Pub Date : 2026-01-12DOI: 10.1016/j.euromechsol.2026.106027
Mozhdeh Erfanian , Carl D. Slater , Edward J. Brambley
A mathematical model for wire rolling is developed, focusing on predicting the lateral spread. This provides, for the first time, an analytic model of lateral spread without any fitting parameters. The model is derived directly from the governing equations, assuming a rigid, perfectly plastic material and exploiting the thinness of the wire (in thickness and width) relative to the roller size. Results are compared against experiments performed on stainless steel wire using diameter rolls, demonstrating accurate predictions of lateral spread across a wide range of wire diameters (–) and reduction ratios (20%–60%), all without the need for fitting parameters. Since the model requires only seconds to compute, the model’s valid range is explored for varying roll diameter, wire diameter, and reduction ratio, and their effects on the resulting lateral spread characterised. The model can serve as a robust tool for validating FE results, guiding process design, and laying the foundation for future improved models. Matlab code to evaluate the model is provided in the supplementary material.
{"title":"Modelling lateral spread in wire flat rolling","authors":"Mozhdeh Erfanian , Carl D. Slater , Edward J. Brambley","doi":"10.1016/j.euromechsol.2026.106027","DOIUrl":"10.1016/j.euromechsol.2026.106027","url":null,"abstract":"<div><div>A mathematical model for wire rolling is developed, focusing on predicting the lateral spread. This provides, for the first time, an analytic model of lateral spread without any fitting parameters. The model is derived directly from the governing equations, assuming a rigid, perfectly plastic material and exploiting the thinness of the wire (in thickness and width) relative to the roller size. Results are compared against experiments performed on stainless steel wire using <span><math><mrow><mn>100</mn><mspace></mspace><mi>mm</mi></mrow></math></span> diameter rolls, demonstrating accurate predictions of lateral spread across a wide range of wire diameters (<span><math><mrow><mn>2</mn><mo>.</mo><mn>96</mn><mspace></mspace><mi>mm</mi></mrow></math></span>–<span><math><mrow><mn>7</mn><mo>.</mo><mn>96</mn><mspace></mspace><mi>mm</mi></mrow></math></span>) and reduction ratios (20%–60%), all without the need for fitting parameters. Since the model requires only seconds to compute, the model’s valid range is explored for varying roll diameter, wire diameter, and reduction ratio, and their effects on the resulting lateral spread characterised. The model can serve as a robust tool for validating FE results, guiding process design, and laying the foundation for future improved models. <span>Matlab</span> code to evaluate the model is provided in the supplementary material.</div></div>","PeriodicalId":50483,"journal":{"name":"European Journal of Mechanics A-Solids","volume":"117 ","pages":"Article 106027"},"PeriodicalIF":4.2,"publicationDate":"2026-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146038059","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 : 2026-01-12DOI: 10.1016/j.euromechsol.2026.106015
Leon Riccius , Iuri B.C.M. Rocha , Joris Bierkens , Hanne Kekkonen , Frans P. van der Meer
Recent advancements in Markov chain Monte Carlo (MCMC) sampling and surrogate modelling have significantly enhanced the feasibility of Bayesian analysis across engineering fields. However, the selection and integration of surrogate models and cutting-edge MCMC algorithms, often depend on ad-hoc decisions. A systematic assessment of their combined influence on accuracy and efficiency is notably lacking. The present work offers a comprehensive comparative study, employing a scalable case study in computational mechanics focused on the inference of spatially varying material parameters, that sheds light on the impact of methodological choices for surrogate modelling and sampling. We show that a priori training of the surrogate model introduces large errors in the posterior estimation even in low to moderate dimensions. We introduce a simple active learning strategy based on the path of the MCMC algorithm that is superior to all a priori trained models, and determine its training data requirements. We demonstrate that the choice of the MCMC algorithm has only a small influence on the amount of training data but no significant influence on the accuracy of the resulting surrogate model. Further, we show that the accuracy of the posterior estimation largely depends on the surrogate model, but not even a tailored surrogate guarantees convergence of the MCMC. Finally, we identify the forward model as the bottleneck in the inference process, not the MCMC algorithm. While related works focus on employing advanced MCMC algorithms, we demonstrate that the training data requirements render the surrogate modelling approach infeasible before the benefits of these gradient-based MCMC algorithms on cheap models can be reaped.
