Pub Date : 2025-12-14DOI: 10.1016/j.finel.2025.104501
E.G. Dutra do Carmo, E.F. Fontes Jr., M.F.F. Santos, W.J. Mansur
Purely convective and convective–diffusive problems with dominant convection, presenting high gradients in directions misaligned with the convective field, are typically stabilized using nonlinear methods, even when the underlying problem is linear. This not only leads to an increase in computational cost but also degrades the accuracy of the gradient of the approximate solution. Therefore, it is desirable to obtain a method that completely stabilizes the approximated solution gradient while ensuring optimal approximation rates for it. In this sense, the Gradient Complete Stabilization Method (GCSM) is proposed in this paper. A rigorous mathematical analysis of the method is performed by elaborating the variational formulation of the diffusive–convective–reactive problem. A robust set of theorems is defined and proved, including the Fundamental Identity Theorem, which plays a central role in enabling gradient stabilization with optimal convergence rates. Several numerical experiments are conducted, comparing accuracy from GCSM against a classic discontinuity capture method, the Consistent Approximate Upwind (CAU). The results demonstrate a marked improvement in performance achieved by the proposed method, especially in the final example, which involves both internal and external boundary layers. In this case, the GCSM delivers solutions that are nearly oscillation-free.
{"title":"The Gradient Complete Stabilization Method (GCSM) for scalar diffusive–convective–reactive problems","authors":"E.G. Dutra do Carmo, E.F. Fontes Jr., M.F.F. Santos, W.J. Mansur","doi":"10.1016/j.finel.2025.104501","DOIUrl":"https://doi.org/10.1016/j.finel.2025.104501","url":null,"abstract":"Purely convective and convective–diffusive problems with dominant convection, presenting high gradients in directions misaligned with the convective field, are typically stabilized using nonlinear methods, even when the underlying problem is linear. This not only leads to an increase in computational cost but also degrades the accuracy of the gradient of the approximate solution. Therefore, it is desirable to obtain a method that completely stabilizes the approximated solution gradient while ensuring optimal approximation rates for it. In this sense, the Gradient Complete Stabilization Method (GCSM) is proposed in this paper. A rigorous mathematical analysis of the method is performed by elaborating the variational formulation of the diffusive–convective–reactive problem. A robust set of theorems is defined and proved, including the Fundamental Identity Theorem, which plays a central role in enabling gradient stabilization with optimal convergence rates. Several numerical experiments are conducted, comparing accuracy from GCSM against a classic discontinuity capture method, the Consistent Approximate Upwind (CAU). The results demonstrate a marked improvement in performance achieved by the proposed method, especially in the final example, which involves both internal and external boundary layers. In this case, the GCSM delivers solutions that are nearly oscillation-free.","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"1 1","pages":""},"PeriodicalIF":3.1,"publicationDate":"2025-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145753512","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}
This paper presents a highly-efficient finite element scheme for the time relaxation model (TRM). The efficiency is achieved through the second-order BDF2 time-stepping scheme with linear extrapolation (BDF2LE). The accuracy of the scheme is also greatly enhanced through the use of the divergence-free Scott-Vogeulis finite elements, and van Cittert approximate deconvolution. A complete finite element analysis is provided, which includes rigorous proofs for the stability, well-possessedness, and convergence of both velocity and pressure solutions. We also demonstrate that the inclusion of the linear time relaxation term preserves the long-time stability of the unregularized BDF2LE scheme. Finally, numerical experiments are presented that demonstrate the added stability and accuracy that time relaxation can provide.
