Computer Methods in Applied Mechanics and Engineering最新文献

{"title":"A peridynamic differential operator (PDDO)-based model for compressible high-speed water droplet impact on a rigid wall","authors":"Mostafa Elyoussef, Martin Pugh, Mamoun Medraj","doi":"10.1016/j.cma.2026.119337","DOIUrl":"https://doi.org/10.1016/j.cma.2026.119337","url":null,"abstract":"Water droplet erosion (WDE) compromises the structural integrity and efficiency of power-generation components, driving extensive research to elucidate its underlying mechanisms. Although finite element (FE) simulations provide insight into impact-induced stress and strain fields, modeling WDE onset and progression remains challenging because conventional FE formulations rely on classical continuum governing equations whose spatial derivatives become invalid at discontinuities. Peridynamics (PD), formulated without spatial derivatives, has proven effective for predicting complex damage patterns and offers a promising framework for investigating WDE mechanisms. Nevertheless, PD research has largely focused on solids, and existing PD-based fluid models mainly target incompressible and weakly compressible flows. Accordingly, this study develops and validates a two-dimensional Peridynamic Differential Operator (PDDO)-based formulation for compressible high-speed water droplet impact on a rigid wall. The PDDO-based formulation employs a horizon-based meshfree discretization of the classical Lagrangian Navier–Stokes equations and incorporates Roe's approximate Riemann solver with a dissipation limiter to improve numerical stability near sharp flow discontinuities. A GPU-accelerated MATLAB implementation incorporates free-surface treatment, a fictitious-layer wall boundary, particle regularization, and a boundary-collision correction. The model captures the key physical features of high-speed droplet impact and agrees well with semi-analytical predictions of maximum and spatially averaged wall pressure over impact velocities of 100–500 m/s, while demonstrating droplet-size independence, accurate early-stage contact-radius evolution, and good agreement of predicted lateral-jet velocities with experimental measurements. The present PDDO framework provides a foundation for future coupling with PD solid formulations, enabling a unified horizon-based computational framework for fluid–structure interaction simulations of WDE.","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"25 1","pages":""},"PeriodicalIF":7.2,"publicationDate":"2026-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148884938","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":"Invariant-manifold-based model reduction for state transition equations of geometrically exact beam dynamics","authors":"Yifan Qi, Shilei Han, Minghe Shan, Qiang Tian","doi":"10.1016/j.cma.2026.119328","DOIUrl":"https://doi.org/10.1016/j.cma.2026.119328","url":null,"abstract":"This paper presents a computationally efficient invariant-manifold-based model reduction framework for the nonlinear dynamics of free beams and beam assemblies. Although geometrically exact formulations provide high fidelity, they become prohibitively expensive for high-dimensional problems. To address this issue, a “temporal discretization followed by reduction” procedure is proposed. This methodology represents a significant advancement over the “reduction followed by temporal discretization” sequence used in the authors’ previous research. By fundamentally restructuring the problem to eliminate the computational bottlenecks of repetitive time integration and Newton iterations, this approach provides a substantially more efficient and streamlined framework for reduced-order modeling. The full-order dynamics are first discretized by the discontinuous Galerkin scheme, which provides unconditional stability and suppresses high-frequency components of the response. Invariant-manifold-based reduction is then applied to the resulting state-transition equations, yielding a very low-dimensional reduced state-transition equation and thereby avoiding repetitive time integration and Newton iterations. Besides this primary innovation, the work provides several key advancements: <ce:italic>(1)</ce:italic> A reformulated state-space governing equation for geometrically exact beams within the floating frame of reference formulation, which eliminates the Lagrange multipliers and explicit frame motion equations required in previous studies. <ce:italic>(2)</ce:italic> An implicit construction of the state-transition relationship in the full-order equations, which preserves the sparse pattern of the large-scale matrices resulting from the temporal discretization and allows the cohomological equations to leverage this sparsity for enhanced performance. <ce:italic>(3)</ce:italic> A diagonal decomposition of the coefficient matrix of the reduced-order dynamics is introduced. This strategy uncouples column-wise higher-order cohomological equations into independent linear systems, leading to efficient computation for manifold construction. Numerical examples demonstrate that the proposed approach achieves the expected convergence rates with respect to the time-step size and the interpolation order of the test and trial functions. By leveraging an explicit state-transition mapping for time marching, the method achieves faster online computation, thereby enhancing its practical applicability for rapid simulation of free-flying beam structures.","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"8 1","pages":""},"PeriodicalIF":7.2,"publicationDate":"2026-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148884942","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":"Smooth