Pub Date : 2025-09-09DOI: 10.1016/j.finel.2025.104438
Nour Habib, Saber El Arem, Amine Ammar
Rock salt, owing to its viscoplastic behavior and structural integrity under high pressure, is a promising candidate for safe and large-scale underground energy storage. This study presents a comprehensive numerical framework for modeling the viscoplastic deformation of rock salt, accounting for both intragranular and grain boundary (GB) deformation mechanisms. Intragranular deformation is modeled using a crystal plasticity approach governed by a power-law relation, capturing the activity of crystallographic slip systems. Concurrently, a cohesive zone model (CZM) is introduced to simulate grain boundary sliding (GBS) and opening via a rate-dependent traction–separation law. This modeling strategy enables a detailed analysis of the coupled interplay between crystal plasticity and intergranular decohesion phenomena.
{"title":"Coupled crystal plasticity-cohesive zone modeling of rock salt viscoplasticity","authors":"Nour Habib, Saber El Arem, Amine Ammar","doi":"10.1016/j.finel.2025.104438","DOIUrl":"10.1016/j.finel.2025.104438","url":null,"abstract":"<div><div>Rock salt, owing to its viscoplastic behavior and structural integrity under high pressure, is a promising candidate for safe and large-scale underground energy storage. This study presents a comprehensive numerical framework for modeling the viscoplastic deformation of rock salt, accounting for both intragranular and grain boundary (GB) deformation mechanisms. Intragranular deformation is modeled using a crystal plasticity approach governed by a power-law relation, capturing the activity of crystallographic slip systems. Concurrently, a cohesive zone model (CZM) is introduced to simulate grain boundary sliding (GBS) and opening via a rate-dependent traction–separation law. This modeling strategy enables a detailed analysis of the coupled interplay between crystal plasticity and intergranular decohesion phenomena.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"252 ","pages":"Article 104438"},"PeriodicalIF":3.5,"publicationDate":"2025-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145027841","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 : 2025-09-08DOI: 10.1016/j.finel.2025.104375
Hongwei Song , Jianping Zhao , Yanren Hou
A novel locally parallel finite element algorithm for addressing the Stokes problem has been developed, leveraging the two-grid method and the unit splitting technique. This innovative algorithm boasts several key advantages: (1) it operates independently of the hyperapproximation property, enhancing its applicability across various scenarios; (2) the decomposition of regions is solely dependent on the unit splitting technique, simplifying the computational process; and (3) by incorporating constraints on local corrections, the algorithm employs the penalized form of the Stokes problem. This strategic choice facilitates the exclusive resolution of the velocity field function under specific assumptions, thereby streamlining the solution process and potentially reducing computational complexity.
{"title":"An expandable local and parallel two-grid finite element scheme for Stokes problem","authors":"Hongwei Song , Jianping Zhao , Yanren Hou","doi":"10.1016/j.finel.2025.104375","DOIUrl":"10.1016/j.finel.2025.104375","url":null,"abstract":"<div><div>A novel locally parallel finite element algorithm for addressing the Stokes problem has been developed, leveraging the two-grid method and the unit splitting technique. This innovative algorithm boasts several key advantages: (1) it operates independently of the hyperapproximation property, enhancing its applicability across various scenarios; (2) the decomposition of regions is solely dependent on the unit splitting technique, simplifying the computational process; and (3) by incorporating constraints on local corrections, the algorithm employs the penalized form of the Stokes problem. This strategic choice facilitates the exclusive resolution of the velocity field function under specific assumptions, thereby streamlining the solution process and potentially reducing computational complexity.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"252 ","pages":"Article 104375"},"PeriodicalIF":3.5,"publicationDate":"2025-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145027842","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 : 2025-09-07DOI: 10.1016/j.finel.2025.104441
Jamal F. Husseini , Eric J. Carey , Evan J. Pineda , Brett A. Bednarcyk , Farhad Pourkamali-Anaraki , Scott E. Stapleton
