Pub Date : 2026-01-11DOI: 10.1016/j.ijsolstr.2026.113843
J.A. López-Fernández , G. Centeno , M.B. Silva , C. Vallellano
This work presents an experimental and numerical investigation of shrink flanging using Conventional Press Forming (CPF) and Single Point Incremental Forming (SPIF). Tests were carried out on aluminium AA2024-T3 sheets to identify failure modes, process windows, and formability limits under compressive loading. Finite Element simulations were developed for both processes, focusing on the evolution of in-plane stresses at the flange edge. A stress-based wrinkling criterion is stablished, and a process window is defined as a function of flange geometry. Results show that SPIF enhances formability and delays wrinkling compared to CPF. However, while CPF exhibits earlier wrinkling, certain cases allow wrinkle ironing, improving the final surface quality. A numerical criterion is introduced to detect wrinkling based on strain differences between the inner and outer surfaces of the sheet, enabling consistent identification of the wrinkling onset across geometries. A stress-based analysis reveals that the critical compressive stress required to initiate wrinkling is significantly lower in CPF and strongly dependent on flange length. Conversely, SPIF maintains a nearly constant wrinkling limit. Based on these findings, a process window was developed to support the selection of the most suitable forming strategy.
{"title":"Predictive analysis of wrinkling in shrink flanging using conventional versus incremental forming","authors":"J.A. López-Fernández , G. Centeno , M.B. Silva , C. Vallellano","doi":"10.1016/j.ijsolstr.2026.113843","DOIUrl":"10.1016/j.ijsolstr.2026.113843","url":null,"abstract":"<div><div>This work presents an experimental and numerical investigation of shrink flanging using Conventional Press Forming (CPF) and Single Point Incremental Forming (SPIF). Tests were carried out on aluminium AA2024-T3 sheets to identify failure modes, process windows, and formability limits under compressive loading. Finite Element simulations were developed for both processes, focusing on the evolution of in-plane stresses at the flange edge. A stress-based wrinkling criterion is stablished, and a process window is defined as a function of flange geometry. Results show that SPIF enhances formability and delays wrinkling compared to CPF. However, while CPF exhibits earlier wrinkling, certain cases allow wrinkle ironing, improving the final surface quality. A numerical criterion is introduced to detect wrinkling based on strain differences between the inner and outer surfaces of the sheet, enabling consistent identification of the wrinkling onset across geometries. A stress-based analysis reveals that the critical compressive stress required to initiate wrinkling is significantly lower in CPF and strongly dependent on flange length. Conversely, SPIF maintains a nearly constant wrinkling limit. Based on these findings, a process window was developed to support the selection of the most suitable forming strategy.</div></div>","PeriodicalId":14311,"journal":{"name":"International Journal of Solids and Structures","volume":"328 ","pages":"Article 113843"},"PeriodicalIF":3.8,"publicationDate":"2026-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145978841","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 : 2026-01-10DOI: 10.1016/j.ijsolstr.2026.113845
Xuyang Zhang , Qiang Chen , Rúben Lourenço , Mohammed El Fallaki Idrissi , Xuefeng Chen , George Chatzigeorgiou , Fodil Meraghni
We propose a thermodynamics-informed multi-head attention neural network (TMANN) framework for predicting elastoplastic behavior under arbitrary loading paths. In contrast to earlier thermodynamics-informed networks that rely solely on internal state variables to encode loading history, the TMANN incorporates a multi-head attention mechanism that explicitly captures the material history sequence, thereby enhancing predictive accuracy and stability. The architecture comprises an attention network for predicting increments of internal state variables and a companion neural network for estimating the Helmholtz free energy at each time step. To ensure physical consistency and strengthen the model’s generalization capability, the loss function explicitly enforces thermodynamic constraints, including non-negative free energy, non-negative dissipation rate, and monotonic accumulation of effective plastic strain. Furthermore, a rolling iterative prediction strategy is implemented to ensure the model’s compatibility with the stepwise nature of arbitrary loading paths, as only the initial stress and strain states are known a priori. The integration of TMANN into ABAQUS through a user material subroutine verifies its practical applicability to structural simulations. The effectiveness of the proposed TMANN is validated through comparisons with classical numerical methods at both the material point level and in structural simulations. New results showcase the TMANN’s robust generalization performance, maintaining high prediction accuracy under incremental loading/unloading and complex random loading scenarios.