{"title":"Regularizing the linearly extrapolated BDF2 scheme for incompressible flows with time relaxation","authors":"Sean Breckling , Jorge Reyes , Sidney Shields , Clifford Watkins","doi":"10.1016/j.finel.2025.104491","DOIUrl":"10.1016/j.finel.2025.104491","url":null,"abstract":"<div><div>This paper presents a highly-efficient finite element scheme for the time relaxation model (TRM). The efficiency is achieved through the second-order BDF2 time-stepping scheme with linear extrapolation (BDF2LE). The accuracy of the scheme is also greatly enhanced through the use of the divergence-free Scott-Vogeulis finite elements, and van Cittert approximate deconvolution. A complete finite element analysis is provided, which includes rigorous proofs for the stability, well-possessedness, and convergence of both velocity and pressure solutions. We also demonstrate that the inclusion of the linear time relaxation term preserves the long-time stability of the unregularized BDF2LE scheme. Finally, numerical experiments are presented that demonstrate the added stability and accuracy that time relaxation can provide.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"254 ","pages":"Article 104491"},"PeriodicalIF":3.5,"publicationDate":"2025-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145731679","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}
Pub Date : 2025-12-05DOI: 10.1016/j.finel.2025.104490
Fengling Chen, Yiqian He, Haitian Yang
A stepwise spatial–temporal finite element algorithm is developed to provide a general numerical tool for solving static viscoelastic problems with integral constitutive equations. The displacement, strain and stress are formulated by the hybrid basis functions based Temporal Finite Element Method (TFEM), and are incorporated into the constitutive relations. The framework is established based on the virtual work principle and the weighted residual technique, and is convenient to cooperate with kinds of numerical schemes for boundary value problems such as FEM and SBFEM. Two criteria are proposed to numerically evaluate error propagation during the step-marching process, which can be used to determine appropriate time-step sizes for prescribed temporal shape functions and spatial FE meshes. Compared with the TFEM algorithm based on differential viscoelastic constitutive equations, the present approach overcomes the order-restriction limitation by employing integral constitutive equations with Prony-series based relaxation moduli. Numerical examples demonstrate the capability and accuracy of the proposed method in handling viscoelastic problems involving material heterogeneity, stress singularity, various relaxation moduli, and different loading forms. The obtained results with various configurations of temporal shape functions and step sizes, exhibit good agreement with analytical solutions and ABAQUS simulations.
{"title":"Integral constitutive equations based temporal finite element modeling for the static viscoelastic problem","authors":"Fengling Chen, Yiqian He, Haitian Yang","doi":"10.1016/j.finel.2025.104490","DOIUrl":"10.1016/j.finel.2025.104490","url":null,"abstract":"<div><div>A stepwise spatial–temporal finite element algorithm is developed to provide a general numerical tool for solving static viscoelastic problems with integral constitutive equations. The displacement, strain and stress are formulated by the hybrid basis functions based Temporal Finite Element Method (TFEM), and are incorporated into the constitutive relations. The framework is established based on the virtual work principle and the weighted residual technique, and is convenient to cooperate with kinds of numerical schemes for boundary value problems such as FEM and SBFEM. Two criteria are proposed to numerically evaluate error propagation during the step-marching process, which can be used to determine appropriate time-step sizes for prescribed temporal shape functions and spatial FE meshes. Compared with the TFEM algorithm based on differential viscoelastic constitutive equations, the present approach overcomes the order-restriction limitation by employing integral constitutive equations with Prony-series based relaxation moduli. Numerical examples demonstrate the capability and accuracy of the proposed method in handling viscoelastic problems involving material heterogeneity, stress singularity, various relaxation moduli, and different loading forms. The obtained results with various configurations of temporal shape functions and step sizes, exhibit good agreement with analytical solutions and ABAQUS simulations.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"254 ","pages":"Article 104490"},"PeriodicalIF":3.5,"publicationDate":"2025-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145685751","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}
Pub Date : 2025-12-03DOI: 10.1016/j.finel.2025.104487
S. Eisenträger , E. Woschke , E.T. Ooi
This paper presents a comparative analysis of the conventional finite element method (FEM) and the unsymmetric finite element method (UFEM) for Serendipity elements (), focusing on two factors: (i) achievable accuracy and (ii) computational costs. The UFEM, based on a Petrov–Galerkin formulation, uses metric shape functions as trial functions and parametric shape functions as test functions. This unique approach enhances the resistance against mesh distortion, as it ensures polynomial completeness of the Ansatz space of unsymmetric finite elements. Hence, higher accuracy can be achieved in complex geometries. However, the unsymmetric nature of UFEM leads to increased computational costs as a result of the added complexity of solving the resulting system of equations. This study provides a quantitative evaluation of the computational burden associated with achieving specific error thresholds for both methods. By analyzing a range of benchmark problems, we identify scenarios in which each method performs optimally, offering practical insights for selecting the appropriate approach based on accuracy demands and computational constraints. Our findings suggest that, while UFEM can produce superior accuracy, its computational efficiency depends on application-specific requirements and available resources.