single-yield-surface formulations for rate-independent crystal plasticity – Theory and numerical implementation","authors":"Alexander Niehüser, Jörn Mosler","doi":"10.1016/j.cma.2026.119301","DOIUrl":"https://doi.org/10.1016/j.cma.2026.119301","url":null,"abstract":"Crystal plasticity theory provides a framework for multiscale analysis of plastic deformation that explicitly incorporates crystallographic information into the constitutive model. However, the classic multi-surface yield criterion exhibits a yield surface with sharp corners, which causes numerical challenges in identifying active slip systems and computing the corresponding plastic slips. In this regard, single-yield-surface formulations offer a promising approach to alleviate these issues by replacing the original non-smooth yield surface with a smooth approximation. In this work, such single-yield-surface formulations are realized through effective yield functions based on the LogSumExp function and the <mml:math altimg=\"si314.svg\" display=\"inline\"><mml:mi>p</mml:mi></mml:math>-norm. Compared with existing effective-yield-function approaches, the proposed formulations are embedded in a hyperelastic crystal plasticity framework and cast within the generalized standard materials (GSM) framework, thereby providing a thermodynamically consistent setting. A new parameter allows the effective yield functions to consistently under- or overestimate the original yield domain, thereby extending formulations that approximate the yield surface only from one side. An a priori estimate relates the LogSumExp and <mml:math altimg=\"si314.svg\" display=\"inline\"><mml:mi>p</mml:mi></mml:math>-norm exponents such that both formulations achieve the same prescribed approximation quality relative to the classic multi-surface yield criterion, enabling an error-controlled parameter selection. Due to the common structure of the governing equations, both models are implemented in a unified fully implicit Newton scheme with a line search strategy and suitable slip-variable predictors. Several numerical examples demonstrate the robustness and efficiency of the proposed effective formulations, including representative volume simulations of a DP800 polycrystal subjected to a deformation path mimicking flat rolling. Compared with an augmented Lagrangian solution of the original multi-surface problem, the LogSumExp and <mml:math altimg=\"si314.svg\" display=\"inline\"><mml:mi>p</mml:mi></mml:math>-norm formulations show comparable accuracy and robustness when their exponents are chosen according to the proposed estimate, while substantially reducing the number of Newton iterations and the computational effort.","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"40 1","pages":""},"PeriodicalIF":7.2,"publicationDate":"2026-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148884941","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":"HUG-VAS: A hierarchical NURBS-based generative model for aortic geometry synthesis and controllable editing","authors":"Pan Du, Mingqi Xu, Xiaozhi Zhu, Jian-Xun Wang","doi":"10.1016/j.cma.2026.119309","DOIUrl":"https://doi.org/10.1016/j.cma.2026.119309","url":null,"abstract":"Accurate, patient-specific vascular geometry is pivotal for diagnosis, planning, and device design, yet existing statistical shape modeling (SSM) pipelines rely on linear priors and topology-specific preprocessing that limit realism, scalability, and interoperability. We present HUG-VAS, a Hierarchical NURBS Generative framework for Vascular models, that unifies NURBS-based 3D shape encoding with diffusion-based generative modeling to synthesize fine-grained, CFD-ready aortic anatomies. HUG-VAS factorizes shape into (i) vessel centerlines generated by a denoising diffusion model and (ii) cross-sectional radius profiles synthesized by a classifier-free guided diffusion model conditioned on the centerline, thereby decoupling and preserving stochastic variability across these two anatomical layers. Beyond unconditional synthesis, we enable training-free, zero-shot conditional generation via diffusion posterior sampling from image-derived prompts (e.g., sparse 3D points, slice contours, or partial surface patches), supporting interactive semi-automatic segmentation, editing and robust reconstruction under degraded imaging. Trained on 21 patient-specific MRA cases, HUG-VAS generates multi-branch aortas with supra-aortic vessels whose biomarker distributions closely match the source cohort, and whose watertight NURBS outputs directly integrate with downstream CFD solvers. To our knowledge, HUG-VAS is the first SSM frameworks to unify NURBS parameterization, hierarchical diffusion, and DPS-based zero-shot conditional generation, enabling reconstruction and completion of vascular geometry from sparse, partial geometric priors without retraining.","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"35 1","pages":""},"PeriodicalIF":7.2,"publicationDate":"2026-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148884940","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":"Frobenius-theory-based scaled boundary finite element solution for variable-coefficient elliptic problems with corner singularities","authors":"Yixin Qian, Zhihao Ren, Yuji Miao, Minggang Tang","doi":"10.1016/j.cma.2026.119326","DOIUrl":"https://doi.org/10.1016/j.cma.2026.119326","url":null,"abstract":"Many engineering problems are described by elliptic partial differential equations (PDEs) with approximate boundary conditions. Sharp corners of boundary geometries may give rise to singularities in solutions. While mainstream finite and boundary element