{"title":"Thermodynamics-informed multi-head attention neural networks for constitutive modelling","authors":"Xuyang Zhang , Qiang Chen , Rúben Lourenço , Mohammed El Fallaki Idrissi , Xuefeng Chen , George Chatzigeorgiou , Fodil Meraghni","doi":"10.1016/j.ijsolstr.2026.113845","DOIUrl":"10.1016/j.ijsolstr.2026.113845","url":null,"abstract":"<div><div>We propose a thermodynamics-informed multi-head attention neural network (TMANN) framework for predicting elastoplastic behavior under arbitrary loading paths. In contrast to earlier thermodynamics-informed networks that rely solely on internal state variables to encode loading history, the TMANN incorporates a multi-head attention mechanism that explicitly captures the material history sequence, thereby enhancing predictive accuracy and stability. The architecture comprises an attention network for predicting increments of internal state variables and a companion neural network for estimating the Helmholtz free energy at each time step. To ensure physical consistency and strengthen the model’s generalization capability, the loss function explicitly enforces thermodynamic constraints, including non-negative free energy, non-negative dissipation rate, and monotonic accumulation of effective plastic strain. Furthermore, a rolling iterative prediction strategy is implemented to ensure the model’s compatibility with the stepwise nature of arbitrary loading paths, as only the initial stress and strain states are known a priori. The integration of TMANN into ABAQUS through a user material subroutine verifies its practical applicability to structural simulations. The effectiveness of the proposed TMANN is validated through comparisons with classical numerical methods at both the material point level and in structural simulations. New results showcase the TMANN’s robust generalization performance, maintaining high prediction accuracy under incremental loading/unloading and complex random loading scenarios.</div></div>","PeriodicalId":14311,"journal":{"name":"International Journal of Solids and Structures","volume":"328 ","pages":"Article 113845"},"PeriodicalIF":3.8,"publicationDate":"2026-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145978842","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 : 2026-01-10DOI: 10.1016/j.ijsolstr.2026.113847
Qianxi Sun , Xiao-Lei Cui , Shijie Yin , Shijian Yuan
The anisotropic parameters of metal tubes are of great significance for calibrating the constitutive model and achieving the high-accuracy simulation of forming thin-walled tubular parts. In this paper, a new method of inclined ring tensile test (IRTT) based on digital image correlation (DIC) technology was established to determine the normal anisotropy coefficients (r values) and stress–strain curves of thin-walled metal tubes in arbitrary directions. The method utilizes blocks with asymmetric geometry to support the parallel segment, thereby avoiding straightening deformation. Meanwhile, a precise calculation formula for the tensile stress in the center section was derived, taking friction into account. Furthermore, finite element analysis (FEA) was employed to investigate the uniformity of tensile stress and the effects of frame moment, straightening deformation (block gap position), and interface friction. It is indicated that the center section is subjected to a uniaxial, uniform stress state. Subsequently, the r values and stress–strain curves of aluminum alloy (AA6061) tubes were obtained in their 15°, 30°, 45°, 60°, 75°, and 90° directions using the IRTT. The r values increase first and then decrease from 0° to 90°, and are all less than 1, reflecting the normal and in-plane anisotropy of flow. The hardening curve in the 0° direction is the lowest, while that in the 90° direction is the highest, and the curves in the other directions lie between them. Ultimately, the effectiveness of these measured parameters was demonstrated for enhancing the prediction accuracy of the constitutive model and FEA. The constitutive model calibrated by r0, r90, and r45 has higher prediction accuracy for the flow behavior under the general plane stress than the model calibrated by r0 and r90 (reducing error from 14.7% to 5.3%). The prediction error of the load–displacement curves is reduced from 4.4% to 1.7% when the measured stress–strain curves in the 45°, 75°, and 90° directions are used as input to FEA.
