Finite Elements in Analysis and Design最新文献

{"title":"A critical comparison of gradient and integral nonlocal damage models: Formulation, numerical predictions and computational aspects","authors":"Guilherme Fonseca Gonçalves ,&nbsp;Igor A. Rodrigues Lopes ,&nbsp;António M. Couto Carneiro ,&nbsp;Francisco M. Andrade Pires","doi":"10.1016/j.finel.2025.104358","DOIUrl":"10.1016/j.finel.2025.104358","url":null,"abstract":"<div><div>This contribution provides a comparative numerical assessment of the two main classes of nonlocal damage models: gradient-enhanced and integral-type strategies. Particular focus is placed on their formulations, mechanical predictions and computational aspects. A constitutive model for finite strain elastoplasticity, coupled with isotropic damage, is adopted in both cases. In-depth descriptions of both nonlocal models are included, encompassing their theoretical framework and numerical treatment. The integral approach introduces nonlocality explicitly, with a given nonlocal operator establishing the relations between neighbouring points, which impact the structure of the stiffness matrix. The gradient strategy treats nonlocality in an implicit fashion, through the addition of a damage diffusion equation in the global equilibrium system. In this paper, a strongly coupled staggered solution scheme is adopted to solve the mechanical and damage problems separately. Three numerical examples showcase the distinct predictions and computational aspects of the two nonlocal models, revealing their fundamental differences. For small nonlocal lengths, in contrast with its integral counterpart, the gradient model circumvents excessive localisation even in the presence of sharp notches. In general, the gradient approach yields more diffuse damage zones and reduced damage magnitudes. These observations are associated with the different formulations of nonlocality, the role of the nonlocal characteristic parameter, and their practical implications. The gradient model also shows advantages in terms of computational efficiency, mesh independence, and implementation simplicity, making it a compelling choice for most engineering applications.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"248 ","pages":"Article 104358"},"PeriodicalIF":3.5,"publicationDate":"2025-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143899718","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Effect of the temporal discretization of contact forces on dynamic contact simulations using singular non-standard quadrature rules for the mass matrix","authors":"Paulo Ricardo Ferreira Rocha ,&nbsp;António Manuel Couto Carneiro ,&nbsp;Francisco Manuel Andrade Pires","doi":"10.1016/j.finel.2025.104357","DOIUrl":"10.1016/j.finel.2025.104357","url":null,"abstract":"<div><div>Spurious Lagrange Multipliers oscillations present a significant challenge in implicit contact dynamics simulations. To mitigate these oscillations, (Hager and Wohlmuth 2007) proposed non-standard quadrature rules for the mass matrix, developing the <span><math><msub><mrow><mi>Q</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> and <span><math><msub><mrow><mi>Q</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> modified mass matrices. This work introduces and evaluates an extension of the <span><math><msub><mrow><mi>Q</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> mass matrix to quadratic elements. Additionally, we investigate the influence of the parameter <span><math><msub><mrow><mi>α</mi></mrow><mrow><mi>c</mi></mrow></msub></math></span>, which governs the temporal discretization of contact forces, on the performance of both consistent and modified mass matrices. Numerical results demonstrate that the proposed formulation effectively preserves the oscillation-suppressing capabilities of the <span><math><msub><mrow><mi>Q</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> mass matrix to quadratic elements. Furthermore, it was observed that for <span><math><mrow><msub><mrow><mi>α</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>=</mo><mn>0</mn></mrow></math></span> the consistent mass matrix displays good results, while for <span><math><mrow><msub><mrow><mi>α</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>=</mo><msub><mrow><mi>α</mi></mrow><mrow><mi>f</mi></mrow></msub></mrow></math></span> the modified mass matrices showcase the best results.