Computer Methods in Applied Mechanics and Engineering最新文献

{"title":"High-throughput machine learning framework for predicting neurite deterioration using MetaFormer attention","authors":"Kuanren Qian ,&nbsp;Genesis Omana Suarez ,&nbsp;Toshihiko Nambara ,&nbsp;Takahisa Kanekiyo ,&nbsp;Yongjie Jessica Zhang","doi":"10.1016/j.cma.2025.118003","DOIUrl":"10.1016/j.cma.2025.118003","url":null,"abstract":"<div><div>Neurodevelopmental disorders (NDDs) cover a variety of conditions, including autism spectrum disorder, attention-deficit/hyperactivity disorder, and epilepsy, which impair the central and peripheral nervous systems. Their high comorbidity and complex etiologies present significant challenges for accurate diagnosis and effective treatments. Conventional clinical and experimental studies are time-intensive, burdening research progress considerably. This paper introduces a high-throughput machine learning (ML) framework for modeling neurite deteriorations associated with NDDs, integrating synthetic data generation, experimental images, and ML models. The synthetic data generator utilizes an isogeometric analysis (IGA)-based phase field model to capture diverse neurite deterioration patterns such as neurite retraction, atrophy, and fragmentation while mitigating the limitations of scarce experimental data. The ML model utilizes MetaFormer-based gated spatiotemporal attention architecture with deep temporal layers and provides fast predictions. The framework effectively captures long-range temporal dependencies and intricate morphological transformations with average errors of 1.9641% and 6.0339% for synthetic and experimental neurite deterioration, respectively. Seamlessly integrating simulations, experiments, and ML framework can guide researchers to make informed experimental decisions by predicting potential experimental outcomes, significantly reducing costs and saving valuable time. It can also advance our understanding of neurite deterioration and provide a scalable solution for exploring complex neurological mechanisms, contributing to the development of targeted treatments.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"442 ","pages":"Article 118003"},"PeriodicalIF":6.9,"publicationDate":"2025-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143868381","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 fourth-order reaction diffusion-based level set method for isogeometric topology optimization","authors":"He Li,&nbsp;Jianhu Shen,&nbsp;Xuyu Zhang,&nbsp;Shiwei Zhou","doi":"10.1016/j.cma.2025.118028","DOIUrl":"10.1016/j.cma.2025.118028","url":null,"abstract":"<div><div>This study presents a fourth-order reaction-diffusion isogeometric optimization method to effectively control curvature variations in minimum mean compliance optimization problems. Using isogeometric analysis with <em>k</em>-refinement technique, the level set function—parameterized using Non-Uniform Rational B-Splines (NURBS) to represent complex geometries while maintaining computational stability accurately—is updated to achieve smoother geometries with higher-order continuity. The elasticity equation is also solved using isogeometric analysis, which preserves precise geometric representation and eliminates the approximation errors associated with finite element analysis. Numerical examples show that the proposed method generates sharper, corner-free complex structures in significantly less computational time than traditional second-order reaction-diffusion methods. For instance, the proposed method produces a 2D quarter annulus under a 40 % volume constraint in just 13 iterations. At the same time, it only needs 20 iterations to yield an elegant 3D serpentine structure in an arbitrarily shaped design domain. The method demonstrates high efficiency, superior accuracy, and enhanced continuity, indicating its potential for various engineering applications.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"442 ","pages":"Article 118028"},"PeriodicalIF":6.9,"publicationDate":"2025-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143868509","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":"An immersed finite-discrete element method (IFDEM) framework for water entry with fracture dynamics","authors":"Lanhao Zhao ,&nbsp;Yingtang Di ,&nbsp;Linyu Shao ,&nbsp;Jia Mao","doi":"10.1016/j.cma.2025.118026","DOIUrl":"10.1016/j.cma.2025.118026","url":null,"abstract":"<div><div>Water entry is a current but challenging topic with numerous applications in engineering. However, little work has been devoted to water entry problems involving contact and fracture dynamics of solid systems. This work presents a complete immersed finite-discrete element method (IFDEM) framework that contains multiphase fluid dynamics, elastodynamics and a fracture model for crack initiation and propagation, fragmentation, collision and the resultant random distribution of solid debris. The fluid domain governed by the Navier-Stokes equations is discretized by fixed Cartesian grid, while the immersed violently evolved fluid-solid interfaces are tracked by a set of Lagrangian points efficiently through the improved direct forcing immersed boundary method (IBM). The formulation of the bidirectional interaction between multiphase