{"title":"Integration of active learning and MCMC sampling for efficient Bayesian calibration of mechanical properties","authors":"Leon Riccius , Iuri B.C.M. Rocha , Joris Bierkens , Hanne Kekkonen , Frans P. van der Meer","doi":"10.1016/j.euromechsol.2026.106015","DOIUrl":"10.1016/j.euromechsol.2026.106015","url":null,"abstract":"<div><div>Recent advancements in Markov chain Monte Carlo (MCMC) sampling and surrogate modelling have significantly enhanced the feasibility of Bayesian analysis across engineering fields. However, the selection and integration of surrogate models and cutting-edge MCMC algorithms, often depend on ad-hoc decisions. A systematic assessment of their combined influence on accuracy and efficiency is notably lacking. The present work offers a comprehensive comparative study, employing a scalable case study in computational mechanics focused on the inference of spatially varying material parameters, that sheds light on the impact of methodological choices for surrogate modelling and sampling. We show that a priori training of the surrogate model introduces large errors in the posterior estimation even in low to moderate dimensions. We introduce a simple active learning strategy based on the path of the MCMC algorithm that is superior to all a priori trained models, and determine its training data requirements. We demonstrate that the choice of the MCMC algorithm has only a small influence on the amount of training data but no significant influence on the accuracy of the resulting surrogate model. Further, we show that the accuracy of the posterior estimation largely depends on the surrogate model, but not even a tailored surrogate guarantees convergence of the MCMC. Finally, we identify the forward model as the bottleneck in the inference process, not the MCMC algorithm. While related works focus on employing advanced MCMC algorithms, we demonstrate that the training data requirements render the surrogate modelling approach infeasible before the benefits of these gradient-based MCMC algorithms on cheap models can be reaped.</div></div>","PeriodicalId":50483,"journal":{"name":"European Journal of Mechanics A-Solids","volume":"117 ","pages":"Article 106015"},"PeriodicalIF":4.2,"publicationDate":"2026-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145976832","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 : 2026-01-12DOI: 10.1016/j.euromechsol.2026.106029
Peng Chen , Ji-Hou Yang , Xiang-Ying Guo , Hua-Ting Liu , Xiao-Dong Yang
This study investigates the use of bistable nonlinear energy sinks (BNES) to suppress multimodal vibrations in axially moving beams. A coupled nonlinear dynamic model of the beam–BNES system is established and discretized using the Galerkin method. The beam's complex eigenfrequencies are analyzed to clarify the effects of axial speed and tensile load on flutter-induced instability. A continuation algorithm is then applied to compute the amplitude–frequency responses of the first two modes, with and without BNES coupling. Three BNES installation configurations are subsequently evaluated to identify the most effective vibration-control strategy. In addition, the influences of external excitation, axial velocity, tensile force, and the stiffness and damping parameters on suppression performance are systematically investigated. Based on the parametric analysis, a particle swarm optimization (PSO) algorithm is further employed to optimize the stiffness and damping parameters of the BNES, aiming to reduce the activation threshold while enhancing vibration suppression performance. The results show that distributing multiple BNES units along the beam provides superior multimode suppression compared with a single absorber. The BNES performance is sensitive to both axial motion and tensile load, and appropriate tuning of excitation level, stiffness, and damping within practical limits can further improve vibration-reduction efficiency.