{"title":"Accurate measurement method for anisotropic parameters of metal tubes in arbitrary directions","authors":"Qianxi Sun , Xiao-Lei Cui , Shijie Yin , Shijian Yuan","doi":"10.1016/j.ijsolstr.2026.113847","DOIUrl":"10.1016/j.ijsolstr.2026.113847","url":null,"abstract":"<div><div>The anisotropic parameters of metal tubes are of great significance for calibrating the constitutive model and achieving the high-accuracy simulation of forming thin-walled tubular parts. In this paper, a new method of inclined ring tensile test (IRTT) based on digital image correlation (DIC) technology was established to determine the normal anisotropy coefficients (<em>r</em> values) and stress–strain curves of thin-walled metal tubes in arbitrary directions. The method utilizes blocks with asymmetric geometry to support the parallel segment, thereby avoiding straightening deformation. Meanwhile, a precise calculation formula for the tensile stress in the center section was derived, taking friction into account. Furthermore, finite element analysis (FEA) was employed to investigate the uniformity of tensile stress and the effects of frame moment, straightening deformation (block gap position), and interface friction. It is indicated that the center section is subjected to a uniaxial, uniform stress state. Subsequently, the <em>r</em> values and stress–strain curves of aluminum alloy (AA6061) tubes were obtained in their 15°, 30°, 45°, 60°, 75°, and 90° directions using the IRTT. The <em>r</em> values increase first and then decrease from 0° to 90°, and are all less than 1, reflecting the normal and in-plane anisotropy of flow. The hardening curve in the 0° direction is the lowest, while that in the 90° direction is the highest, and the curves in the other directions lie between them. Ultimately, the effectiveness of these measured parameters was demonstrated for enhancing the prediction accuracy of the constitutive model and FEA. The constitutive model calibrated by <em>r</em><sub>0</sub>, <em>r</em><sub>90</sub>, and <em>r</em><sub>45</sub> has higher prediction accuracy for the flow behavior under the general plane stress than the model calibrated by <em>r</em><sub>0</sub> and <em>r</em><sub>90</sub> (reducing error from 14.7% to 5.3%). The prediction error of the load–displacement curves is reduced from 4.4% to 1.7% when the measured stress–strain curves in the 45°, 75°, and 90° directions are used as input to FEA.</div></div>","PeriodicalId":14311,"journal":{"name":"International Journal of Solids and Structures","volume":"328 ","pages":"Article 113847"},"PeriodicalIF":3.8,"publicationDate":"2026-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145978767","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 : 2026-01-09DOI: 10.1016/j.ijsolstr.2026.113841
Xinlei Peng , Liguo Zang , Jing Sun , Guoquan Yang , Fen Lin , Yaoji Deng , Haichao Zhou
This paper introduces a ring design theory for a two dimensional double-U honeycomb (2D DUH) structure, applied to the structural design of inserts body for the inserts supporting run-flat tire (ISRFT). The objective is to reduce the overall mass of ISRFTs without compromising their mechanical characteristics. Firstly, finite element modeling is performed on the ISRFT, with model accuracy validated through tire bench test. Then, the ring design theory for 2D DUH structures is applied to the inserts body, comparing its mechanical characteristics before and after design. Finally, a steady-state temperature field is established for the ISRFT, and the tire’s deflation process is discretized to investigate changes in the thermo-mechanical characteristics of the inserts body during deflation. The results indicate that test errors are minimal, the model demonstrates accuracy, and the mechanical characteristics of the 2D DUH inserts body remain unaffected by mass reduction. Furthermore, during deflation, when tire pressure drops to 6 kPa, the load-bearing mechanism of the ISRFT undergoes a transformation, and the thermo-mechanical characteristics of the 2D DUH inserts body change. The research findings provide valuable insights for designing high-performance 2D DUH structures, revealing their significant potential for engineering applications.