{"title":"Unsymmetric Serendipity finite elements: Performance analysis","authors":"S. Eisenträger , E. Woschke , E.T. Ooi","doi":"10.1016/j.finel.2025.104487","DOIUrl":"10.1016/j.finel.2025.104487","url":null,"abstract":"<div><div>This paper presents a comparative analysis of the conventional finite element method (FEM) and the unsymmetric finite element method (UFEM) for Serendipity elements (<span><math><mrow><mi>p</mi><mo>≤</mo><mn>3</mn></mrow></math></span>), focusing on two factors: (i) achievable accuracy and (ii) computational costs. The UFEM, based on a Petrov–Galerkin formulation, uses <em>metric</em> shape functions as <em>trial</em> functions and <em>parametric</em> shape functions as <em>test</em> functions. This unique approach enhances the resistance against mesh distortion, as it ensures polynomial completeness of the Ansatz space of unsymmetric finite elements. Hence, higher accuracy can be achieved in complex geometries. However, the unsymmetric nature of UFEM leads to increased computational costs as a result of the added complexity of solving the resulting system of equations. This study provides a quantitative evaluation of the computational burden associated with achieving specific error thresholds for both methods. By analyzing a range of benchmark problems, we identify scenarios in which each method performs optimally, offering practical insights for selecting the appropriate approach based on accuracy demands and computational constraints. Our findings suggest that, while UFEM can produce superior accuracy, its computational efficiency depends on application-specific requirements and available resources.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"254 ","pages":"Article 104487"},"PeriodicalIF":3.5,"publicationDate":"2025-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145659097","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}
This paper introduces a compact and time-efficient reduced-order modelling method for conducting thermal–mechanical analyses and studying material nonlinearities in power electronic modules (PEMs). Thermal–mechanical analyses in reduced-order modelling research typically follow a sequential coupling approach, where the thermal model is solved first, allowing the resulting temperature distributions to serve as loads in the mechanical system. In this study, a direct coupling method is employed for the thermomechanical analysis, enabling the simultaneous evaluation of the thermal and structural governing equations to determine thermal and directional deformation distributions, with temperature and deformations as the degrees of freedom (DOFs) of the coupled system. A novel approach, utilising the Krylov subspace-based model order reduction (MOR) process, the Newmark and Newton–Raphson algorithms within the reduced-order modelling framework, have been developed for analysing material nonlinearity in PEMs. The time domain responses, i.e., the transient ROM solutions, align remarkably well with the corresponding FOM solutions. The inelastic strains and plastic work results demonstrate strong consistency for materials having time-independent (plasticity) and time-dependent (creep and viscoplasticity) nonlinearities. Responses of the reduced-order model (ROM) in the frequency (Laplace) domain are analysed in contrast to its full-order model (FOM) to evaluate its characteristics and show suitability within the required expansion points. The MOR process provides a significantly compact ROM order of just 2020 for reduced-dimensional computation, achieving up to an 83% reduction in computational time compared to its FOM order of approximately 400,000400,000. The reduced-order modelling approach is implemented using the MATLAB coding environment.