fluid and breakable bodies is derived from the exact velocity boundary condition, and the physical law, i.e., the true divergence-free condition could be satisfied. In addition to capturing the free water surface by the conservative level set (CLS) method that has been widely applied in multiphase flow, the surface normal correction is carried out by a signed distance function so that both the conservation and accuracy could be ensured. The finite-discrete element method (FDEM) is developed to handle the elastic deformation, fragmentation and contact mechanism of solid bodies that are divided into finite elements with zero-thickness joint elements embedded in each pair of adjacent elements. Therefore, this complete approach could cope with the entire continuous-discontinuous evolution process of complex solid systems during water entry, and the strong coupling is enhanced through a stagger iterative technique by solving the fluid and solid domain repeatedly until they converge. The present solver is then tested against a number of benchmark problems, which demonstrate the physical accuracy and reliability. Additional investigations are complemented to showcase the capability of the advanced framework to model water entry phenomena across a variety of scenarios involving dynamic fracture, multi-body contact and the resultant large displacement, which also indicate its significant application potential in engineering.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"442 ","pages":"Article 118026"},"PeriodicalIF":6.9,"publicationDate":"2025-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143868513","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":"Nonintrusive projection-based reduced order modeling using stable learned differential operators","authors":"Aviral Prakash ,&nbsp;Yongjie Jessica Zhang","doi":"10.1016/j.cma.2025.117946","DOIUrl":"10.1016/j.cma.2025.117946","url":null,"abstract":"<div><div>Nonintrusive projection-based reduced order models (ROMs) are essential for dynamics prediction in multi-query applications where underlying governing equations are known but the access to the source of the underlying full order model (FOM) is unavailable; that is, FOM is a glass-box. This article proposes a <em>learn-then-project</em> approach for nonintrusive model reduction. In the first step of this approach, high-dimensional stable sparse learned differential operators (S-LDOs) are determined using the generated data. In the second step, the ordinary differential equations, comprising these S-LDOs, are used with suitable dimensionality reduction and low-dimensional subspace projection methods to provide equations for the evolution of reduced states. This approach allows easy integration into the existing intrusive ROM framework to enable nonintrusive model reduction while allowing the use of Petrov–Galerkin projections. The applicability of the proposed approach is demonstrated for Galerkin and LSPG projection-based ROMs through four numerical experiments: 1-D scalar advection, 1-D Burgers, 2-D scalar advection and 1-D scalar advection–diffusion–reaction equations. The results indicate that the proposed nonintrusive ROM strategy provides accurate and stable dynamics prediction.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"442 ","pages":"Article 117946"},"PeriodicalIF":6.9,"publicationDate":"2025-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143858692","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":"State Space Kriging model for emulating complex nonlinear dynamical systems under stochastic excitation","authors":"Kai Cheng ,&nbsp;Iason Papaioannou ,&nbsp;MengZe Lyu ,&nbsp;Daniel Straub","doi":"10.1016/j.cma.2025.117987","DOIUrl":"10.1016/j.cma.2025.117987","url":null,"abstract":"<div><div>Surrogate modeling can drastically reduce the computational efforts when evaluating complex nonlinear dynamical systems subjected to stochastic excitation. However, existing surrogate modeling techniques suffer from the “curse of dimensionality”<!--> <!-->when emulating complex nonlinear systems due to the discretization of the stochastic excitation. In this work, we present a new surrogate model framework for efficient performance assessment of complex nonlinear dynamical systems with external stochastic excitations. Instead of learning the high-dimensional map from the stochastic excitation to model the response quantity of interest, we propose to learn the system dynamics in state space form, through a sparse Kriging model. The resulting surrogate model is termed state space Kriging (S2K) model. Sparsity in the Kriging model is achieved by selecting an informative training subset from the whole observed training time histories. We propose a tailored technique for designing the training time histories of state vector and its derivative, aimed at enhancing the robustness of the S2K prediction. We compare the performance of S2K model to the NARX (auto-regressive with exogenous input) model with various benchmarks. The results show that S2K outperforms the NARX model up to several orders of magnitude in accuracy. It yields an accurate prediction of complex nonlinear dynamical systems under stochastic excitation with only a few training time histories. This work paves the way for broader application of state space surrogate modeling for emulating stochastic dynamical systems in various scenarios that require the rapid evaluation of response trajectories of systems subject to stochastic excitations.