{"title":"Structural design of inserts supporting run-flat tires and thermo-mechanical characteristics study of discretized deflation process","authors":"Xinlei Peng , Liguo Zang , Jing Sun , Guoquan Yang , Fen Lin , Yaoji Deng , Haichao Zhou","doi":"10.1016/j.ijsolstr.2026.113841","DOIUrl":"10.1016/j.ijsolstr.2026.113841","url":null,"abstract":"<div><div>This paper introduces a ring design theory for a two dimensional double-U honeycomb (2D DUH) structure, applied to the structural design of inserts body for the inserts supporting run-flat tire (ISRFT). The objective is to reduce the overall mass of ISRFTs without compromising their mechanical characteristics. Firstly, finite element modeling is performed on the ISRFT, with model accuracy validated through tire bench test. Then, the ring design theory for 2D DUH structures is applied to the inserts body, comparing its mechanical characteristics before and after design. Finally, a steady-state temperature field is established for the ISRFT, and the tire’s deflation process is discretized to investigate changes in the thermo-mechanical characteristics of the inserts body during deflation. The results indicate that test errors are minimal, the model demonstrates accuracy, and the mechanical characteristics of the 2D DUH inserts body remain unaffected by mass reduction. Furthermore, during deflation, when tire pressure drops to 6 kPa, the load-bearing mechanism of the ISRFT undergoes a transformation, and the thermo-mechanical characteristics of the 2D DUH inserts body change. The research findings provide valuable insights for designing high-performance 2D DUH structures, revealing their significant potential for engineering applications.</div></div>","PeriodicalId":14311,"journal":{"name":"International Journal of Solids and Structures","volume":"328 ","pages":"Article 113841"},"PeriodicalIF":3.8,"publicationDate":"2026-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145978761","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 analyzes the nonlinear vibrations and dynamic instability of two-directional functionally graded (2DFG) conical shells. To this end, the shell dynamic model is derived using the first-order shear deformation theory (FSDT) and nonlinear strain–displacement relations. The shell is subjected to a time-varying axial parametric force and harmonic external transverse excitation. In this article, a new hybrid solution method is used. Specifically, the generalized differential quadrature method (GDQM) is applied to solve the eigenvalue problem and obtain the mode shape vectors. These mode shapes are then used to discretize the equations using the Galerkin method. The multiple time scale method (MTSM) is used to analyze the nonlinear dynamics of the system. Initially, the shell’s nonlinear frequency response is obtained from steady-state motion, followed by an evaluation of the system’s nonlinear dynamic behavior in two resonance regions: primary and parametric. Finally, the effects of conical shell parameters such as the amplitude of the parametric and external excitation, detuning parameter, structural damping, FG power indices, semi-vertex angle, thickness-to-length ratio, and boundary conditions on the maximum amplitude and hardening behavior of the frequency response at primary resonance, as well as the dynamic instability of the shell, are investigated.
{"title":"Nonlinear vibrations and dynamic instability analysis of a two-directional functionally graded conical shell under parametric and external excitations","authors":"Amin Rezaeezadeh , Babak Mirzaei Moghaddam , Ali Mohammadi , Arash Eftekhari","doi":"10.1016/j.ijsolstr.2025.113826","DOIUrl":"10.1016/j.ijsolstr.2025.113826","url":null,"abstract":"<div><div>This paper analyzes the nonlinear vibrations and dynamic instability of two-directional functionally graded (2DFG) conical shells. To this end, the shell dynamic model is derived using the first-order shear deformation theory (FSDT) and nonlinear strain–displacement relations. The shell is subjected to a time-varying axial parametric force and harmonic external transverse excitation. In this article, a new hybrid solution method is used. Specifically, the generalized differential quadrature method (GDQM) is applied to solve the eigenvalue problem and obtain the mode shape vectors. These mode shapes are then used to discretize the equations using the Galerkin method. The multiple time scale method (MTSM) is used to analyze the nonlinear dynamics of the system. Initially, the shell’s nonlinear frequency response is obtained from steady-state motion, followed by an evaluation of the system’s nonlinear dynamic behavior in two resonance regions: primary and parametric. Finally, the effects of conical shell parameters such as the amplitude of the parametric and external excitation, detuning parameter, structural damping, FG power indices, semi-vertex angle, thickness-to-length ratio, and boundary conditions on the maximum amplitude and hardening behavior of the frequency response at primary resonance, as well as the dynamic instability of the shell, are investigated.</div></div>","PeriodicalId":14311,"journal":{"name":"International Journal of Solids and Structures","volume":"329 ","pages":"Article 113826"},"PeriodicalIF":3.8,"publicationDate":"2026-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146036729","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 : 2026-01-07DOI: 10.1016/j.ijsolstr.2026.113831