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"248 ","pages":"Article 104357"},"PeriodicalIF":3.5,"publicationDate":"2025-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143870037","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Phase-field simulation of particles rigid body motion at the early stage of sintering in powder bed fusion with electron beam: A proposal for computational efficiency","authors":"Manuela Galati ,&nbsp;Giovanni Rizza","doi":"10.1016/j.finel.2025.104359","DOIUrl":"10.1016/j.finel.2025.104359","url":null,"abstract":"<div><div>The sintering of powder particles prior to full melting is a defining feature of the powder bed fusion with electron beam (PBF-EB) process, distinguishing it from other metal additive manufacturing techniques. Sintering involves the movement of atoms toward contact points between adjacent particles, leading to neck formation and growth. This atomic movement is driven by the high working temperatures of PBF-EB, which activate diffusion mechanisms and induce rigid body motion (RBM) of particles. While research on the numerical analysis of diffusion is growing, the motion of the particles occurring during the PBF-EB and its relevance are still unexplored. This work uses a phase field model to capture the physics of early-stage sintering in PBF-EB, incorporating both diffusion and RBM driven by vacancy migration. The influence of RBM parameters on neck formation and growth during the sintering of Ti6Al4V particles under PBF-EB conditions is investigated. Simulations encompass different process phases and durations (from seconds to hours), including the preheating of the layer and the cooling of the build. In addition, this work addresses the computational challenges of modelling RBM and proposes a novel approach to enhancing diffusion coefficients to emulate RBM effects, significantly reducing simulation times. Results indicate that incorporating RBM accelerates sintering and leads to larger neck formation compared to diffusion alone, although computational time increases by 30 %. Consequently, RBM should be prioritised in scenarios where its impact is critical, such as the preheating phase of PBF-EB. In contrast, during the process, the neck growth can be analysed by the novel proposed approach which significantly enhances computational efficiency while effectively capturing the influence of RBM on neck growth.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"248 ","pages":"Article 104359"},"PeriodicalIF":3.5,"publicationDate":"2025-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143855676","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 efficient physics-based model order reduction for geometrically nonlinear solid mechanics","authors":"Phani Ram Babbepalli,&nbsp;Joris J.C. Remmers,&nbsp;Olaf van der Sluis","doi":"10.1016/j.finel.2025.104351","DOIUrl":"10.1016/j.finel.2025.104351","url":null,"abstract":"<div><div>Model order reduction simplifies detailed and complex Finite Element (FE) models by solving a reduced set of equations, typically through projection methods. This work proposes a physics-based model order reduction technique that circumvents the need for training data to solve quasi-static geometrically non-linear solid mechanics utilizing the concept of modal derivatives. This method comprises two key components. Firstly, the modified Gram–Schmidt process is incorporated to ensure an orthogonal projection in the reduction procedure. Secondly, a greedy selection algorithm that constructs the projection function with the most significant modal derivatives. This proposed method is applied to various test cases, showcasing its validity and efficacy in diverse scenarios.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"248 ","pages":"Article 104351"},"PeriodicalIF":3.5,"publicationDate":"2025-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143842739","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Advances in data-driven reduced order models using two-stage dimension reduction for coupled viscous flow and transport","authors":"Roberto M. Velho ,&nbsp;Adriano M.A. Côrtes ,&nbsp;Gabriel F. Barros ,&nbsp;Fernando A. Rochinha ,&nbsp;Alvaro L.G.A. Coutinho","doi":"10.1016/j.finel.2025.104355","DOIUrl":"10.1016/j.finel.2025.104355","url":null,"abstract":"<div><div>This study presents advances in non-intrusive data-driven reduced order model techniques for parametric partial differential equations based on a two-stage machine learning method, using a feedforward neural network and an autoencoder after a linear dimensionality reduction. Reduced order models are important tools for enabling many query tasks, typical of uncertainty quantification, optimization, and control, which are essential ingredients in digital twins and digital shadows. We exemplify the use of the proposed technique with two examples: the Rayleigh–Bénard problem, modeling convective heat flow, and a 2D lock-exchange setup, modeling gravity currents. Both cases are described by parametric systems of nonlinear partial differential equations governing coupled viscous flow and transport, showing complex dynamics. The models’ performances are rigorously assessed on data within and outside the interval of parameters used for training. We observe that the results yield values within acceptable limits for unseen scenarios and a substantial increase in runtime efficiency.