{"title":"Vibration analysis and vibration reduction strategy for an axially moving beam with a bistable nonlinear energy sinks","authors":"Peng Chen , Ji-Hou Yang , Xiang-Ying Guo , Hua-Ting Liu , Xiao-Dong Yang","doi":"10.1016/j.euromechsol.2026.106029","DOIUrl":"10.1016/j.euromechsol.2026.106029","url":null,"abstract":"<div><div>This study investigates the use of bistable nonlinear energy sinks (BNES) to suppress multimodal vibrations in axially moving beams. A coupled nonlinear dynamic model of the beam–BNES system is established and discretized using the Galerkin method. The beam's complex eigenfrequencies are analyzed to clarify the effects of axial speed and tensile load on flutter-induced instability. A continuation algorithm is then applied to compute the amplitude–frequency responses of the first two modes, with and without BNES coupling. Three BNES installation configurations are subsequently evaluated to identify the most effective vibration-control strategy. In addition, the influences of external excitation, axial velocity, tensile force, and the stiffness and damping parameters on suppression performance are systematically investigated. Based on the parametric analysis, a particle swarm optimization (PSO) algorithm is further employed to optimize the stiffness and damping parameters of the BNES, aiming to reduce the activation threshold while enhancing vibration suppression performance. The results show that distributing multiple BNES units along the beam provides superior multimode suppression compared with a single absorber. The BNES performance is sensitive to both axial motion and tensile load, and appropriate tuning of excitation level, stiffness, and damping within practical limits can further improve vibration-reduction efficiency.</div></div>","PeriodicalId":50483,"journal":{"name":"European Journal of Mechanics A-Solids","volume":"117 ","pages":"Article 106029"},"PeriodicalIF":4.2,"publicationDate":"2026-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146038063","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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.euromechsol.2026.106025
Kangcheng Yin , Bo Yuan , Zhenyuan Xu , Zibo Sun , Qingchao Sun , Xiaokai Mu
Severe surface thermal distortion poses a significant challenge to the application of carbon fiber-reinforced polymer (CFRP) in lightweight reflectors. Minor deviations in the manufacturing process can lead to remarkable thermal deformation, hindering efforts to optimize fabrication techniques. This study investigates the impact mechanisms of process deviations during the layup and curing stages of CFRP reflector production on thermal distortion and introduces an integrated fabrication process that combines anti-symmetric folding layup with pre-curing technology. This innovative approach enhances the middle plane symmetry of the laminate, thereby significantly reducing thermal distortion on the surface of CFRP reflectors. Experimental samples were fabricated using the newly developed process and compared to those produced using conventional methods in terms of surface thermal distortion. The results demonstrate that, compared to the symmetric layup process, the integrated fabrication process achieves a 53.45 % reduction in the peak-to-valley value of surface thermal distortion, underscoring its significant prospect for advancing engineering applications.
{"title":"An integrated fabrication process for reducing thermal distortion of the CFRP reflector surface","authors":"Kangcheng Yin , Bo Yuan , Zhenyuan Xu , Zibo Sun , Qingchao Sun , Xiaokai Mu","doi":"10.1016/j.euromechsol.2026.106025","DOIUrl":"10.1016/j.euromechsol.2026.106025","url":null,"abstract":"<div><div>Severe surface thermal distortion poses a significant challenge to the application of carbon fiber-reinforced polymer (CFRP) in lightweight reflectors. Minor deviations in the manufacturing process can lead to remarkable thermal deformation, hindering efforts to optimize fabrication techniques. This study investigates the impact mechanisms of process deviations during the layup and curing stages of CFRP reflector production on thermal distortion and introduces an integrated fabrication process that combines anti-symmetric folding layup with pre-curing technology. This innovative approach enhances the middle plane symmetry of the laminate, thereby significantly reducing thermal distortion on the surface of CFRP reflectors. Experimental samples were fabricated using the newly developed process and compared to those produced using conventional methods in terms of surface thermal distortion. The results demonstrate that, compared to the symmetric layup process, the integrated fabrication process achieves a 53.45 % reduction in the peak-to-valley value of surface thermal distortion, underscoring its significant prospect for advancing engineering applications.</div></div>","PeriodicalId":50483,"journal":{"name":"European Journal of Mechanics A-Solids","volume":"117 ","pages":"Article 106025"},"PeriodicalIF":4.2,"publicationDate":"2026-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145977414","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 examines nonlinear fracture behavior for two-dimensional hexagonal piezoelectric quasicrystal media weakened by a penny-shaped crack. An electric polarization saturation model is developed for a penny-shaped crack in this material. The nonlinear fracture model is governed by a set of boundary integral-differential equations involving normal phonon displacement and electric potential discontinuities—collectively termed extended displacement discontinuities—as the variables to be determined. Analytical solutions of the extended displacement discontinuities, extended stress intensity factors and electric yielding zone are derived for uniformly applied electric and normal phonon loadings. Based on boundary element method and extended displacement discontinuity method, a numerical method for annular loadings is proposed to solve the boundary integral-differential equations. At the same time, we propose a numerical iterative method, which can effectively solve the size of electric yielding zone. Numerical results are utilized to cross-validate the obtained analytical solutions and the proposed numerical method. Graphical illustrations are provided to demonstrate the distributions of the key physical quantities obtained by the above two methods. The analytical and numerical solutions developed in this study offer effective methodologies for further investigations of other piezoelectric quasicrystals.
