlike the cVAE, which encodes both the design space and the design target, the UcVAE encodes only the design space. In the encoder of the UcVAE, the number of training parameters is significantly reduced compared to the cVAE, resulting in a shorter training time while maintaining comparable performance. Given desired pattern images, the trained UcVAE can generate multiple process condition solutions that produce high-fidelity hierarchical patterns.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"438 ","pages":"Article 117848"},"PeriodicalIF":6.9,"publicationDate":"2025-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143474592","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 Frenet immersed finite element method for elliptic interface problems: An error analysis","authors":"Slimane Adjerid ,&nbsp;Tao Lin ,&nbsp;Haroun Meghaichi","doi":"10.1016/j.cma.2025.117829","DOIUrl":"10.1016/j.cma.2025.117829","url":null,"abstract":"<div><div>This article presents an error analysis of the recently introduced Frenet immersed finite element (IFE) method. The Frenet IFE space employed in this method is constructed to be locally conforming to the function space of the associated weak form for the interface problem. This article further establishes a critical trace inequality for the Frenet IFE functions. These features enable us to prove that the Frenet IFE method converges optimally under mesh refinement in both <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> and energy norms.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"438 ","pages":"Article 117829"},"PeriodicalIF":6.9,"publicationDate":"2025-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143465287","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":"Three dimensional isogeometric boundary element method for acoustic problems with viscothermal losses","authors":"Ahmed Mostafa Shaaban,&nbsp;Simone Preuss,&nbsp;Steffen Marburg","doi":"10.1016/j.cma.2025.117843","DOIUrl":"10.1016/j.cma.2025.117843","url":null,"abstract":"<div><div>An isogeometric analysis is proposed for solving acoustic problems in fluids with significant thermal and viscous dissipation. The approach is based on the Kirchhoff decomposition, which simplifies the governing linearized conservation laws for mass, momentum, and energy by dividing the physical problem into three superimposed modal wave fields; acoustic, thermal, and viscous fields. The wave fields are coupled by boundary conditions and solved as time-harmonic Helmholtz problems using an isogeometric boundary element method.</div><div>The proposed solution benefits from isogeometric analysis in modeling exact geometries with high continuity, achieving accurate results while adopting moderate degrees of freedom. The basic idea of isogeometric analysis is to use the same spline basis functions to approximate both the geometry and the physical variables, allowing for a direct connection between computer-aided design tools and analysis models. Moreover, the solution profits from the boundary element approach not requiring volumetric domain discretization or far-field truncation.</div><div>3D exterior and interior test cases are discussed to validate the proposed method. The results are verified by an analytical solution and other competing numerical methods showing significant savings in degrees of freedom. Furthermore, an interior field analysis reveals the dissipative behavior inside thin boundary layers at the fluid–structure interface. A comparison with the lossless case emphasizes the added value of accounting for viscothermal losses, which were previously neglected in isogeometric analysis of acoustic problems. Despite the ill-conditioning of the system combining the acoustic, thermal, and viscous contributions, the problem can be solved via LU decomposition with iterative refinement.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"438 ","pages":"Article 117843"},"PeriodicalIF":6.9,"publicationDate":"2025-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143465288","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":"Hemodynamics modeling with physics-informed neural networks: A progressive boundary complexity approach","authors":"Xi Chen ,&nbsp;Jianchuan Yang ,&nbsp;Xu Liu ,&nbsp;Yong He ,&nbsp;Qiang Luo ,&nbsp;Mao Chen ,&nbsp;Wenqi Hu","doi":"10.1016/j.cma.2025.117851","DOIUrl":"10.1016/j.cma.2025.117851","url":null,"abstract":"<div><div>Hemodynamic analysis is essential for assessing cardiovascular health. Computational fluid dynamics (CFD) methods, while precise, are computationally expensive and lack transfer learning capabilities, requiring recalculation for varying boundaries. Machine-learning methods, despite powerful data-fitting abilities, heavily rely on labeled datasets, limiting their use in clinical settings where data is scarce. To alleviate data dependency, Physics-Informed Neural Networks (PINNs) embed physical laws directly into the loss function, allowing model parameter transfer across varying geometries. However, traditional PINNs struggle with complex domains like stenosed vessels, leading to inefficiency and reduced accuracy. To tackle this challenge, we propose the Boundary Progressive PINN (BP-PINN). By introducing boundary complexity, BP-PINN reconstructs vascular boundaries at varying smoothness levels. Training begins with simple models and progressively incorporating