{"title":"Reduced-Order Modelling for Thermal–Mechanical Analysis of Power Electronic Modules","authors":"Sheikh Hassan , Stoyan Stoyanov , Pushparajah Rajaguru , Christopher Bailey","doi":"10.1016/j.finel.2025.104488","DOIUrl":"10.1016/j.finel.2025.104488","url":null,"abstract":"<div><div>This paper introduces a compact and time-efficient reduced-order modelling method for conducting thermal–mechanical analyses and studying material nonlinearities in power electronic modules (PEMs). Thermal–mechanical analyses in reduced-order modelling research typically follow a sequential coupling approach, where the thermal model is solved first, allowing the resulting temperature distributions to serve as loads in the mechanical system. In this study, a direct coupling method is employed for the thermomechanical analysis, enabling the simultaneous evaluation of the thermal and structural governing equations to determine thermal and directional deformation distributions, with temperature and deformations as the degrees of freedom (DOFs) of the coupled system. A novel approach, utilising the Krylov subspace-based model order reduction (MOR) process, the Newmark and Newton–Raphson algorithms within the reduced-order modelling framework, have been developed for analysing material nonlinearity in PEMs. The time domain responses, i.e., the transient ROM solutions, align remarkably well with the corresponding FOM solutions. The inelastic strains and plastic work results demonstrate strong consistency for materials having time-independent (plasticity) and time-dependent (creep and viscoplasticity) nonlinearities. Responses of the reduced-order model (ROM) in the frequency (Laplace) domain are analysed in contrast to its full-order model (FOM) to evaluate its characteristics and show suitability within the required expansion points. The MOR process provides a significantly compact ROM order of just 20<span><math><mo>×</mo></math></span>20 for reduced-dimensional computation, achieving up to an 83% reduction in computational time compared to its FOM order of approximately 400,000<span><math><mo>×</mo></math></span>400,000. The reduced-order modelling approach is implemented using the MATLAB coding environment.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"253 ","pages":"Article 104488"},"PeriodicalIF":3.5,"publicationDate":"2025-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145598939","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}
Pub Date : 2025-11-20DOI: 10.1016/j.finel.2025.104486
Komlavi Mawuli Senyo , Loup Plantevin , Thibaut Chaise , Eric Feulvarch , Jean-Michel Bergheau , Daniel Nélias
Compression techniques such as shot peening, laser shock peening, and water jet peening are commonly employed to induce residual compressive stresses in mechanical components. These residual stresses play a crucial role in preventing the initiation and propagation of cracks. An innovative method known as the ElectroMagnetic pulse Peening (EMP) process utilizes magnetic forces to introduce residual compressive stresses in mechanical components. The EMP process shares similarities with the ElectroMagnetic Forming (EMF) process, which has been extensively studied through numerical and experimental investigations. Existing numerical studies predominantly feature axisymmetric 2D simulations, with limited availability of 3D simulations due to numerical constraints regarding computing time and resources. Since the EMP process shares similarities with EMF, similar challenges arise with respect to computational resources and time. This paper presents an innovative approach for the 3D simulation of residual stresses induced by the EMP process, based on efficient 2D axisymmetric calculations of the electromagnetic fields. The main objective of this approach is to simulate the mechanical impact of electromagnetic pulses applied by sweeping a surface, in order to analyze the stress distribution in the overlapping regions. First, the 2D model used to simulate electromagnetic phenomena is presented, and the 2D-to-3D transfer technique developed is detailed for computing residual stresses in 3D. Subsequently, the validity of this approach is established through a comparative study between 2D and 3D mechanical results for a single electromagnetic pulse. Finally, a multiple-pulse simulation is conducted to investigate the effect of overlapping treatment regions on an AA6061 aluminum alloy. The outcomes of this study are discussed in terms of the residual stresses at the subsurface.
