Computer Methods in Applied Mechanics and Engineering最新文献

{"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}

{"title":"Simultaneous shape and topology optimization on unstructured grids","authors":"Vilmer Dahlberg ,&nbsp;Anna Dalklint ,&nbsp;Mathias Wallin","doi":"10.1016/j.cma.2025.117830","DOIUrl":"10.1016/j.cma.2025.117830","url":null,"abstract":"<div><div>In this work we present a simultaneous shape and topology optimization framework that generates large-scale 3D designs on unstructured grids. We consider a “parameter-free” shape optimization approach, wherein the nodal coordinates in the finite element mesh serve as design variables. To regularize the design changes we use a PDE-based filter, similar to the filtering techniques used in topology optimization. We present a variant of the “parameter-free” shape optimization where we allow not only design variables on the surface, but also in the bulk of the domain. To combat mesh quality issues we employ adaptive mesh refinement based on a Riemannian metric. The numerical algorithm is implemented in C++ and uses PETSc for efficient shape and topology optimization of complex 3D geometries on unstructured grids. We verify our “parameter-free” shape optimization on two examples, and compare different variations of the shape filter. Finally, we demonstrate the power and flexibility of our simultaneous shape and topology optimization framework on a dam-like geometry.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"438 ","pages":"Article 117830"},"PeriodicalIF":6.9,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143429471","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":"Robust equilibrium optimization method for dynamic characteristics of mechanical structures with hybrid uncertainties","authors":"Jin Cheng ,&nbsp;Honghui Wang ,&nbsp;Shuoshuo Shen ,&nbsp;Weifei Hu ,&nbsp;Zhenyu Liu ,&nbsp;Jianrong Tan","doi":"10.1016/j.cma.2025.117838","DOIUrl":"10.1016/j.cma.2025.117838","url":null,"abstract":"<div><div>For complex products such as high-speed presses, it is imperative to optimize the dynamic characteristics of their moving components to avoid resonance, thereby ensuring safe and stable operation. Dynamic characteristic optimization of mechanical structures considering multi-source uncertainties remains a challenging task due to the violent confliction among multiple objectives and multiple constraints. In this paper, a novel robust equilibrium optimization method for dynamic characteristics of mechanical structures with hybrid uncertainties is proposed. Firstly, the dynamic robust equilibrium optimization model is established with multi-source uncertainties described as truncated probabilistic variables and interval variables. Subsequently, a novel angular proximity coefficient is defined to assess the constraint feasibility of design vectors. Further, a quantitative metric named the overall robust equilibrium degree (ORED) is proposed to evaluate the overall robustness of all objective and constraint performance indices for feasible design vectors. On this basis, all the feasible design vectors are directly ranked according to their OREDs, thereby achieving the optimal design of mechanical structures. The robust equilibrium optimization is realized by integrating Kriging models, Monte Carlo simulation (MCS) and nested genetic algorithm (GA). The effectiveness and feasibility of the proposed method are demonstrated through a numerical example and two engineering case studies involving a high-speed press slider and an unmanned aerial vehicle (UAV).</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"438 ","pages":"Article 117838"},"PeriodicalIF":6.9,"publicationDate":"2025-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143422190","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":"Data-driven reliability-based topology optimization by using the extended multi scale finite element method and neural network approach","authors":"Zeng Meng ,&nbsp;Shunsheng Lv ,&nbsp;Yongxin Gao ,&nbsp;Changting Zhong ,&nbsp;Kang An","doi":"10.1016/j.cma.2025.117837","DOIUrl":"10.1016/j.cma.2025.117837","url":null,"abstract":"<div><div>Solving reliability-based topology optimization (RBTO) problems requires highly computational demand in finite element and sensitivity analyses, particularly for obtaining high-resolution results. To overcome this issue, a new data-driven RBTO framework is introduced by using the problem-independent machine learning method, which aims to significantly decrease the computational time incurred by finite element and sensitivity analyses. Subsequently, a novel neural networks model is established by using deep learning techniques, while the offline training serves as a surrogate model for calculating the numerical basic function. Furthermore, a novel sensitivity analysis method has been developed, which utilizes the basic function and deep learning neural networks to map the sensitivity information from the macroscopic level to the microscopic level. The results illustrate that the proposed method can substantially decrease the computational time of RBTO with high-resolution results.