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"248 ","pages":"Article 104355"},"PeriodicalIF":3.5,"publicationDate":"2025-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143837999","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 implementation of the finite element method in hybrid classical/quantum computers","authors":"Abhishek Arora ,&nbsp;Benjamin M. Ward ,&nbsp;Caglar Oskay","doi":"10.1016/j.finel.2025.104354","DOIUrl":"10.1016/j.finel.2025.104354","url":null,"abstract":"<div><div>This manuscript presents the Quantum Finite Element Method (Q-FEM) developed for use in noisy intermediate-scale quantum (NISQ) computers and employs the variational quantum linear solver (VQLS) algorithm. The proposed method leverages the classical FEM procedure to perform the unitary decomposition of the stiffness matrix and employs generator functions to design explicit quantum circuits corresponding to the unitaries. Q-FEM keeps the structure of the finite element discretization intact allowing for the use of variable element lengths and material coefficients in FEM discretization. The proposed method is tested on a steady-state heat equation discretized using linear and quadratic shape functions. Numerical verification studies are performed on the IBM QISKIT simulator and it is demonstrated that Q-FEM is effective in converging to the correct solution for a variety of problems and model discretizations, including with different element lengths, variable coefficients, and different boundary conditions. The formalism developed herein is general and can be extended to problems with higher dimensions. However, numerical examples also demonstrate that the number of parameters for the variational ansatz scale exponentially with the number of qubits, and increases the odds of convergence. Moreover, the deterioration of system conditioning with problem size results in barren plateaus and convergence difficulties.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"248 ","pages":"Article 104354"},"PeriodicalIF":3.5,"publicationDate":"2025-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143834011","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Accuracy of post-processing projections for displacement based finite element simulations in room acoustics","authors":"A.S. Nayak ,&nbsp;A. Prieto ,&nbsp;D. Fernández-Comesaña","doi":"10.1016/j.finel.2025.104349","DOIUrl":"10.1016/j.finel.2025.104349","url":null,"abstract":"<div><div>In the low-frequency range, time-harmonic room acoustic models are often solved numerically by discretizing the Helmholtz equation with finite element methods, resulting in the scalar acoustic pressure field. An alternative approach is to apply finite element methods to a vector-valued form of the Helmholtz equation, formulated in terms of the Lagrangian displacement field. In this case, computing the acoustic pressure field is required as a post-processing step. The present article focuses on this alternative approach and proposes local post-processing techniques based on Sobolev projections to compute the acoustic pressure from the displacement field solution obtained through a standard finite element method employing Raviart–Thomas discretizations. Projections of varying order and their implementations through weak formulations are demonstrated for continuous and discontinuous Galerkin procedures. The accuracy of these projection techniques is evaluated against the exact analytical solution across different benchmark cases. Additionally, their robustness is measured against noisy displacement data and the computational performance is demonstrated using a realistic auditorium example. The study demonstrates the applicability of the post-processing techniques in room acoustics and suggests that the <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>-projection is the most accurate and robust technique among the proposed methods.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"248 ","pages":"Article 104349"},"PeriodicalIF":3.5,"publicationDate":"2025-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143834010","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Parametric solutions of coupled Thermo-Hydro-Mechanical problems in real time with Proper Generalized Decomposition","authors":"Arash Moaven ,&nbsp;Thierry J. Massart ,&nbsp;Sergio Zlotnik","doi":"10.1016/j.finel.2025.104352","DOIUrl":"10.1016/j.finel.2025.104352","url":null,"abstract":"<div><div>Proper Generalized Decomposition (PGD) is a Model Order Reduction (MOR) technique used in this study to solve parametric transient Thermo-Hydro-Mechanical (THM) problems in porous media, with focus on deep geological repositories. PGD enables computing real-time solutions for THM parametric problems, which are critical in applications like enhanced oil recovery, geothermal energy, and nuclear waste disposal. This study offers two key contributions. First, it describes the separated discrete operators required by PGD to account for material and geometrical parameters in transient THM problems. Second, it explores the effectiveness of PGD through three repository model problems: (1) parametrized by rock material properties (elastic modulus, thermal and hydraulic conductivity), (2) geometrically parametrized by canister spacing, and (3) a combined four-parameter model demonstrating PGD’s ability to handle multiparameter problems. The results show that PGD applied for THM processes in porous media provides efficient, real-time solutions for complex problems, significantly enhancing computational performance to allow its incorporation in multiquery and real-time scenarios.