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"442 ","pages":"Article 117987"},"PeriodicalIF":6.9,"publicationDate":"2025-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143858693","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":"Handling geometrical variability in nonlinear reduced order modeling through Continuous Geometry-Aware DL-ROMs","authors":"Simone Brivio,&nbsp;Stefania Fresca,&nbsp;Andrea Manzoni","doi":"10.1016/j.cma.2025.117989","DOIUrl":"10.1016/j.cma.2025.117989","url":null,"abstract":"<div><div>Deep Learning-based Reduced Order Models (DL-ROMs) provide nowadays a well-established class of accurate surrogate models for complex physical systems described by parameterised PDEs, by nonlinearly compressing the solution manifold into a handful of latent coordinates. Until now, design and application of DL-ROMs mainly focused on physically parameterised problems. Within this work, we provide a novel extension of these architectures to problems featuring geometrical variability and parameterised domains, namely, we propose Continuous Geometry-Aware DL-ROMs (CGA-DL-ROMs). In particular, the space-continuous nature of the proposed architecture matches the need to deal with <em>multi-resolution</em> datasets, which are quite common in the case of geometrically parameterised problems. Moreover, CGA-DL-ROMs are endowed with a strong inductive bias that makes them aware of geometrical parametrizations, thus enhancing both the compression capability and the overall performance of the architecture. Within this work, we justify our findings through a thorough theoretical analysis, and we practically validate our claims by means of a series of numerical tests encompassing physically-and-geometrically parameterised PDEs, ranging from the unsteady Navier–Stokes equations for fluid dynamics to advection–diffusion–reaction equations for mathematical biology.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"442 ","pages":"Article 117989"},"PeriodicalIF":6.9,"publicationDate":"2025-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143851645","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":"Direct coupling of continuum and shell elements in large deformation problems","authors":"Astrid Pechstein ,&nbsp;Michael Neunteufel","doi":"10.1016/j.cma.2025.118002","DOIUrl":"10.1016/j.cma.2025.118002","url":null,"abstract":"<div><div>In many applications, thin shell-like structures are integrated within or attached to volumetric bodies. This includes reinforcements placed in soft matrix material in lightweight structure design, or hollow structures that are partially or completely filled. Finite element simulations of such setups are highly challenging. A brute force discretization of structural as well as volumetric parts using well-shaped three-dimensional elements may be accurate, but leads to problems of enormous computational complexity even for simple models. One desired alternative is the use of shell elements for thin-walled parts, as such a discretization greatly alleviates size restrictions on the underlying finite element mesh. However, the coupling of different formulations within a single framework is often not straightforward and may lead to locking if not done carefully. Neunteufel and Schöberl proposed a mixed shell element where, apart from displacements of the center surface, bending moments are used as independent unknowns. These elements were not only shown to be locking free and highly accurate in large-deformation regime, but also do not require differentiability of the shell surface and can handle kinked and branched shell structures. They can directly be coupled to classical volume elements of arbitrary order by sharing displacement degrees of freedom at the center surface, thus achieving the desired coupled discretization. As the elements can be used on unstructured meshes, adaptive mesh refinement based on local stress and bending moments can be used. We present computational results that confirm exceptional accuracy for problems where thin-walled structures are embedded as reinforcements within soft matrix material.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"442 ","pages":"Article 118002"},"PeriodicalIF":6.9,"publicationDate":"2025-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143855910","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":"Minimum-residual a posteriori error estimates for HDG discretizations of the Helmholtz equation","authors":"Liliana Camargo ,&nbsp;Sergio Rojas ,&nbsp;Patrick Vega","doi":"10.1016/j.cma.2025.117981","DOIUrl":"10.1016/j.cma.2025.117981","url":null,"abstract":"<div><div>We propose and analyze two a posteriori error indicators for hybridizable discontinuous Galerkin (HDG) discretizations of the Helmholtz equation. These indicators are built to minimize the residual associated with a local superconvergent postprocessing scheme for the primal variable, measured in a dual norm of an enlarged discrete test space. The residual minimization is reformulated into equivalent local saddle-point problems, yielding a superconvergent postprocessed approximation of the primal variable in the asymptotic regime for sufficiently regular exact solutions and a built-in residual representation with minimal computational effort. Both error indicators are based on frequency-dependent postprocessing schemes and verify reliability and efficiency estimates for a frequency-weighted <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>-error for the scalar unknown and the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-error for the flux. We illustrate our theoretical findings through ad-hoc numerical experiments.