{"title":"3D simulation of residual stresses induced by ElectroMagnetic pulse Peening process","authors":"Komlavi Mawuli Senyo , Loup Plantevin , Thibaut Chaise , Eric Feulvarch , Jean-Michel Bergheau , Daniel Nélias","doi":"10.1016/j.finel.2025.104486","DOIUrl":"10.1016/j.finel.2025.104486","url":null,"abstract":"<div><div>Compression techniques such as shot peening, laser shock peening, and water jet peening are commonly employed to induce residual compressive stresses in mechanical components. These residual stresses play a crucial role in preventing the initiation and propagation of cracks. An innovative method known as the ElectroMagnetic pulse Peening (EMP) process utilizes magnetic forces to introduce residual compressive stresses in mechanical components. The EMP process shares similarities with the ElectroMagnetic Forming (EMF) process, which has been extensively studied through numerical and experimental investigations. Existing numerical studies predominantly feature axisymmetric 2D simulations, with limited availability of 3D simulations due to numerical constraints regarding computing time and resources. Since the EMP process shares similarities with EMF, similar challenges arise with respect to computational resources and time. This paper presents an innovative approach for the 3D simulation of residual stresses induced by the EMP process, based on efficient 2D axisymmetric calculations of the electromagnetic fields. The main objective of this approach is to simulate the mechanical impact of electromagnetic pulses applied by sweeping a surface, in order to analyze the stress distribution in the overlapping regions. First, the 2D model used to simulate electromagnetic phenomena is presented, and the 2D-to-3D transfer technique developed is detailed for computing residual stresses in 3D. Subsequently, the validity of this approach is established through a comparative study between 2D and 3D mechanical results for a single electromagnetic pulse. Finally, a multiple-pulse simulation is conducted to investigate the effect of overlapping treatment regions on an AA6061 aluminum alloy. The outcomes of this study are discussed in terms of the residual stresses at the subsurface.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"253 ","pages":"Article 104486"},"PeriodicalIF":3.5,"publicationDate":"2025-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145560124","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}
Pub Date : 2025-11-20DOI: 10.1016/j.finel.2025.104484
R.P. Cardoso Coelho, F.M. Andrade Pires
This work presents methodological and computational advances to a multiscale micromechanical framework for modelling transformation-induced plasticity (TRIP) steels, explicitly coupling martensitic phase transformation and multi-phase crystallographic slip within an RVE-based homogenisation setting. Building upon the framework of Cardoso Coelho et al. (2023), we introduce a series of enhancements aimed at improving computational efficiency, expanding modelling capabilities, and increasing predictive fidelity. The numerical implementation is restructured to exploit cache-optimised data access, branchless return-mapping algorithms, selective Jacobian assembly, and explicitly vectorised linear solvers, resulting in significant reductions in computational cost, particularly for martensite-dominated loading scenarios. A mixed stress–strain-driven homogenisation scheme is formulated, enabling independent control of specific stress and strain components, thus improving the representation of experimentally observed strain-controlled uniaxial tests. Model calibration and validation are performed against experimental data using a composite Bayesian optimisation strategy, showing excellent agreement with measured stress–strain responses and a consistent prediction of martensite volume fraction evolution. Additional energetic contributions are investigated to refine the description of transformation kinetics, further enhancing model accuracy. Overall, this work delivers a robust, high-performance multiscale computational framework for TRIP steels, advancing predictive modelling capabilities for phase-transforming materials and supporting more reliable virtual material design.