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"247 ","pages":"Article 104352"},"PeriodicalIF":3.5,"publicationDate":"2025-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143792338","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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-based damage model with EAS approach to model isotropic continuum damage in hyperelastic materials","authors":"Krishna Murthy Pabbu ,&nbsp;Nelson Muthu ,&nbsp;Tarkes Dora Pallicity","doi":"10.1016/j.finel.2025.104350","DOIUrl":"10.1016/j.finel.2025.104350","url":null,"abstract":"<div><div>The models used for damage evolution in hyperelastic regime typically depend on material parameters like dissipation and the damage threshold. The rupture of cross-linked chains is a fundamental aspect of damage in rubbery polymers. To address this, a new reduction factor has been introduced, which extends the existing damage evolution law by incorporating a polynomial order <span><math><mi>n</mi></math></span>. This formulation is designed to precisely represent the isotropic continuum damage that occurs in nearly incompressible hyperelastic materials. The incompressibility constraint is handled by using an enhanced assumed strain (EAS) approach by enhancing the Green Lagrangian strain. Hence the total strain at a point is additively decomposed into compatible and enhanced strains. The proposed model is validated through the analysis of four standard problems — uni and biaxial tension, plate with hole and double edge notch involving a nearly incompressible Neo-Hookean material model. This validation includes varying the polynomial order to assess its impact on the results. All problems are resolved using generalized displacement control technique which is essential for handling displacement loading and observing the force–displacement response beyond the peak load.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"247 ","pages":"Article 104350"},"PeriodicalIF":3.5,"publicationDate":"2025-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143777545","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 Hybrid finite element implementation of two-potential constitutive model of dielectric elastomers","authors":"Kamalendu Ghosh ,&nbsp;Bhavesh Shrimali","doi":"10.1016/j.finel.2025.104348","DOIUrl":"10.1016/j.finel.2025.104348","url":null,"abstract":"<div><div>There has been an increasing interest in the constitutive modeling of dielectric elastomers due to their potential in enabling new technologies such as soft robotics, actuators and haptic devices. Under realistic time-dependent loadings, dielectric elastomers are inherently dissipative. They dissipate energy both through viscous deformation and through friction in their electric polarization process. However, a majority of constitutive models and their corresponding Finite Element (FE) implementations consider only mechanical dissipation. The main reason for this bias is that the mechanical relaxation time of dielectric elastomers is much larger than their electric relaxation time. However, accounting for electric dissipation, in addition to mechanical dissipation, is crucial when dealing with applied alternating electric fields. A fully coupled 3-D constitutive model for isotropic and incompressible dielectric elastomers was proposed by Ghosh and Lopez-Pamies (2021). In this paper, we critically investigate the numerical scheme proposed in this paper to solve the initial boundary value problem (IBVP) that describes the time-dependent behavior of dielectric elastomers. We find that the scheme in Ghosh and Lopez-Pamies (2021), employing a fifth-order explicit Runge–Kutta time discretization, may lead to excessively small or nonphysical time steps for IBVPs simulating the behavior of real-world elastomers. This is because of the stark contrast in the relaxation times of mechanical dissipation and electric polarization. To this end, we first present a stable implicit time-integration algorithm that overcomes the unrealistic time-step constraints imposed by the fifth-order explicit Runge–Kutta algorithm in Ghosh and Lopez-Pamies (2021). We then deploy the algorithm along with a conforming FE discretization to solve the IBVP. We present implementations of the mixed-FE formulation of the governing equations for dielectric elastomers in <span>FEniCSx</span>. We also show that the numerical scheme is robust, accurate, capable of handling finite deformations, the incompressibility constraint of the rubber, and general time-dependent loading conditions. In the last part, the FE code is deployed to validate the experimental findings describing the electromechanical behavior of VHB 4910 (from 3M) under a complex time-dependent electromechanical load as studied in Hossain et al. (2015).</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"247 ","pages":"Article 104348"},"PeriodicalIF":3.5,"publicationDate":"2025-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143759997","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}