Peidong Li , Guanlin Lv , Weidong Li , Haidong Fan , Qingyuan Wang , Kun Zhou
Solid-state batteries (SSBs) exhibit excellent electrochemical performance in terms of high energy density and safety as compared to conventional lithium-ion batteries due to their solid-state electrolytes paired with a lithium metal electrode. However, the performance of SSBs degrades during charging and discharging cycles, and the degradation mechanisms remain elusive due to the complex multi-physics behaviors of SSBs. In this work, a fully coupled, thermodynamically consistent electro-chemo-thermo-mechanical model is developed within the phase-field framework to investigate the failure mechanisms of SSBs, focusing on fractures induced by multi-physics loading. The multi-physics phase-field model consists of the electrochemical transport equation for Li-ions, the Poisson equation for electric fields, the heat conduction equation for temperature evolution, the equilibrium equations for materials undergoing large deformations, the Butler–Volmer kinetics for electrode–electrolyte interfaces, and the phase-field equation for fracture evolution. The model also incorporates a tension–compression decomposition of finite strain energy and a temperature- and concentration-dependent fracture toughness. Simulation results reveal several typical failure patterns in SSBs, including intra-particle cracking in electrodes, through-thickness fracture of solid electrolytes, and interfacial delamination at electrode/electrolyte interfaces, all of which are strongly regulated by the interplay of electrochemical cycling, Joule heating, and chemo-mechanical swelling. These findings highlight the dominant role of electro-chemo-thermo-mechanical couplings in triggering fracture and provide quantitative insights into the degradation pathways of SSBs. The developed model provides a comprehensive multiphysics framework to guide the optimization of battery materials, reduce failure risks in SSBs, and improve their electrochemical performance.
{"title":"Fully coupled electro-chemo-thermo-mechanical phase-field fracture modeling for solid-state batteries","authors":"Peidong Li , Guanlin Lv , Weidong Li , Haidong Fan , Qingyuan Wang , Kun Zhou","doi":"10.1016/j.ijsolstr.2026.113831","DOIUrl":"10.1016/j.ijsolstr.2026.113831","url":null,"abstract":"<div><div>Solid-state batteries (SSBs) exhibit excellent electrochemical performance in terms of high energy density and safety as compared to conventional lithium-ion batteries due to their solid-state electrolytes paired with a lithium metal electrode. However, the performance of SSBs degrades during charging and discharging cycles, and the degradation mechanisms remain elusive due to the complex multi-physics behaviors of SSBs. In this work, a fully coupled, thermodynamically consistent electro-chemo-thermo-mechanical model is developed within the phase-field framework to investigate the failure mechanisms of SSBs, focusing on fractures induced by multi-physics loading. The multi-physics phase-field model consists of the electrochemical transport equation for Li-ions, the Poisson equation for electric fields, the heat conduction equation for temperature evolution, the equilibrium equations for materials undergoing large deformations, the Butler–Volmer kinetics for electrode–electrolyte interfaces, and the phase-field equation for fracture evolution. The model also incorporates a tension–compression decomposition of finite strain energy and a temperature- and concentration-dependent fracture toughness. Simulation results reveal several typical failure patterns in SSBs, including intra-particle cracking in electrodes, through-thickness fracture of solid electrolytes, and interfacial delamination at electrode/electrolyte interfaces, all of which are strongly regulated by the interplay of electrochemical cycling, Joule heating, and chemo-mechanical swelling. These findings highlight the dominant role of electro-chemo-thermo-mechanical couplings in triggering fracture and provide quantitative insights into the degradation pathways of SSBs. The developed model provides a comprehensive multiphysics framework to guide the optimization of battery materials, reduce failure risks in SSBs, and improve their electrochemical performance.</div></div>","PeriodicalId":14311,"journal":{"name":"International Journal of Solids and Structures","volume":"328 ","pages":"Article 113831"},"PeriodicalIF":3.8,"publicationDate":"2026-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145978706","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 : 2026-01-06DOI: 10.1016/j.ijsolstr.2026.113832
P. Fernández-Pisón , L.M. Santana , Q. Sellam , V. Farrugia , Y. Madi , J. Besson