Composite microstructures are susceptible to localized stress concentrations between close or touching fibers where failure can initiate and propagate. Typically, representative volume elements are used to predict mechanical response by simulating random microstructure arrangements under different loading configurations. However, these simulations can be prohibitively expensive when considering large microstructures or closely packed fibers. The current work aims to provide a computationally efficient method for predicting homogenized and local properties of composite microstructures through a novel finite element mesh referred to as the fixed triangulation-mesh model. This triangulation-based meshing algorithm uses configured element sizes where the highest stresses occur and higher order elements to capture stress gradients between closely packed fibers. An efficient homogenization technique to fully characterize the stiffness matrix of the composite without the need for individual load perturbations or stress integration was derived and implemented. A progressive damage model using the smeared crack approach was implemented with higher order elements to simulate post-peak softening. The results for stiffness, transverse strength, and in-plane shear strength were verified against the high fidelity generalized method of cells for different microstructures of varying fiber volume fractions. Then, a comparison was made to a refined mesh finite element model with linear elements and a toughened matrix. The fixed triangulation-mesh model showed good agreement between the high fidelity generalized method of cells and linear element models, and computation time was reduced by approximately 104 times for the low-toughness matrix, and 55 times for the toughened matrix.
{"title":"An efficient higher-order triangulation based micromechanical model for fiber composites","authors":"Jamal F. Husseini , Eric J. Carey , Evan J. Pineda , Brett A. Bednarcyk , Farhad Pourkamali-Anaraki , Scott E. Stapleton","doi":"10.1016/j.finel.2025.104441","DOIUrl":"10.1016/j.finel.2025.104441","url":null,"abstract":"<div><div>Composite microstructures are susceptible to localized stress concentrations between close or touching fibers where failure can initiate and propagate. Typically, representative volume elements are used to predict mechanical response by simulating random microstructure arrangements under different loading configurations. However, these simulations can be prohibitively expensive when considering large microstructures or closely packed fibers. The current work aims to provide a computationally efficient method for predicting homogenized and local properties of composite microstructures through a novel finite element mesh referred to as the fixed triangulation-mesh model. This triangulation-based meshing algorithm uses configured element sizes where the highest stresses occur and higher order elements to capture stress gradients between closely packed fibers. An efficient homogenization technique to fully characterize the stiffness matrix of the composite without the need for individual load perturbations or stress integration was derived and implemented. A progressive damage model using the smeared crack approach was implemented with higher order elements to simulate post-peak softening. The results for stiffness, transverse strength, and in-plane shear strength were verified against the high fidelity generalized method of cells for different microstructures of varying fiber volume fractions. Then, a comparison was made to a refined mesh finite element model with linear elements and a toughened matrix. The fixed triangulation-mesh model showed good agreement between the high fidelity generalized method of cells and linear element models, and computation time was reduced by approximately 104 times for the low-toughness matrix, and 55 times for the toughened matrix.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"252 ","pages":"Article 104441"},"PeriodicalIF":3.5,"publicationDate":"2025-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145009041","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 : 2025-09-04DOI: 10.1016/j.finel.2025.104419
Hameed S. Lamy , David Avila , Mauricio Aristizabal , David Restrepo , Harry Millwater , Arturo Montoya
This study presents an enhanced approach for conducting sensitivity analysis of nonlinear problems involving a combination of geometric nonlinearities and follower loads, particularly those involving displacement-dependent forces. The method utilizes the complex-variable finite element method (ZFEM), incorporating complex algebra into the conventional finite element incremental-iterative procedure to achieve highly accurate derivative calculations. A crucial task in this process is computing a complex-valued, non-constant external force that depends on a complex-valued displacement. The key innovation lies in overcoming challenges associated with sensitivity computation for geometric nonlinearities and follower loads through a streamlined and computationally efficient methodology that can be integrated with commercial finite element software. The method enhances implementation efficiency by avoiding the need for intricate analytical derivations and not depending on unstable numerical approximations, such as the Finite Difference Method (FDM). ZFEM’s versatility and robustness were verified against sensitivity analytical solutions for cantilever beam problems undergoing large elastic rotations and displacements under static and dynamic loading conditions. The numerical examples demonstrated excellent agreement with analytical solutions and finite differencing results, maintaining accuracy and stability across all cases. This research demonstrates that ZFEM significantly increases accessibility for computing sensitivities in complex solid mechanics problems, providing a user-friendly and efficient method for both static and dynamic scenarios involving geometric and follower loads.