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"441 ","pages":"Article 117981"},"PeriodicalIF":6.9,"publicationDate":"2025-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143847674","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":"Predicting crack nucleation and propagation in brittle materials using Deep Operator Networks with diverse trunk architectures","authors":"Elham Kiyani ,&nbsp;Manav Manav ,&nbsp;Nikhil Kadivar ,&nbsp;Laura De Lorenzis ,&nbsp;George Em Karniadakis","doi":"10.1016/j.cma.2025.117984","DOIUrl":"10.1016/j.cma.2025.117984","url":null,"abstract":"<div><div>Phase-field modeling reformulates fracture problems as energy minimization problems and enables a comprehensive characterization of the fracture process, including crack nucleation, propagation, merging and branching, without relying on ad-hoc assumptions. However, the numerical solution of phase-field fracture problems is characterized by a high computational cost. To address this challenge, in this paper, we employ a deep neural operator (DeepONet) consisting of a branch network and a trunk network to solve brittle fracture problems. We explore three distinct approaches that vary in their trunk network configurations. In the first approach, we demonstrate the effectiveness of a two-step DeepONet, which results in a simplification of the learning task. In the second approach, we employ a physics-informed DeepONet, whereby the mathematical expression of the energy is integrated into the trunk network’s loss to enforce physical consistency. The integration of physics also results in a substantially smaller data size needed for training. In the third approach, we replace the neural network in the trunk with a Kolmogorov–Arnold Network and train it without the physics loss. Using these methods, we model crack nucleation in a one-dimensional homogeneous bar under prescribed end displacements, as well as crack propagation and branching in single edge-notched specimens with varying notch lengths subjected to tensile and shear loading. We show that the networks predict the solution fields accurately and the error in the predicted fields is localized near the crack.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"441 ","pages":"Article 117984"},"PeriodicalIF":6.9,"publicationDate":"2025-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143850176","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":"Floating projection topology optimization framework for efficient design of bi-connected 3D acoustic metamaterials","authors":"Gengwang Yan ,&nbsp;Yingli Li ,&nbsp;Weibai Li ,&nbsp;Jiahui Yan ,&nbsp;Song Yao ,&nbsp;Xiaodong Huang","doi":"10.1016/j.cma.2025.118020","DOIUrl":"10.1016/j.cma.2025.118020","url":null,"abstract":"<div><div>Phononic crystals (PnCs) and acoustic metamaterials (AMs) are advanced functional materials engineered to achieve broad bandgaps for wave manipulation through optimized spatial distribution. Despite significant progress, the efficient design of three-dimensional AMs with bi-connected topologies remains a major challenge using conventional topology optimization methods. The novel floating projection topology optimization (FPTO) framework integrated with the Method of Moving Asymptotes (MMA) solver is developed to create and maximize bandgaps between specific dispersion curves. A key innovation of our approach is the incorporation of effective permeability constraints derived from homogenization theory, which ensures sufficient bi-connectivity of air/solid domains essential for practical applications. The optimized topologies exhibiting various-order bandgaps correlate with the equivalent number of air cavities, as revealed through eigenmode analysis and complex band structures. We thoroughly examined the optimization process across various mesh resolutions and permeability constraints to establish robust design guidelines. Both numerical calculations and experimental measurements of sound transmission loss (STL) validate the effectiveness of the optimized topologies for sound attenuation. Additionally, specific wave propagation paths can be engineered by introducing strategic defect features into the perfect lattices. This FPTO framework provides a robust platform for bandgap optimization and inverse design of PnCs and AMs, enabling the development of sophisticated acoustic devices.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"441 ","pages":"Article 118020"},"PeriodicalIF":6.9,"publicationDate":"2025-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143844966","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}