Hydrogen embrittlement (HE) poses a major challenge for safe hydrogen transport, particularly in repurposed natural gas pipelines. Trace oxygen additions can mitigate HE, yet their effectiveness remains insufficiently understood. This study examines the influence of 50–500 vppm oxygen in gaseous HE on a modern E355 mod. steel using sub-size tensile specimens. Tests were performed at and bar, with strain rates of and s−1. In pure hydrogen, the reduction of area decreased from 80% in air to 55% ( bar, fast rate), 45% ( bar, fast rate), and 40% ( bar, slow rate), indicating severe embrittlement. Oxygen additions progressively recovered ductility, with inhibition effectiveness rising from 35–50% (50 vppm and bar) to 80% (500 vppm and bar). Fractography revealed reduced hydrogen-induced surface cracking and enhanced ductile features with increasing oxygen content. Finite-element simulations employed a modified nonlocal GTN model coupled with hydrogen diffusion, extended here with an ad hoc diffusion boundary condition to represent oxygen-induced inhibition. To our knowledge, this is the first FE framework to explicitly account for environmental inhibition effects. The model successfully reproduced key experimental trends, including oxygen-mediated ductility recovery, strain-rate-sensitive stress drops, and the transition from surface- to internally-initiated damage. This integrated experimental-modeling approach provides a mechanistic basis for interpreting oxygen-mediated inhibition, quantifies the beneficial effect of trace oxygen, and establishes a foundation for predictive assessments of hydrogen uptake and damage evolution in steels under potential pipeline inhibition conditions.
{"title":"Oxygen-mediated inhibition of gaseous hydrogen embrittlement in pipeline steels: sub-size specimen testing and coupled diffusion-damage modeling","authors":"P. Fernández-Pisón , L.M. Santana , Q. Sellam , V. Farrugia , Y. Madi , J. Besson","doi":"10.1016/j.ijsolstr.2026.113832","DOIUrl":"10.1016/j.ijsolstr.2026.113832","url":null,"abstract":"<div><div>Hydrogen embrittlement (HE) poses a major challenge for safe hydrogen transport, particularly in repurposed natural gas pipelines. Trace oxygen additions can mitigate HE, yet their effectiveness remains insufficiently understood. This study examines the influence of 50–500 vppm oxygen in gaseous HE on a modern E355 mod. steel using sub-size tensile specimens. Tests were performed at <span><math><mrow><mn>100</mn></mrow></math></span> and <span><math><mrow><mn>200</mn></mrow></math></span> bar, with strain rates of <span><math><mrow><mn>1</mn><mo>×</mo><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mo>−</mo><mn>5</mn></mrow></msup></mrow></math></span> and <span><math><mrow><mn>5</mn><mo>×</mo><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mo>−</mo><mn>4</mn></mrow></msup></mrow></math></span> s<sup>−1</sup>. In pure hydrogen, the reduction of area decreased from 80% in air to 55% (<span><math><mrow><mn>100</mn></mrow></math></span> bar, fast rate), 45% (<span><math><mrow><mn>200</mn></mrow></math></span> bar, fast rate), and 40% (<span><math><mrow><mn>100</mn></mrow></math></span> bar, slow rate), indicating severe embrittlement. Oxygen additions progressively recovered ductility, with inhibition effectiveness rising from 35–50% (50 vppm and <span><math><mrow><mn>100</mn></mrow></math></span> bar) to 80% (500 vppm and <span><math><mrow><mn>200</mn></mrow></math></span> bar). Fractography revealed reduced hydrogen-induced surface cracking and enhanced ductile features with increasing oxygen content. Finite-element simulations employed a modified nonlocal GTN model coupled with hydrogen diffusion, extended here with an <em>ad hoc</em> diffusion boundary condition to represent oxygen-induced inhibition. To our knowledge, this is the first FE framework to explicitly account for environmental inhibition effects. The model successfully reproduced key experimental trends, including oxygen-mediated ductility recovery, strain-rate-sensitive stress drops, and the transition from surface- to internally-initiated damage. This integrated experimental-modeling approach provides a mechanistic basis for interpreting oxygen-mediated inhibition, quantifies the beneficial effect of trace oxygen, and establishes a foundation for predictive assessments of hydrogen uptake and damage evolution in steels under potential pipeline inhibition conditions.</div></div>","PeriodicalId":14311,"journal":{"name":"International Journal of Solids and Structures","volume":"329 ","pages":"Article 113832"},"PeriodicalIF":3.8,"publicationDate":"2026-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145996483","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 : 2026-01-04DOI: 10.1016/j.ijsolstr.2026.113830
Xin Song , Ning Han , Huiping Qi , Yong Hu , Wen Yang , Zhenjiang Li , Zhengyi Jiang , Lu Jia
In this study, a multi-scale damage analysis method coupling an improved GTN and Cohesive Zone Model is developed. The Precise and efficient inversion of model parameters was achieved through a differential evolution algorithm. The reconstructed microstructure via image recognition is introduced into finite element simulations, and the damage evolution patterns in duplex titanium alloys during thread rolling are studied. The results show that the established model accurately reproduces both the macroscopic mechanical response and microcrack propagation. Further predictions indicate that damage concentration occurs predominantly at the thread root regions. The microcrack initiation at α/β phase interfaces and loss of deformation coordination. The study provides a framework linking microstructural mechanisms to macroscopic performance, enabling precise prediction and control of damage during titanium alloy plastic deformation processes.