{"title":"Sensitivity analysis for problems exhibiting geometric nonlinearities and follower loads using the complex-variable finite element method","authors":"Hameed S. Lamy , David Avila , Mauricio Aristizabal , David Restrepo , Harry Millwater , Arturo Montoya","doi":"10.1016/j.finel.2025.104419","DOIUrl":"10.1016/j.finel.2025.104419","url":null,"abstract":"<div><div>This study presents an enhanced approach for conducting sensitivity analysis of nonlinear problems involving a combination of geometric nonlinearities and follower loads, particularly those involving displacement-dependent forces. The method utilizes the complex-variable finite element method (ZFEM), incorporating complex algebra into the conventional finite element incremental-iterative procedure to achieve highly accurate derivative calculations. A crucial task in this process is computing a complex-valued, non-constant external force that depends on a complex-valued displacement. The key innovation lies in overcoming challenges associated with sensitivity computation for geometric nonlinearities and follower loads through a streamlined and computationally efficient methodology that can be integrated with commercial finite element software. The method enhances implementation efficiency by avoiding the need for intricate analytical derivations and not depending on unstable numerical approximations, such as the Finite Difference Method (FDM). ZFEM’s versatility and robustness were verified against sensitivity analytical solutions for cantilever beam problems undergoing large elastic rotations and displacements under static and dynamic loading conditions. The numerical examples demonstrated excellent agreement with analytical solutions and finite differencing results, maintaining accuracy and stability across all cases. This research demonstrates that ZFEM significantly increases accessibility for computing sensitivities in complex solid mechanics problems, providing a user-friendly and efficient method for both static and dynamic scenarios involving geometric and follower loads.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"251 ","pages":"Article 104419"},"PeriodicalIF":3.5,"publicationDate":"2025-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144988480","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 study presents the numerical modeling of frames composed of thin-walled beams with open cross-section subjected to large torsions by a High Order Continuation Method (HOCM), based on Asymptotic Numerical Method (ANM) techniques. The theoretical model is developed using beam kinematics, which accounts for flexion-torsion coupling and large rotations. The connection between beams is ensured by joints (stiffening plates) to avoid local deformations, mathematically modeled by compatibility conditions applied to the connection nodes. The equilibrium equations are established using the minimization of the Lagrangian. Discretization is performed with a two-node beam element having seven degrees of freedom per node. The transformation from local to global reference frames is done using Euler angles for the first six degrees of freedom, while the transformation of the seventh degree of freedom is related to the transmission of warping between elements. The equilibrium equations are solved using a HOCM. Tested examples of frames of thin-walled beams with open cross-section subjected to different loadings and boundary conditions are investigated. The obtained results are compared with those calculated by the commercial software ABAQUS and with those from the literature.