{"title":"Efficient and accurate multiscale modelling of TRIP steels: Advanced numerical strategies and experimental validation","authors":"R.P. Cardoso Coelho, F.M. Andrade Pires","doi":"10.1016/j.finel.2025.104484","DOIUrl":"10.1016/j.finel.2025.104484","url":null,"abstract":"<div><div>This work presents methodological and computational advances to a multiscale micromechanical framework for modelling transformation-induced plasticity (TRIP) steels, explicitly coupling martensitic phase transformation and multi-phase crystallographic slip within an RVE-based homogenisation setting. Building upon the framework of Cardoso Coelho et al. (2023), we introduce a series of enhancements aimed at improving computational efficiency, expanding modelling capabilities, and increasing predictive fidelity. The numerical implementation is restructured to exploit cache-optimised data access, branchless return-mapping algorithms, selective Jacobian assembly, and explicitly vectorised linear solvers, resulting in significant reductions in computational cost, particularly for martensite-dominated loading scenarios. A mixed stress–strain-driven homogenisation scheme is formulated, enabling independent control of specific stress and strain components, thus improving the representation of experimentally observed strain-controlled uniaxial tests. Model calibration and validation are performed against experimental data using a composite Bayesian optimisation strategy, showing excellent agreement with measured stress–strain responses and a consistent prediction of martensite volume fraction evolution. Additional energetic contributions are investigated to refine the description of transformation kinetics, further enhancing model accuracy. Overall, this work delivers a robust, high-performance multiscale computational framework for TRIP steels, advancing predictive modelling capabilities for phase-transforming materials and supporting more reliable virtual material design.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"253 ","pages":"Article 104484"},"PeriodicalIF":3.5,"publicationDate":"2025-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145559925","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}
Embedded finite element formulations have gained increased attention for modeling strong discontinuities in solid mechanics problems, as they eliminate the need for mesh conformity required by discrete fracture models. While several such formulations have been extensively studied, particularly regarding strategies to mitigate stress locking, less is understood about the causes and possible remedies to the spurious stress oscillations along cohesive discontinuities. In this work, we employ the Enhanced Assumed Strain framework to derive two of the most popular formulation types: the Kinematically Optimal Symmetric (KOS) and the Statically and Kinematically Optimal Nonsymmetric (SKON). We investigate their performance in a broad range of scenarios, including stick and slip contact conditions, in both two and three dimensions, using linear and quadratic finite elements. Our results show that the SKON formulation consistently yields smoother cohesive stress fields by enforcing local equilibrium in a strong sense. While spurious oscillations are effectively eliminated under stick conditions, small-amplitude oscillations may persist under slip conditions; however, they are significantly reduced compared to the KOS formulation. Finally, we demonstrate the application of the SKON formulation to a fault reactivation problem, confirming its capability to accurately capture stress evolution and assess fault reactivation risk.
{"title":"Behavior of cohesive stresses in embedded finite elements based on the strong discontinuity approach","authors":"Danilo Cavalcanti , Cristian Mejia , Caio Souza , Carlos A. Mendes , Ignasi de-Pouplana , Guillermo Casas , Deane Roehl","doi":"10.1016/j.finel.2025.104485","DOIUrl":"10.1016/j.finel.2025.104485","url":null,"abstract":"<div><div>Embedded finite element formulations have gained increased attention for modeling strong discontinuities in solid mechanics problems, as they eliminate the need for mesh conformity required by discrete fracture models. While several such formulations have been extensively studied, particularly regarding strategies to mitigate stress locking, less is understood about the causes and possible remedies to the spurious stress oscillations along cohesive discontinuities. In this work, we employ the Enhanced Assumed Strain framework to derive two of the most popular formulation types: the Kinematically Optimal Symmetric (KOS) and the Statically and Kinematically Optimal Nonsymmetric (SKON). We investigate their performance in a broad range of scenarios, including stick and slip contact conditions, in both two and three dimensions, using linear and quadratic finite elements. Our results show that the SKON formulation consistently yields smoother cohesive stress fields by enforcing local equilibrium in a strong sense. While spurious oscillations are effectively eliminated under stick conditions, small-amplitude oscillations may persist under slip conditions; however, they are significantly reduced compared to the KOS formulation. Finally, we demonstrate the application of the SKON formulation to a fault reactivation problem, confirming its capability to accurately capture stress evolution and assess fault reactivation risk.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"253 ","pages":"Article 104485"},"PeriodicalIF":3.5,"publicationDate":"2025-11-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145559904","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}
Pub Date : 2025-11-08DOI: 10.1016/j.finel.2025.104473
Rahul Verma , David Codoni , Craig Johansen , A. Korobenko
This study evaluates the performance of the Spalart–Allmaras (SA) turbulence model within a finite element framework. The streamline upwind Petrov–Galerkin (SUPG) method is employed as a stabilization technique to provide numerical stability. The proposed formulation solves the three-dimensional Navier–Stokes (N-S) equations expressed in primitive variables. The robustness and accuracy of the stabilized framework, incorporating the one-equation SA turbulence model, are assessed across a wide range of Mach numbers using benchmark test cases. The results demonstrate the effectiveness of the present approach in modeling high-speed turbulent flows, including separated boundary layers and shock wave interactions.