{"title":"Study on the damage mechanism of titanium alloy threads during roll forming based on a machine learning-assisted multi-scale damage model","authors":"Xin Song , Ning Han , Huiping Qi , Yong Hu , Wen Yang , Zhenjiang Li , Zhengyi Jiang , Lu Jia","doi":"10.1016/j.ijsolstr.2026.113830","DOIUrl":"10.1016/j.ijsolstr.2026.113830","url":null,"abstract":"<div><div>In this study, a multi-scale damage analysis method coupling an improved GTN and Cohesive Zone Model is developed. The Precise and efficient inversion of model parameters was achieved through a differential evolution algorithm. The reconstructed microstructure via image recognition is introduced into finite element simulations, and the damage evolution patterns in duplex titanium alloys during thread rolling are studied. The results show that the established model accurately reproduces both the macroscopic mechanical response and microcrack propagation. Further predictions indicate that damage concentration occurs predominantly at the thread root regions. The microcrack initiation at α/β phase interfaces and loss of deformation coordination. The study provides a framework linking microstructural mechanisms to macroscopic performance, enabling precise prediction and control of damage during titanium alloy plastic deformation processes.</div></div>","PeriodicalId":14311,"journal":{"name":"International Journal of Solids and Structures","volume":"328 ","pages":"Article 113830"},"PeriodicalIF":3.8,"publicationDate":"2026-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145940177","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 : 2026-01-03DOI: 10.1016/j.ijsolstr.2026.113829
Xiaodong Xia , Ruiyang Li , Zheng Zhong
In contrast to the conventional piezoelectric sensor, the CNT-based nanocomposite strain sensor (CNCSS) serves as a new category of high-performance strain sensor. The bottleneck for evaluating sensing capacities of CNCSS lies in the nonlinear electromechanical coupling mechanism and extra high computational costs of multi-scale simulation. In this paper, a novel multi-scale FE2 model and a machine learning accelerated FE-RNN computational model have both been developed on the strain sensing capacities of high-performance CNCSS. First, a multi-scale electromechanically coupled FE2 model is established for the CNCSS with a realistic configuration. The electromechanically coupled mechanism is illustrated by a loading-dependent tunneling model, which is highly dependent on the tunneling distance between the adjacent CNTs. The developed coupled FE2 model is able to predict the strain sensing performance of CNCSS with a macroscopic configuration while considering specific microstructural characteristics. Then, an electromechanically coupled recurrent neural network (RNN) surrogate model is utilized to accelerate the FE2 model in the microscopic scale. The developed FE-RNN model can accelerate the microscopic simulation of RVE for a continuous range of microstructural parameters. The predicted sensing characteristics via the developed FE2 model and accelerated FE-RNN model are both highly consistent with the experiment of CNT/epoxy nanocomposite strain sensor under a realistic configuration. Especially at the high strain loading, the predicted results reflect the sharp increase of sensing capacities for CNCSS. The accelerated FE-RNN approach is concluded to possess the advantage over the FE2 model on the structural analysis by significantly reducing the computational costs by 97%. The developed FE-RNN scheme is capable of providing rapid design instructions for the microstructure of high-performance strain sensors.