methods perform well for smooth solutions, the accuracy and convergence rate degrade near the corners. The scaled boundary finite element method (SBFEM) is capable of resolving corner singularities with no need for analytical singular functions. Nevertheless, existing SBFEM schemes cannot natively accommodate corner singularity behaviors alongside variable-coefficient effects. This work develops a generalized SBFEM framework for variable-coefficient elliptic PDEs. A Frobenius-theory-based algorithm is derived to build complete fundamental solution spaces and eliminate eigenvalue resonance. Theoretical derivation reveals that corner singularity characteristics are mainly controlled by the constant term of diffusion coefficients. Single-subdomain benchmark cases against the spectral element method (SEM) and extended finite element method (XFEM) verify the method’s accuracy, convergence, and stability for singular modeling. Additional multi-subdomain examples demonstrate its scalability and applicability to engineering problems.","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"23 1","pages":""},"PeriodicalIF":7.2,"publicationDate":"2026-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148884939","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 multi-phase hygro-mechanical phase-field model for drying shrinkage of concrete","authors":"Songsong Meng, Haiming Liu, Maurizio Guadagnini, Yufeng Lai, Yang Jiang, Xu Long, Kypros Pilakoutas","doi":"10.1016/j.cma.2026.119344","DOIUrl":"https://doi.org/10.1016/j.cma.2026.119344","url":null,"abstract":"Drying shrinkage cracks induced by moisture loss can govern the durability and service life of concrete structures. However, capturing the coupled mechanisms of moisture transport, capillary stress development, and fracture within the heterogeneous microstructure of concrete remains challenging with conventional finite element method. This study presents a multi-scale hygro-mechanical phase-field framework for simulating drying-shrinkage-induced cracking at the mesoscale. The proposed framework couples moisture diffusion with an elasto-plastic phase-field formulation, in which shrinkage deformation is driven by capillary stress arising from moisture loss within the pore and interfacial transition zone phases. The heterogeneous structure of concrete, including aggregates, mortar, interfacial transition zone, and pore networks, is explicitly represented using Monte Carlo-based aggregate generation and Voronoi tessellation. This framework enables a fully coupled analysis of internal relative humidity evolution, shrinkage deformation, and damage propagation. The proposed model is validated against experimental measurements, showing good agreement in both relative humidity evolution and drying shrinkage development. Parametric investigations further demonstrate the ability of the framework to capture the influence of water/cement ratio, porosity, and environmental conditions on shrinkage and damage state. The proposed approach provides a robust tool for analysing hygro-mechanical interactions in cementitious materials and offers improved predictive capability for durability and long-term performance.","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"13 1","pages":""},"PeriodicalIF":7.2,"publicationDate":"2026-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148884943","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":"Towards quantum accelerated large-scale topology optimization","authors":"Zisheng Ye,&nbsp;Wenxiao Pan","doi":"10.1016/j.cma.2026.118819","DOIUrl":"10.1016/j.cma.2026.118819","url":null,"abstract":"<div><div>We present an efficient topology optimization (TO) method that not only enhances computational efficiency on classical computing but also provides a practical pathway for leveraging quantum computing to achieve further acceleration. The method targets large-scale, multi-material TO of three-dimensional (3D) continuum structures, beyond prior quantum TO studies limited to small-scale and single-material problems. Building on our discrete-variable TO framework (DVTO-MT), which employs multi-cut optimization and trust regions to reduce iteration counts and thereby PDE solver calls, the proposed method introduces a modified Dantzig-Wolfe (MDW) decomposition to further reduce per-iteration optimization time. The MDW method exploits the block-angular structure of the problem to decompose the mixed-integer linear program (MILP) into reduced-size global and local sub-problems. Evaluations on large-scale 3D bridge design problems demonstrate orders-of-magnitude reductions in computational time, with robust performance even for designs exceeding 50 million variables where classical MILP solvers fail to converge. Furthermore, the computationally intensive local sub-problems are transformed into equivalent quadratic unconstrained binary optimization (QUBO) formulations for quantum acceleration. The resulting QUBOs require only sparse qubit connectivity, a crucial consideration for near-term quantum hardware, and linear construction cost, offering the potential for an additional order-of-magnitude speedup. All observed and estimated speedups become more significant with increasing problem size and when extending from single-material to multi-material designs, highlighting the potential of the proposed method, coupled with quantum computing, to address the scale and complexity of real-world TO challenges.