{"title":"Analysis of the stability of frames composed of thin-walled beams with open cross-section using a High Order Continuation Method","authors":"Zaenab Bakhach , Bouazza Braikat , Abdellah Hamdaoui , Noureddine Damil","doi":"10.1016/j.finel.2025.104437","DOIUrl":"10.1016/j.finel.2025.104437","url":null,"abstract":"<div><div>This study presents the numerical modeling of frames composed of thin-walled beams with open cross-section subjected to large torsions by a High Order Continuation Method (HOCM), based on Asymptotic Numerical Method (ANM) techniques. The theoretical model is developed using <span><math><mrow><mn>3</mn><mi>D</mi></mrow></math></span> beam kinematics, which accounts for flexion-torsion coupling and large rotations. The connection between beams is ensured by joints (stiffening plates) to avoid local deformations, mathematically modeled by compatibility conditions applied to the connection nodes. The equilibrium equations are established using the minimization of the Lagrangian. Discretization is performed with a two-node beam element having seven degrees of freedom per node. The transformation from local to global reference frames is done using Euler angles for the first six degrees of freedom, while the transformation of the seventh degree of freedom is related to the transmission of warping between elements. The equilibrium equations are solved using a HOCM. Tested examples of frames of thin-walled beams with open cross-section subjected to different loadings and boundary conditions are investigated. The obtained results are compared with those calculated by the commercial software ABAQUS and with those from the literature.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"251 ","pages":"Article 104437"},"PeriodicalIF":3.5,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144932278","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 : 2025-08-30DOI: 10.1016/j.finel.2025.104431
Pierre-Eliot Malleval , Victor Matray , Faisal Amlani , Ronan Scanff , Frédéric Feyel , David Néron
Nonlinear finite element analysis (FEA) relies heavily on iterative methods such as the Newton–Raphson algorithm, with computational cost primarily driven by the repeated solution of large linear systems (global stage) and the evaluation of nonlinear constitutive laws (local stage). This work proposes a neural network-based surrogate to accelerate the local stage by approximating explicit constitutive models. A compact feed-forward neural network is trained on synthetic data generated from standard material laws and embedded into the commercial solver SimcenterTM Samcef®, replacing the local integration of nonlinear equations. To ensure accuracy and robustness, a residual-based safeguard is introduced to restore the original physics-based model when neural network predictions are insufficient. To further explore the benefits of the proposed approach in reducing overall simulation cost, the method is also applied within a reduced-order modeling framework. While such techniques effectively reduce the cost of solving large linear systems, the evaluation of nonlinear terms often remains a dominant bottleneck. The surrogate is therefore also assessed using the nonlinear model reduction method available in Samcef, namely the LATIN-PGD approach, although a detailed study of this method is not the focus of this paper. Beyond simplified test cases, the method is implemented and validated in full-scale, industrially relevant simulations involving elasto-viscoplastic materials. Results from academic and industrial-scale applications, including a high-pressure turbine blade, demonstrate that the proposed approach significantly reduces computation time while preserving solution accuracy. These findings highlight the potential of combining data-driven surrogates with residual-controlled correction to enhance the efficiency and scalability of nonlinear FEA workflows under realistic conditions.
{"title":"Accelerating nonlinear finite element analysis via residual-aware neural network constitutive models","authors":"Pierre-Eliot Malleval , Victor Matray , Faisal Amlani , Ronan Scanff , Frédéric Feyel , David Néron","doi":"10.1016/j.finel.2025.104431","DOIUrl":"10.1016/j.finel.2025.104431","url":null,"abstract":"<div><div>Nonlinear finite element analysis (FEA) relies heavily on iterative methods such as the Newton–Raphson algorithm, with computational cost primarily driven by the repeated solution of large linear systems (global stage) and the evaluation of nonlinear constitutive laws (local stage). This work proposes a neural network-based surrogate to accelerate the local stage by approximating explicit constitutive models. A compact feed-forward neural network is trained on synthetic data generated from standard material laws and embedded into the commercial solver Simcenter<sup>TM</sup> Samcef®, replacing the local integration of nonlinear equations. To ensure accuracy and robustness, a residual-based safeguard is introduced to restore the original physics-based model when neural network predictions are insufficient. To further explore the benefits of the proposed approach in reducing overall simulation cost, the method is also applied within a reduced-order modeling framework. While such techniques effectively reduce the cost of solving large linear systems, the evaluation of nonlinear terms often remains a dominant bottleneck. The surrogate is therefore also assessed using the nonlinear model reduction method available in <em>Samcef</em>, namely the LATIN-PGD approach, although a detailed study of this method is not the focus of this paper. Beyond simplified test cases, the method is implemented and validated in full-scale, industrially relevant simulations involving elasto-viscoplastic materials. Results from academic and industrial-scale applications, including a high-pressure turbine blade, demonstrate that the proposed approach significantly reduces computation time while preserving solution accuracy. These findings highlight the potential of combining data-driven surrogates with residual-controlled correction to enhance the efficiency and scalability of nonlinear FEA workflows under realistic conditions.