{"title":"Nonlinear fracture analysis of a penny-shaped crack in two-dimensional hexagonal piezoelectric quasicrystal media","authors":"Yuan Li , Shuhang Tang , Minghao Zhao , Jingli Ren","doi":"10.1016/j.euromechsol.2026.106020","DOIUrl":"10.1016/j.euromechsol.2026.106020","url":null,"abstract":"<div><div>This study examines nonlinear fracture behavior for two-dimensional hexagonal piezoelectric quasicrystal media weakened by a penny-shaped crack. An electric polarization saturation model is developed for a penny-shaped crack in this material. The nonlinear fracture model is governed by a set of boundary integral-differential equations involving normal phonon displacement and electric potential discontinuities—collectively termed extended displacement discontinuities—as the variables to be determined. Analytical solutions of the extended displacement discontinuities, extended stress intensity factors and electric yielding zone are derived for uniformly applied electric and normal phonon loadings. Based on boundary element method and extended displacement discontinuity method, a numerical method for annular loadings is proposed to solve the boundary integral-differential equations. At the same time, we propose a numerical iterative method, which can effectively solve the size of electric yielding zone. Numerical results are utilized to cross-validate the obtained analytical solutions and the proposed numerical method. Graphical illustrations are provided to demonstrate the distributions of the key physical quantities obtained by the above two methods. The analytical and numerical solutions developed in this study offer effective methodologies for further investigations of other piezoelectric quasicrystals.</div></div>","PeriodicalId":50483,"journal":{"name":"European Journal of Mechanics A-Solids","volume":"117 ","pages":"Article 106020"},"PeriodicalIF":4.2,"publicationDate":"2026-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146077639","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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.euromechsol.2026.106019
J.C. Zhu , M. Ben Bettaieb , F. Abed-Meraim , B. Jia , J. Li
Shear stress is recognized as a critical factor influencing the ductile failure process. In the present work, we investigate ductile failure initiation under shear-dominated loading by identifying the onset of strain localization, which is predicted using a rigorous bifurcation analysis. Micromechanical computations are performed using cubic voided unit cells (UCs) subjected to fully periodic boundary conditions. Proportional stressing is imposed to keep constant stress triaxiality (T) and Lode parameter (L) throughout the deformation history of UCs. In the proportional stressing, two loading configurations are realized to comparatively study the effect of shear stress component for a given pair of T and L: normal stresses (without shear) versus normal stresses combined with one shear stress component. The effects of initial porosity and void configuration (pattern of voids arrangement) are also systematically analyzed. The results show that the influence of shear stress is strongly modulated by the amount of the initial porosity. While shear stress promotes strain localization at low initial porosity, it conversely delays it at high initial porosity within a specific range of Lode parameters. This porosity-dependent trend reversal is rationalized by a transition from a ligament-thinning-dominated failure mode to an intervoid-shearing-dominated failure mode as the stress state varies. Furthermore, for a given overall initial porosity, the void configuration significantly affects the critical strain locus, the extent of which depends on the imposed triaxiality. These findings provide valuable micromechanical insights for refining predictive modeling in engineering applications.