boundary details to capture complex flow characteristics. Without any labeled data, BP-PINN was successfully applied to 22 patient-specific cases, achieving L2 errors of 0.036 for velocity and 0.057 for pressure compared to CFD ground truth. Furthermore, compared to fractional flow reserve (FFR), the invasive gold standard for diagnosing myocardial ischemia, the non-invasive FFR predicted by BP-PINN attained the highest overall diagnostic accuracy of 90.9 %, outperforming vanilla-PINNs (81.8 %). Additionally, BP-PINN leveraged pretrained models with similar boundary complexities, enabling efficient stent preoperative planning. The proposed method evaluated the effects of five stenting strategies on the hemodynamic environment, achieving an average computation time of under 3 min per case. Finally, the framework was extended to solve heat equation, Poisson equation and Helmholtz equation in irregular domains, demonstrating superior accuracy compared to baseline methods.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"438 ","pages":"Article 117851"},"PeriodicalIF":6.9,"publicationDate":"2025-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143454474","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":"Advanced deep learning framework for multi-scale prediction of mechanical properties from microstructural features in polycrystalline materials","authors":"Zihao Gao ,&nbsp;Changsheng Zhu ,&nbsp;Canglong Wang ,&nbsp;Yafeng Shu ,&nbsp;Shuo Liu ,&nbsp;Jintao Miao ,&nbsp;Lei Yang","doi":"10.1016/j.cma.2025.117844","DOIUrl":"10.1016/j.cma.2025.117844","url":null,"abstract":"<div><div>The intricate relationship between the microstructure of materials and their mechanical properties remains a significant challenge in the field of materials science. This study introduces a novel deep learning framework aimed at predicting mechanical properties from both global and local perspectives. Taking the dual-phase Ti-6Al-4V alloy as an example, we first predict stress–strain curves and yield strength under complex microstructural conditions to describe global mechanical behavior, followed by an analysis of the distribution of the local stress field and stress concentration phenomena. To achieve this, we employ an improved graph attention network (IGAT), which effectively captures complex intergranular relationships and enables accurate predictions of global properties by integrating node features with graph structural information. Additionally, a three-dimensional conditional denoising diffusion probabilistic model (3D-cDDPM) was developed for local stress field analysis, generating detailed stress field distributions through an iterative denoising process and capturing stress concentration phenomena in critical microstructural regions. The results demonstrate that this framework effectively predicts multiscale mechanical responses in various microstructural configurations. The IGAT model achieves a mean relative error (MRE) of 0. 399% on the set of tests for global performance prediction, outperforming both the graph convolutional network (GCN) and the three-dimensional convolutional neural network (3D-CNN). For local stress field predictions, the 3D-cDDPM maintains an error range of 0.4% to 7%, with the generated stress distribution maps closely matching the ground truth. This work advances the development of material design and performance optimization methods, providing critical insights into the integration of computational modeling with materials science.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"438 ","pages":"Article 117844"},"PeriodicalIF":6.9,"publicationDate":"2025-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143454331","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 spatiotemporal order-reduced Gaussian process for dynamic full-field multi-physics prediction of hypervelocity collisions in real-time with limited data","authors":"Zhuosen Wang,&nbsp;Yunguo Cheng,&nbsp;Chensen Ding","doi":"10.1016/j.cma.2025.117810","DOIUrl":"10.1016/j.cma.2025.117810","url":null,"abstract":"<div><div>Data-driven evaluation of full-field variables over time poses considerable challenges and little explored. Therefore, we propose a novel dynamic parallel spatiotemporal order reduced Gaussian Process scheme (Dyna-PSTORGP) to accurately predict the full-field, time-sequenced multi-physics responses of hypervelocity collisions in real-time using limited data. In which, we first propose parallel and reduction in space and temporal dimensionalities and investigate the optimal temporal reconstruction method, establishing the spatial-temporal unified latent (feature) spaces that efficiently decouple the strong nonlinear and multi-physics dynamic responses. Next, we propose a hierarchical parallel multi-Gaussian Processes model, emulating the maps from initial input conditions to spatiotemporal order-reduced dynamic response. This hierarchical parallelism operates on two levels: an inner parallel modeling across each component of order-reduced spatial output within individual time steps, and an outer parallel modeling across the reduced time steps. This dual-layered structure not only enhances computational efficiency and enables accurate dynamic response predictions across spatiotemporal scales, effectively addressing the common issue of error accumulation in sequential prediction, but also ensures rapid