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"251 ","pages":"Article 104431"},"PeriodicalIF":3.5,"publicationDate":"2025-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144916296","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 : 2025-08-28DOI: 10.1016/j.finel.2025.104433
M. Benítez , A. Bermúdez , P. Fontán , I. Martínez , P. Salgado
In this paper, we introduce a novel numerical procedure for solving fully coupled thermo-electrical-mechanical problems using implicit Runge–Kutta time integration within a purely Lagrangian finite element framework. Our formulation, grounded in continuum mechanics, accurately captures the interdependence of mechanical, thermal, and electrical effects under large deformations. It features a fully coupled thermo-electrical-mechanical Lagrangian model with an elasto-viscoplastic constitutive law, considers six primary variables –velocity, temperature, electric potential, plastic deformation gradient, an internal strain hardening variable, and a Lagrange multiplier for enforcing contact conditions– and employs a pure-Lagrangian description. This ensures the computational domain remains fixed and known a priori, simplifies the tracking of free surfaces, and eliminates convective terms. To validate our approach, we solve several axisymmetric benchmark problems and analyze convergence rates in both time and space. Moreover, our numerical results show excellent agreement with the solution obtained using commercial packages for an in-die electric upsetting process.
{"title":"A pure-Lagrangian finite element approach for solving thermo-electrical-mechanical models. Application to electric upsetting","authors":"M. Benítez , A. Bermúdez , P. Fontán , I. Martínez , P. Salgado","doi":"10.1016/j.finel.2025.104433","DOIUrl":"10.1016/j.finel.2025.104433","url":null,"abstract":"<div><div>In this paper, we introduce a novel numerical procedure for solving fully coupled thermo-electrical-mechanical problems using implicit Runge–Kutta time integration within a purely Lagrangian finite element framework. Our formulation, grounded in continuum mechanics, accurately captures the interdependence of mechanical, thermal, and electrical effects under large deformations. It features a fully coupled thermo-electrical-mechanical Lagrangian model with an elasto-viscoplastic constitutive law, considers six primary variables –velocity, temperature, electric potential, plastic deformation gradient, an internal strain hardening variable, and a Lagrange multiplier for enforcing contact conditions– and employs a pure-Lagrangian description. This ensures the computational domain remains fixed and known a priori, simplifies the tracking of free surfaces, and eliminates convective terms. To validate our approach, we solve several axisymmetric benchmark problems and analyze convergence rates in both time and space. Moreover, our numerical results show excellent agreement with the solution obtained using commercial packages for an in-die electric upsetting process.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"251 ","pages":"Article 104433"},"PeriodicalIF":3.5,"publicationDate":"2025-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144907628","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 : 2025-08-26DOI: 10.1016/j.finel.2025.104432
Yassir Wardi, Pisey Keo, Mohammed Hjiaj
In this paper, we present a novel 3D nonlinear formulation for two-layered composite beams that accounts for interlayer slip in both longitudinal and lateral directions. Warping effects are included in a simplified manner, assuming that the warping of each layer does not contribute to the stress resultants of each section, allowing the use of the classical St. Venant warping function to define the warping shape of each subsection. The second-order approximation of the Green–Lagrange strain tensor, combined with linear constitutive laws, is integrated into the principle of virtual work to derive the tangent stiffness matrix of the composite element and its corresponding internal force. To address membrane and slip locking issues, we propose a new averaging strain technique, complemented by quadratic interpolation functions for the axial displacement of the two layers. To account for large displacements and rotations, the co-rotational approach is adopted. The co-rotated local reference frame is constructed by connecting end nodes located at the shear center of the bottom layer of the composite beam. As a result, special treatments are employed to address eccentric forces applied to the top layer of the composite beam. Finally, the performance of the proposed formulation is evaluated using four representative examples.