{"title":"Influence of shear stress on ductile failure initiation: a micromechanical analysis of strain localization","authors":"J.C. Zhu , M. Ben Bettaieb , F. Abed-Meraim , B. Jia , J. Li","doi":"10.1016/j.euromechsol.2026.106019","DOIUrl":"10.1016/j.euromechsol.2026.106019","url":null,"abstract":"<div><div>Shear stress is recognized as a critical factor influencing the ductile failure process. In the present work, we investigate ductile failure initiation under shear-dominated loading by identifying the onset of strain localization, which is predicted using a rigorous bifurcation analysis. Micromechanical computations are performed using cubic voided unit cells (UCs) subjected to fully periodic boundary conditions. Proportional stressing is imposed to keep constant stress triaxiality (<em>T</em>) and Lode parameter (<em>L</em>) throughout the deformation history of UCs. In the proportional stressing, two loading configurations are realized to comparatively study the effect of shear stress component for a given pair of <em>T</em> and <em>L</em>: normal stresses (without shear) <em>versus</em> normal stresses combined with one shear stress component. The effects of initial porosity and void configuration (pattern of voids arrangement) are also systematically analyzed. The results show that the influence of shear stress is strongly modulated by the amount of the initial porosity. While shear stress promotes strain localization at low initial porosity, it conversely delays it at high initial porosity within a specific range of Lode parameters. This porosity-dependent trend reversal is rationalized by a transition from a ligament-thinning-dominated failure mode to an intervoid-shearing-dominated failure mode as the stress state varies. Furthermore, for a given overall initial porosity, the void configuration significantly affects the critical strain locus, the extent of which depends on the imposed triaxiality. These findings provide valuable micromechanical insights for refining predictive modeling in engineering applications.</div></div>","PeriodicalId":50483,"journal":{"name":"European Journal of Mechanics A-Solids","volume":"117 ","pages":"Article 106019"},"PeriodicalIF":4.2,"publicationDate":"2026-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145976834","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 : 2026-01-08DOI: 10.1016/j.euromechsol.2026.106022
Daifeng Yang , Jianbo Chen , Yining Zhang , Perk Lin Chong , Eric Li
This study extends our previous research on the cactus stem-inspired bionic multi-cell tube (CSBMT) by conducting a deeper investigation aimed at further enhancing its crashworthiness performance. Finite element analysis (FEA) was employed to investigate the energy absorption performance of CSBMT under varying geometric parameters, including the number of corners (N), inner diameter (Di), and outer angle (β). Additional analyses examined the influence of oblique loading (0°–30°) and gradient wall thickness distributions (n = 0.2–5.0). The results indicate that increasing N and Di significantly improves the specific energy absorption (SEA), while a larger β and smaller n enhance load uniformity and deformation stability. Compared with the baseline configuration, the optimal design achieved a 74.9 % improvement in SEA. Compared with 16 classical thin-walled energy-absorbing structures, the CSBMT exhibited superior energy absorption and load-bearing capacity under 20° oblique loading. Furthermore, a multi-objective structural optimization of the CSBMT was performed using the Non-dominated Sorting Genetic Algorithm II (NSGA-II), and a compromise solution was identified based on the minimum distance criterion. The optimized structure exhibited a well-balanced performance between energy absorption efficiency and peak load control. The findings provide valuable insights for the design of bio-inspired energy-absorbing structures in crashworthiness applications.
{"title":"Parametric and multi-objective optimization analysis of cactus stem-inspired bionic multi-cell tubes for enhanced crashworthiness","authors":"Daifeng Yang , Jianbo Chen , Yining Zhang , Perk Lin Chong , Eric Li","doi":"10.1016/j.euromechsol.2026.106022","DOIUrl":"10.1016/j.euromechsol.2026.106022","url":null,"abstract":"<div><div>This study extends our previous research on the cactus stem-inspired bionic multi-cell tube (CSBMT) by conducting a deeper investigation aimed at further enhancing its crashworthiness performance. Finite element analysis (FEA) was employed to investigate the energy absorption performance of CSBMT under varying geometric parameters, including the number of corners (<em>N</em>), inner diameter (<em>D</em><sub><em>i</em></sub>), and outer angle (<em>β</em>). Additional analyses examined the influence of oblique loading (0°–30°) and gradient wall thickness distributions (<em>n</em> = 0.2–5.0). The results indicate that increasing <em>N</em> and <em>D</em><sub><em>i</em></sub> significantly improves the specific energy absorption (SEA), while a larger <em>β</em> and smaller <em>n</em> enhance load uniformity and deformation stability. Compared with the baseline configuration, the optimal design achieved a 74.9 % improvement in SEA. Compared with 16 classical thin-walled energy-absorbing structures, the CSBMT exhibited superior energy absorption and load-bearing capacity under 20° oblique loading. Furthermore, a multi-objective structural optimization of the CSBMT was performed using the Non-dominated Sorting Genetic Algorithm II (NSGA-II), and a compromise solution was identified based on the minimum distance criterion. The optimized structure exhibited a well-balanced performance between energy absorption efficiency and peak load control. The findings provide valuable insights for the design of bio-inspired energy-absorbing structures in crashworthiness applications.</div></div>","PeriodicalId":50483,"journal":{"name":"European Journal of Mechanics A-Solids","volume":"117 ","pages":"Article 106022"},"PeriodicalIF":4.2,"publicationDate":"2026-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145925623","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 : 2026-01-08DOI: 10.1016/j.euromechsol.2026.106023