training and prediction with confidence intervals. Moreover, we investigated different kernels and sensitivity to assess the effects of varying initial conditions in hypervelocity collisions, revealing the collision inclination angle exerts a greater influence on the damage response than both the direction angle and collision velocity. Numerical examples, including simulations on the Whipple shield and space station, validate the Dyna-PSTORGP model's capability for rapid parallel construction and training, completing in seconds (e.g., 12.8 s) with a limited dataset (e.g., 125 samples). The model achieves real-time, high-precision multi-physics predictions for complex nonlinear hypervelocity collisions (e.g., 1.9 s) and consistently maintains high accuracy (e.g., relative errors &lt;5 %) across full-field, high-dimensional scenarios (e.g., 1,134,172 degrees of freedom).</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"438 ","pages":"Article 117810"},"PeriodicalIF":6.9,"publicationDate":"2025-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143454473","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 bioinspired multi-layer assembly method for mechanical metamaterials with extreme properties using topology optimization","authors":"Peng Yin ,&nbsp;Baotong Li ,&nbsp;Yue Zhang ,&nbsp;Bang Li ,&nbsp;Jun Hong ,&nbsp;Xiaohu Li ,&nbsp;Xiaoming Chen ,&nbsp;Jinyou Shao","doi":"10.1016/j.cma.2025.117850","DOIUrl":"10.1016/j.cma.2025.117850","url":null,"abstract":"<div><div>Inspired by the hierarchical distribution pattern of natural bamboo, this study presents a multi-layer assembly strategy for the design of mechanical metamaterials with extreme properties. Firstly, the material spatial layout is constructed by employing a bio-inspired arrangement with two types of cells distributed in a staggered manner. Based on this arrangement, a new theoretical model for evaluating material properties is then developed, which in turn determines the requirements of extreme material properties on cell properties. Finally, to obtain materials with extreme mechanical properties, a topology optimization method is adopted for the generation of cell geometries with the needed properties. The numerical experiment results indicate that compared to the homogeneous material consisting of basic cells, the Young's modulus of assembled metamaterials with similar density is enhanced by more than three orders of magnitude and up to 6273 times. Further, a series of materials with extreme Young's modulus approaching the theoretical limit are identified by geometric parameter optimization for specific topologies. Such metamaterials based on assembly strategies are capable of taking full advantage of geometric variations to enhance mechanical properties, thus having a wide range of applications in various fields such as energy absorption, impact protection, and strain sensing.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"438 ","pages":"Article 117850"},"PeriodicalIF":6.9,"publicationDate":"2025-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143445323","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":"Self-support structure topology optimization for multi-axis additive manufacturing incorporated with curved layer slicing","authors":"Shuzhi Xu ,&nbsp;Jikai Liu ,&nbsp;Dong He ,&nbsp;Kai Tang ,&nbsp;Kentaro Yaji","doi":"10.1016/j.cma.2025.117841","DOIUrl":"10.1016/j.cma.2025.117841","url":null,"abstract":"<div><div>Multi-axis additive manufacturing significantly surpasses traditional 3-axis systems by utilizing multiple axes of motions that constructs complex three-dimensional structures with reduced need of supports. However, process planning for the curved layer slicing determines the interactions between the part and supports, and consequently, self-support topology optimization requires a numerically tractable process planning algorithm to derive the sensitivities, which however, has yet been achieved. To fill the gap, we develop a structural topology optimization method for multi-axis additive manufacturing, which features in achieving the self-support effect by deeply incorporating the curved layer slicing. Specifically, a process scalar field is generated on top of a domain of pseudo-densities by solving a heat diffusion equation and a Poisson equation, through which the geodesics included in the scalar field facilitate the curved layer slicing and any geometric information about the layers are derivable on the pseudo-densities because of the tractable numerical processing routine. Then, self-support constraints for multi-axis additive manufacturing can be established by measuring the curved layer normals and the part boundary gradients. Coupled with the density variables for topology optimization, our proposed method could concurrently optimize the part structure and its curved slicing pattern, maximizing the structural physical performance while eliminating the need of supports. Finally, we validated and discussed the effectiveness of our method through a series of numerical tests and provided a workflow to show the strong correlation between our optimized results and the actual spatial paths.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"438 ","pages":"Article 117841"},"PeriodicalIF":6.9,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143429910","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}