{"title":"Efficient co-rotational formulation for 3D composite beams with two-directional interlayer slip","authors":"Yassir Wardi, Pisey Keo, Mohammed Hjiaj","doi":"10.1016/j.finel.2025.104432","DOIUrl":"10.1016/j.finel.2025.104432","url":null,"abstract":"<div><div>In this paper, we present a novel 3D nonlinear formulation for two-layered composite beams that accounts for interlayer slip in both longitudinal and lateral directions. Warping effects are included in a simplified manner, assuming that the warping of each layer does not contribute to the stress resultants of each section, allowing the use of the classical St. Venant warping function to define the warping shape of each subsection. The second-order approximation of the Green–Lagrange strain tensor, combined with linear constitutive laws, is integrated into the principle of virtual work to derive the tangent stiffness matrix of the composite element and its corresponding internal force. To address membrane and slip locking issues, we propose a new averaging strain technique, complemented by quadratic interpolation functions for the axial displacement of the two layers. To account for large displacements and rotations, the co-rotational approach is adopted. The co-rotated local reference frame is constructed by connecting end nodes located at the shear center of the bottom layer of the composite beam. As a result, special treatments are employed to address eccentric forces applied to the top layer of the composite beam. Finally, the performance of the proposed formulation is evaluated using four representative examples.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"251 ","pages":"Article 104432"},"PeriodicalIF":3.5,"publicationDate":"2025-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144903065","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 : 2025-08-22DOI: 10.1016/j.finel.2025.104435
Matteo Sorrenti, Marco Gherlone
<div><div>This work presents some numerical and experimental validations of the free-vibration behaviour of thick sandwich beams using the mixed {3,2}-Refined Zigzag Theory (<span><math><mrow><msubsup><mtext>RZT</mtext><mrow><mo>{</mo><mrow><mn>3</mn><mo>,</mo><mn>2</mn></mrow><mo>}</mo></mrow><mrow><mo>(</mo><mi>m</mi><mo>)</mo></mrow></msubsup></mrow></math></span>). The <span><math><mrow><msubsup><mtext>RZT</mtext><mrow><mo>{</mo><mrow><mn>3</mn><mo>,</mo><mn>2</mn></mrow><mo>}</mo></mrow><mrow><mo>(</mo><mi>m</mi><mo>)</mo></mrow></msubsup></mrow></math></span> formulation enhances the Timoshenko's kinematics with a piece-wise zigzag cubic distribution of the axial displacement, and a smoothed parabolic variation for the transverse deflection. Simultaneously, an a-priori assumption is made for the transverse normal stress and the transverse shear one: the former is assumed to be a third-order power series expansion of the thickness coordinate, while the latter is derived through the integration of Cauchy's equations. The equations of motion and consistent boundary conditions for the free-vibration problem are derived through the Hellinger-Reissner (HR) theorem. Taking advantage of the C<sup>0</sup>-continuity requirement in the mixed governing functional, a simple two-node beam finite element (FE) is formulated, i.e., the <span><math><mrow><mn>2</mn><mi>B</mi><mo>−</mo><msubsup><mtext>RZT</mtext><mrow><mo>{</mo><mrow><mn>3</mn><mo>,</mo><mn>2</mn></mrow><mo>}</mo></mrow><mrow><mo>(</mo><mi>m</mi><mo>)</mo></mrow></msubsup></mrow></math></span> element. The analytical and FE performances of the proposed <span><math><mrow><msubsup><mtext>RZT</mtext><mrow><mo>{</mo><mrow><mn>3</mn><mo>,</mo><mn>2</mn></mrow><mo>}</mo></mrow><mrow><mo>(</mo><mi>m</mi><mo>)</mo></mrow></msubsup></mrow></math></span> model are first addressed by means of a comparison with high-fidelity 3D FE models. Subsequently, an experimental campaign