Y. Gholami , R. Ansari , H. Rouhi
This study aims to investigate the geometrically nonlinear forced vibration behavior of micro-scale plates made of functionally graded materials (FGMs) by developing a variational numerical approach that accounts for strain gradient effects. The proposed approach, which is based on the variational differential quadrature technique, is capable of addressing the problem with arbitrary geometry (e.g. quadrilateral plate, annular sector plate, triangular plate, etc.). Besides, Mindlin's strain gradient theory is applied that leads to a formulation which encompasses the modified versions of strain gradient and couple stress theories (MSGT & MCST). An important novelty of present work is its vector-matrix presentation which can be beneficial for researchers working on numerical methods. Based on Hamilton's principle together with Mindlin's plate theory, the governing equations are derived. In the numerical results, the effects of thickness-to-material length-scale parameter on the frequency-response curves of FG plates with various shapes are analyzed. Also, comparisons are made between the predictions of MCST, MSGT as well as the classical theory. The results indicate that strain gradient terms have a pronounced influence on the nonlinear dynamic response of FGM microplates, giving rise to evident stiffening behavior and noticeable changes in the frequency–response curves. These observations highlight the importance of using higher-order continuum models to achieve reliable predictions of nonlinear forced vibration behavior at the micro-scale.
{"title":"Nonlinear forced vibrations of FGM microplates: a numerical approach in the context of Mindlin's strain gradient elasticity","authors":"Y. Gholami , R. Ansari , H. Rouhi","doi":"10.1016/j.euromechsol.2026.106023","DOIUrl":"10.1016/j.euromechsol.2026.106023","url":null,"abstract":"<div><div>This study aims to investigate the geometrically nonlinear forced vibration behavior of micro-scale plates made of functionally graded materials (FGMs) by developing a variational numerical approach that accounts for strain gradient effects. The proposed approach, which is based on the variational differential quadrature technique, is capable of addressing the problem with arbitrary geometry (e.g. quadrilateral plate, annular sector plate, triangular plate, etc.). Besides, Mindlin's strain gradient theory is applied that leads to a formulation which encompasses the modified versions of strain gradient and couple stress theories (MSGT & MCST). An important novelty of present work is its vector-matrix presentation which can be beneficial for researchers working on numerical methods. Based on Hamilton's principle together with Mindlin's plate theory, the governing equations are derived. In the numerical results, the effects of thickness-to-material length-scale parameter on the frequency-response curves of FG plates with various shapes are analyzed. Also, comparisons are made between the predictions of MCST, MSGT as well as the classical theory. The results indicate that strain gradient terms have a pronounced influence on the nonlinear dynamic response of FGM microplates, giving rise to evident stiffening behavior and noticeable changes in the frequency–response curves. These observations highlight the importance of using higher-order continuum models to achieve reliable predictions of nonlinear forced vibration behavior at the micro-scale.</div></div>","PeriodicalId":50483,"journal":{"name":"European Journal of Mechanics A-Solids","volume":"117 ","pages":"Article 106023"},"PeriodicalIF":4.2,"publicationDate":"2026-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146188232","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 : 2026-01-08DOI: 10.1016/j.euromechsol.2026.106021
Hussein Zahran , Aleksandr Zinovev , Dmitry Terentyev , Ali Aouf , Magd Abdel Wahab
Qualification of Reduced Activation Ferritic-Martensitic (RAFM) steels for fusion reactors require Low Cycle Fatigue (LCF) testing including experiments after irradiation. Cyclic softening curves from these tests help reduce the conservatism of RCC-MRx. In this work, Deep Neural Network (DNN) is used to predict the cyclic softening curves for irradiated and non-irradiated RAFM steels. Cyclic softening for specimens tested under different conditions are gathered from literature. Three samples are used in this study with increased number of points obtained per curve. The results showed that increasing the number of points per curve reduced the overfitting of the training set. This is shown through the increase of the accuracy scores for both the validation and prediction sets. SHapley Additive exPlanation (SHAP) analysis is performed to understand how the DNN model interprets the effect of the input features on the output. The DNN model with the tuned hyperparameters is used to predict the cyclic softening curves of the prediction sets. The curves show very good agreement between the experimental and predicted curves for both irradiated and non-irradiated material.