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"438 ","pages":"Article 117837"},"PeriodicalIF":6.9,"publicationDate":"2025-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143429470","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 high-order implicit time integration method for linear and nonlinear dynamics with efficient computation of accelerations","authors":"Daniel O’Shea,&nbsp;Xiaoran Zhang,&nbsp;Shayan Mohammadian,&nbsp;Chongmin Song","doi":"10.1016/j.cma.2025.117831","DOIUrl":"10.1016/j.cma.2025.117831","url":null,"abstract":"<div><div>An algorithm for a family of self-starting high-order implicit time integration schemes with controllable numerical dissipation is proposed for both linear and nonlinear transient problems. This work builds on the previous works of the authors on elastodynamics by presenting a new algorithm that eliminates the need for factorization of the mass matrix providing benefit for the solution of nonlinear problems. The improved algorithm directly obtains the acceleration at the same order of accuracy of the displacement and velocity using vector operations (without additional equation solutions). The nonlinearity is handled by numerical integration within a time step to achieve the desired order of accuracy. The new algorithm fully retains the desirable features of the previous works: 1. The order of accuracy is not affected by the presence of external forces and physical damping; 2. The amount of numerical dissipation in the algorithm is controlled by a user-specified parameter <span><math><msub><mrow><mi>ρ</mi></mrow><mrow><mi>∞</mi></mrow></msub></math></span>, leading to schemes ranging from perfectly nondissipative <span><math><mi>A</mi></math></span>-stable to <span><math><mi>L</mi></math></span>-stable; 3. The effective stiffness matrix is a linear combination of the mass, damping, and stiffness matrices as in the trapezoidal rule, leading to high efficiency for large-scale problems. The proposed algorithm, with its elegance and computational advantages, is shown to replicate the numerical results demonstrated on linear problems in previous works. Additional numerical examples of linear and nonlinear vibration and wave propagation are presented herein. Notably, the proposed algorithms show the same convergence rates for nonlinear problems as linear problems, and very high accuracy. It was found that second-order time integration methods commonly used in commercial software produce significantly polluted acceleration responses for a common class of wave propagation problems. The high-order time integration schemes presented here perform noticeably better at suppressing spurious high-frequency oscillations and producing reliable and usable acceleration responses. The source code written in <span>MATLAB</span> is available for download at: <span><span>https://github.com/ChongminSong/HighOrderTimeIngt_PartialFraction.git</span><svg><path></path></svg></span>.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"438 ","pages":"Article 117831"},"PeriodicalIF":6.9,"publicationDate":"2025-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143422193","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":"Global-local adaptive meshing method for phase-field fracture modeling","authors":"FengYu Cheng,&nbsp;Hao Yu,&nbsp;Quan Wang,&nbsp;HanWei Huang,&nbsp;WenLong Xu,&nbsp;HengAn Wu","doi":"10.1016/j.cma.2025.117846","DOIUrl":"10.1016/j.cma.2025.117846","url":null,"abstract":"<div><div>This work develops a global-local adaptive meshing method for the phase-field model of brittle fracture, offering flexible adjustment of mesh density to produce seamless and high-quality adaptive meshes. The method first establishes a direct mapping from phase-field values and displacement errors to a normalized nodal density field, which is used to control the computational accuracy. On this basis, a sampling procedure is performed by detecting the maximum value to progressively place sampling nodes, ensuring that first-level nodes are placed globally while preserving crack location information. Subsequently, a hexagonal seeding algorithm is used to multiply nodes, where the spacing of generated seeds (i.e., higher-level nodes) is adaptively adjusted based on local nodal density requirements to regulate element sizes. A spatial assessment algorithm is utilized to compare the expected nodal spacing of the newly generated node with its distance to existing nodes, which serves as a termination criterion for the loop of the seeding algorithm and effectively prevents the occurrence of low-quality elements. After the seeding process of all nodes is completed, all generated nodes are connected by constrained Delaunay triangulation. This method has been discussed under classical brittle fracture cases with various control parameters (e.g., the mapping function, the expected maximum/minimum element size, and the distance factor) to validate its advantage of reducing degrees of freedom and improving solution efficiency.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"438 ","pages":"Article 117846"},"PeriodicalIF":6.9,"publicationDate":"2025-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143422191","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}