is conducted using LASER Doppler Vibrometry (LDV) to evaluate the modal parameters of a series of thick sandwich beams made of aluminium alloy face-sheets and Rohacell® WF110 core. The experimental results concerning the natural frequencies and modal shapes of the thick sandwich beam specimens under free-free boundary conditions are compared with those given by <span><math><mrow><msubsup><mtext>RZT</mtext><mrow><mo>{</mo><mrow><mn>3</mn><mo>,</mo><mn>2</mn></mrow><mo>}</mo></mrow><mrow><mo>(</mo><mi>m</mi><mo>)</mo></mrow></msubsup></mrow></math></span> and high-fidelity 3D FE models. The numerical-experimental assessment highlights the effect of core and face-sheet thickness on frequency estimations, as well as the complexity of reproducing in the numerical model the experimental uncertainties. In general, the <span><math><mrow><mn>2</mn><mi>B</mi><mo>−</mo><msubsup><mtext>RZT</mtext><mrow><mo>{</mo><mrow><mn>3</mn><mo>,</mo><mn>2</mn></mrow><mo>}</mo></mrow><mrow><mo>(</mo><mi>m</mi><mo>)</mo></mrow></msubsup></mrow></math></span
{"title":"An experimental and numerical dynamic study of thick sandwich beams using a mixed {3,2}-RZT formulation","authors":"Matteo Sorrenti, Marco Gherlone","doi":"10.1016/j.finel.2025.104435","DOIUrl":"10.1016/j.finel.2025.104435","url":null,"abstract":"<div><div>This work presents some numerical and experimental validations of the free-vibration behaviour of thick sandwich beams using the mixed {3,2}-Refined Zigzag Theory (<span><math><mrow><msubsup><mtext>RZT</mtext><mrow><mo>{</mo><mrow><mn>3</mn><mo>,</mo><mn>2</mn></mrow><mo>}</mo></mrow><mrow><mo>(</mo><mi>m</mi><mo>)</mo></mrow></msubsup></mrow></math></span>). The <span><math><mrow><msubsup><mtext>RZT</mtext><mrow><mo>{</mo><mrow><mn>3</mn><mo>,</mo><mn>2</mn></mrow><mo>}</mo></mrow><mrow><mo>(</mo><mi>m</mi><mo>)</mo></mrow></msubsup></mrow></math></span> formulation enhances the Timoshenko's kinematics with a piece-wise zigzag cubic distribution of the axial displacement, and a smoothed parabolic variation for the transverse deflection. Simultaneously, an a-priori assumption is made for the transverse normal stress and the transverse shear one: the former is assumed to be a third-order power series expansion of the thickness coordinate, while the latter is derived through the integration of Cauchy's equations. The equations of motion and consistent boundary conditions for the free-vibration problem are derived through the Hellinger-Reissner (HR) theorem. Taking advantage of the C<sup>0</sup>-continuity requirement in the mixed governing functional, a simple two-node beam finite element (FE) is formulated, i.e., the <span><math><mrow><mn>2</mn><mi>B</mi><mo>−</mo><msubsup><mtext>RZT</mtext><mrow><mo>{</mo><mrow><mn>3</mn><mo>,</mo><mn>2</mn></mrow><mo>}</mo></mrow><mrow><mo>(</mo><mi>m</mi><mo>)</mo></mrow></msubsup></mrow></math></span> element. The analytical and FE performances of the proposed <span><math><mrow><msubsup><mtext>RZT</mtext><mrow><mo>{</mo><mrow><mn>3</mn><mo>,</mo><mn>2</mn></mrow><mo>}</mo></mrow><mrow><mo>(</mo><mi>m</mi><mo>)</mo></mrow></msubsup></mrow></math></span> model are first addressed by means of a comparison with high-fidelity 3D FE models. Subsequently, an experimental campaign is conducted using LASER Doppler Vibrometry (LDV) to evaluate the modal parameters of a series of thick sandwich beams made of aluminium alloy face-sheets and Rohacell® WF110 core. The experimental results concerning the natural frequencies and modal shapes of the thick sandwich beam specimens under free-free boundary conditions are compared with those given by <span><math><mrow><msubsup><mtext>RZT</mtext><mrow><mo>{</mo><mrow><mn>3</mn><mo>,</mo><mn>2</mn></mrow><mo>}</mo></mrow><mrow><mo>(</mo><mi>m</mi><mo>)</mo></mrow></msubsup></mrow></math></span> and high-fidelity 3D FE models. The numerical-experimental