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"453 ","pages":"Article 118819"},"PeriodicalIF":7.3,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146191973","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 learning-based domain decomposition method","authors":"Rui Wu ,&nbsp;Nikola Kovachki ,&nbsp;Burigede Liu","doi":"10.1016/j.cma.2026.118799","DOIUrl":"10.1016/j.cma.2026.118799","url":null,"abstract":"<div><div>Recent developments in mechanical, aerospace, and structural engineering have driven a growing need for efficient ways to model and analyze structures at much larger and more complex scales than before. While established numerical methods like the Finite Element Method remain reliable, they often struggle with computational cost and scalability when dealing with large and geometrically intricate problems. In recent years, neural network-based methods have shown promise because of their ability to efficiently approximate nonlinear mappings. However, most existing neural approaches are still largely limited to simple domains, which makes it difficult to apply to real-world partial differential equations (PDEs) involving complex geometries. In this paper, we propose a learning-based domain decomposition method (L-DDM) that addresses this gap. Our approach uses a single, pre-trained neural operator-originally trained on simple domains-as a surrogate model within a domain decomposition scheme, allowing us to tackle large and complicated domains efficiently. We provide a general theoretical result on the existence of neural operator approximations in the context of domain decomposition solution of abstract PDEs. We then demonstrate our method by accurately approximating solutions to elliptic PDEs with discontinuous microstructures in complex geometries, using a physics-pretrained neural operator (PPNO). Our results show that this approach not only outperforms current state-of-the-art methods on these challenging problems, but also offers resolution-invariance and strong generalization to microstructural patterns unseen during training.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"453 ","pages":"Article 118799"},"PeriodicalIF":7.3,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146161065","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":"Polynomial chaos expansion for operator learning","authors":"Himanshu Sharma ,&nbsp;Lukáš Novák ,&nbsp;Michael Shields","doi":"10.1016/j.cma.2026.118796","DOIUrl":"10.1016/j.cma.2026.118796","url":null,"abstract":"<div><div>Operator learning (OL) has emerged as a powerful tool in scientific machine learning (SciML) for approximating mappings between infinite-dimensional functional spaces. One of its main applications is learning the solution operator of partial differential equations (PDEs). While much of the progress in this area has been driven by deep neural network-based approaches such as Deep Operator Networks (DeepONet) and Fourier Neural Operator (FNO), recent work has begun to explore traditional machine learning methods for OL. In this work, we introduce polynomial chaos expansion (PCE) as an OL method. PCE has been widely used for uncertainty quantification (UQ) and has recently gained attention in the context of SciML. For OL, we establish a mathematical framework that enables PCE to approximate operators in both purely data-driven and physics-informed settings. The proposed framework reduces the task of learning the operator to solving a system of equations for the PCE coefficients. Moreover, the framework provides UQ by simply post-processing the PCE coefficients, without any additional computational cost. We apply the proposed method to a diverse set of PDE problems to demonstrate its capabilities. Numerical results demonstrate the strong performance of the proposed method in both OL and UQ tasks, achieving excellent numerical accuracy and computational efficiency.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"453 ","pages":"Article 118796"},"PeriodicalIF":7.3,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146161061","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 sparse basis for equilibrium stress fields with application for direct data-driven mechanics","authors":"Erik Prume ,&nbsp;Chenyi Ji ,&nbsp;Stefanie Reese ,&nbsp;Michael Ortiz","doi":"10.1016/j.cma.2026.118803","DOIUrl":"10.1016/j.cma.2026.118803","url":null,"abstract":"<div><div>We present a new class of solvers for direct data-driven mechanical problems based on a sparse basis representation of equilibrium stress fields. Our first contribution is an efficient algorithm for computing the required sparse null-space basis on tetrahedral meshes.</div><div>Only a single QR decomposition is needed to compute a small remaining set of dense basis vectors associated with boundary conditions and topological holes which can be handled efficiently via a partitioned Cholesky factorization. Building on this, we demonstrate how standard iterative solvers-such as the Newton-Raphson method-can be applied to direct data-driven formulations.</div><div>The proposed approach is particularly valuable for challenging problems with complex data distributions requiring systematic exploration of the space of equilibrium stress fields. To this end, we introduce an algorithm that constructs a hierarchical solution set through an eigenvalue decomposition in the joint space of equilibrium stress and compatible strain fields. We demonstrate the proposed methodology with a numerical example involving brittle fracture with probabilistic tensile strength. The resulting family of failure patterns offers valuable insights for uncertainty quantification and design decision-making.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"453 ","pages":"Article 118803"},"PeriodicalIF":7.3,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146152936","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}