{"title":"A multi-scale electromechanically coupled FE2 model on the sensing capacities of CNT-based nanocomposite strain sensor: A machine learning accelerated scheme","authors":"Xiaodong Xia , Ruiyang Li , Zheng Zhong","doi":"10.1016/j.ijsolstr.2026.113829","DOIUrl":"10.1016/j.ijsolstr.2026.113829","url":null,"abstract":"<div><div>In contrast to the conventional piezoelectric sensor, the CNT-based nanocomposite strain sensor (CNCSS) serves as a new category of high-performance strain sensor. The bottleneck for evaluating sensing capacities of CNCSS lies in the nonlinear electromechanical coupling mechanism and extra high computational costs of multi-scale simulation. In this paper, a novel multi-scale FE<sup>2</sup> model and a machine learning accelerated FE-RNN computational model have both been developed on the strain sensing capacities of high-performance CNCSS. First, a multi-scale electromechanically coupled FE<sup>2</sup> model is established for the CNCSS with a realistic configuration. The electromechanically coupled mechanism is illustrated by a loading-dependent tunneling model, which is highly dependent on the tunneling distance between the adjacent CNTs. The developed coupled FE<sup>2</sup> model is able to predict the strain sensing performance of CNCSS with a macroscopic configuration while considering specific microstructural characteristics. Then, an electromechanically coupled recurrent neural network (RNN) surrogate model is utilized to accelerate the FE<sup>2</sup> model in the microscopic scale. The developed FE-RNN model can accelerate the microscopic simulation of RVE for a continuous range of microstructural parameters. The predicted sensing characteristics via the developed FE<sup>2</sup> model and accelerated FE-RNN model are both highly consistent with the experiment of CNT/epoxy nanocomposite strain sensor under a realistic configuration. Especially at the high strain loading, the predicted results reflect the sharp increase of sensing capacities for CNCSS. The accelerated FE-RNN approach is concluded to possess the advantage over the FE<sup>2</sup> model on the structural analysis by significantly reducing the computational costs by 97%. The developed FE-RNN scheme is capable of providing rapid design instructions for the microstructure of high-performance strain sensors.</div></div>","PeriodicalId":14311,"journal":{"name":"International Journal of Solids and Structures","volume":"328 ","pages":"Article 113829"},"PeriodicalIF":3.8,"publicationDate":"2026-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145940092","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 : 2026-01-02DOI: 10.1016/j.ijsolstr.2025.113825
Filip Sjövall, Mathias Wallin
This paper combines density-based topology optimization (TO) with a “contact aware” shape optimization (SO) which combines the design freedom of TO with the precise boundary representation of SO. Using gradient based optimization, the objective is to design structures in frictionless contact, including the shape of the contacting surfaces. SO is performed on each contacting structure which defines its own TO domain and contact is modeled at the interface between the domains using a mortar formulation combined with the penalty method. The SO uses the finite element node coordinate parameterization, and to avoid undesired shape changes that can result in e.g. jagged boundaries or excessive interference between two contacting grids, a PDE-based filter is used. Two formulations are investigated, one that sequentially uses TO and then SO and one that uses them simultaneously.
{"title":"Shape and topology optimization for contact applications","authors":"Filip Sjövall, Mathias Wallin","doi":"10.1016/j.ijsolstr.2025.113825","DOIUrl":"10.1016/j.ijsolstr.2025.113825","url":null,"abstract":"<div><div>This paper combines density-based topology optimization (TO) with a “contact aware” shape optimization (SO) which combines the design freedom of TO with the precise boundary representation of SO. Using gradient based optimization, the objective is to design structures in frictionless contact, including the shape of the contacting surfaces. SO is performed on each contacting structure which defines its own TO domain and contact is modeled at the interface between the domains using a mortar formulation combined with the penalty method. The SO uses the finite element node coordinate parameterization, and to avoid undesired shape changes that can result in e.g. jagged boundaries or excessive interference between two contacting grids, a PDE-based filter is used. Two formulations are investigated, one that sequentially uses TO and then SO and one that uses them simultaneously.</div></div>","PeriodicalId":14311,"journal":{"name":"International Journal of Solids and Structures","volume":"328 ","pages":"Article 113825"},"PeriodicalIF":3.8,"publicationDate":"2026-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145978763","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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