assessment highlights the effect of core and face-sheet thickness on frequency estimations, as well as the complexity of reproducing in the numerical model the experimental uncertainties. In general, the <span><math><mrow><mn>2</mn><mi>B</mi><mo>−</mo><msubsup><mtext>RZT</mtext><mrow><mo>{</mo><mrow><mn>3</mn><mo>,</mo><mn>2</mn></mrow><mo>}</mo></mrow><mrow><mo>(</mo><mi>m</mi><mo>)</mo></mrow></msubsup></mrow></math></span","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"251 ","pages":"Article 104435"},"PeriodicalIF":3.5,"publicationDate":"2025-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144885420","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 : 2025-08-18DOI: 10.1016/j.finel.2025.104434
Sihua Hu , Xing Luo , Wei Xiang
This paper presents a p-version finite element framework for analyzing the thermal fracture behavior of quasi-brittle materials under coupled thermo-mechanical loadings. The proposed formulation, based on the hierarchical quadrature element method (HQEM), enables accurate capture of temperature gradients even on relatively coarse meshes. Its accuracy in simulating heat conduction and thermally induced deformation is validated against ABAQUS results.
The HQEM is integrated with the virtual crack closure method to compute fracture parameters under combined thermal and mechanical loadings, significantly reducing mesh refinement and preprocessing effort compared to conventional h-version FEM. To efficiently track complex crack paths, a minimum-increment remeshing strategy is introduced, which controls element growth while preserving the geometric accuracy of crack paths during iterative crack propagation analysis, significantly reducing the computational cost associated with frequent remeshing. Applications to four representative numerical examples demonstrate excellent agreement with existing literature, confirming the reliability and accuracy of the proposed approach for coupled thermo-mechanical fracture analysis.
{"title":"Integration of hierarchical quadrature element method with a minimum-increment remeshing strategy for simulating coupled thermo-mechanical fracture in quasi-brittle materials","authors":"Sihua Hu , Xing Luo , Wei Xiang","doi":"10.1016/j.finel.2025.104434","DOIUrl":"10.1016/j.finel.2025.104434","url":null,"abstract":"<div><div>This paper presents a <em>p</em>-version finite element framework for analyzing the thermal fracture behavior of quasi-brittle materials under coupled thermo-mechanical loadings. The proposed formulation, based on the hierarchical quadrature element method (HQEM), enables accurate capture of temperature gradients even on relatively coarse meshes. Its accuracy in simulating heat conduction and thermally induced deformation is validated against ABAQUS results.</div><div>The HQEM is integrated with the virtual crack closure method to compute fracture parameters under combined thermal and mechanical loadings, significantly reducing mesh refinement and preprocessing effort compared to conventional <em>h</em>-version FEM. To efficiently track complex crack paths, a minimum-increment remeshing strategy is introduced, which controls element growth while preserving the geometric accuracy of crack paths during iterative crack propagation analysis, significantly reducing the computational cost associated with frequent remeshing. Applications to four representative numerical examples demonstrate excellent agreement with existing literature, confirming the reliability and accuracy of the proposed approach for coupled thermo-mechanical fracture analysis.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"251 ","pages":"Article 104434"},"PeriodicalIF":3.5,"publicationDate":"2025-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144861159","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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