{"title":"Assessment of the Spalart–Allmaras turbulence model in a stabilized finite element framework for hypersonic turbulent flows using pressure-primitive variables","authors":"Rahul Verma , David Codoni , Craig Johansen , A. Korobenko","doi":"10.1016/j.finel.2025.104473","DOIUrl":"10.1016/j.finel.2025.104473","url":null,"abstract":"<div><div>This study evaluates the performance of the Spalart–Allmaras (SA) turbulence model within a finite element framework. The streamline upwind Petrov–Galerkin (SUPG) method is employed as a stabilization technique to provide numerical stability. The proposed formulation solves the three-dimensional Navier–Stokes (N-S) equations expressed in primitive variables. The robustness and accuracy of the stabilized framework, incorporating the one-equation SA turbulence model, are assessed across a wide range of Mach numbers using benchmark test cases. The results demonstrate the effectiveness of the present approach in modeling high-speed turbulent flows, including separated boundary layers and shock wave interactions.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"253 ","pages":"Article 104473"},"PeriodicalIF":3.5,"publicationDate":"2025-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145461930","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}
In this paper, the thermo-mechanical-electro-magnetic enriched finite element method (TMEM-EFEM) is proposed to analyze static models of magneto-electro-elastic smart structures. An improvement over the traditional finite element method (FEM) is that the displacement, electric and magnetic fields are fitted by interpolation covering functions. The support domain of the node is constructed by a series of triangular elements. Although the concept of support domain is used, the proposed method does not require high computational cost to solve the extent of the support domain. The feasibility of TMEM-EFEM is demonstrated by a series of numerical examples. The proposed method is proven to be efficient under coarse and distorted meshes. Besides, the adaptive mesh refinement (AMR) technology is used to locally refine functionally graded magneto-electro-elastic smart structures in interested areas under a coarse mesh. The generalized strain energy criterion is used in the AMR technology. Through a series of numerical examples, the high accuracy of the proposed method under the AMR partitioning scheme is demonstrated. The results show that the values of displacement uz, electric potential Φ and magnetic potential Ψ decrease with the increase of exponential factors. The computational efficiency of TMEM-EFEM is significantly higher than that of FEM, which verifies the correctness and effectiveness of this method.
{"title":"The adaptive thermo-mechanical-electro-magnetic enriched finite element method for statics analysis of functionally graded magneto-electro-elastic structures","authors":"Liming Zhou , Guangyu Liang , Jiye Wang , Panpan Zhu","doi":"10.1016/j.finel.2025.104476","DOIUrl":"10.1016/j.finel.2025.104476","url":null,"abstract":"<div><div>In this paper, the thermo-mechanical-electro-magnetic enriched finite element method (TMEM-EFEM) is proposed to analyze static models of magneto-electro-elastic smart structures. An improvement over the traditional finite element method (FEM) is that the displacement, electric and magnetic fields are fitted by interpolation covering functions. The support domain of the node is constructed by a series of triangular elements. Although the concept of support domain is used, the proposed method does not require high computational cost to solve the extent of the support domain. The feasibility of TMEM-EFEM is demonstrated by a series of numerical examples. The proposed method is proven to be efficient under coarse and distorted meshes. Besides, the adaptive mesh refinement (AMR) technology is used to locally refine functionally graded magneto-electro-elastic smart structures in interested areas under a coarse mesh. The generalized strain energy criterion is used in the AMR technology. Through a series of numerical examples, the high accuracy of the proposed method under the AMR partitioning scheme is demonstrated. The results show that the values of displacement <em>u</em><sub><em>z</em></sub>, electric potential <em>Φ</em> and magnetic potential <em>Ψ</em> decrease with the increase of exponential factors. The computational efficiency of TMEM-EFEM is significantly higher than that of FEM, which verifies the correctness and effectiveness of this method.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"253 ","pages":"Article 104476"},"PeriodicalIF":3.5,"publicationDate":"2025-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145473076","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}
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