{"title":"A deep learning approach to predict cyclic softening behaviour of irradiated and non-irradiated RAFM steels under low cycle fatigue","authors":"Hussein Zahran , Aleksandr Zinovev , Dmitry Terentyev , Ali Aouf , Magd Abdel Wahab","doi":"10.1016/j.euromechsol.2026.106021","DOIUrl":"10.1016/j.euromechsol.2026.106021","url":null,"abstract":"<div><div>Qualification of Reduced Activation Ferritic-Martensitic (RAFM) steels for fusion reactors require Low Cycle Fatigue (LCF) testing including experiments after irradiation. Cyclic softening curves from these tests help reduce the conservatism of RCC-MRx. In this work, Deep Neural Network (DNN) is used to predict the cyclic softening curves for irradiated and non-irradiated RAFM steels. Cyclic softening for specimens tested under different conditions are gathered from literature. Three samples are used in this study with increased number of points obtained per curve. The results showed that increasing the number of points per curve reduced the overfitting of the training set. This is shown through the increase of the accuracy scores for both the validation and prediction sets. SHapley Additive exPlanation (SHAP) analysis is performed to understand how the DNN model interprets the effect of the input features on the output. The DNN model with the tuned hyperparameters is used to predict the cyclic softening curves of the prediction sets. The curves show very good agreement between the experimental and predicted curves for both irradiated and non-irradiated material.</div></div>","PeriodicalId":50483,"journal":{"name":"European Journal of Mechanics A-Solids","volume":"117 ","pages":"Article 106021"},"PeriodicalIF":4.2,"publicationDate":"2026-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145976833","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 : 2026-01-08DOI: 10.1016/j.euromechsol.2026.106018
Monzer Daoud , Régis Kubler
Shot-peening is a surface treatment process widely employed to enhance the fatigue life of metallic components by inducing compressive residual stresses beneath the surface. However, such components often contain surface or subsurface geometrical defects that can reduce fatigue life. Accurate understanding of the resulting residual mechanical fields near these defects is essential for integrating shot-peening into the design process and accurately predicting the fatigue life. This study investigates the evolution of residual mechanical fields both near and far from an artificial hole (800 μm in diameter and 400 μm in depth), as well as the associated edge-hole distortion after shot-peening. A finite element framework was employed to compare two approaches: a multi-impact shot-peening model and an eigenstrain reconstruction method incorporating elastoplastic behavior. Both approaches were applied to TRIP780 steel, using experimental material parameters as inputs and experimental residual stress profiles for validation. Results showed that the multi-impact shot-peening model successfully simulated the localized plastic deformation adjacent to the hole, where strain concentration and distortion extended up to 200 μm from the edge. Although the eigenstrain method could not reproduce the edge-hole distortion, it generated comparatively similar localized plastic deformation near the hole and provided accurate residual stress predictions at distances beyond 200 μm from the hole, owing to inputs from the multi-impact shot-peening model. Both approaches indicated that the radial stresses were more influenced by the hole than the tangential ones.
{"title":"Shot-peening simulations with artificial surface defect using multiple impacts and eigenstrain reconstruction method","authors":"Monzer Daoud , Régis Kubler","doi":"10.1016/j.euromechsol.2026.106018","DOIUrl":"10.1016/j.euromechsol.2026.106018","url":null,"abstract":"<div><div>Shot-peening is a surface treatment process widely employed to enhance the fatigue life of metallic components by inducing compressive residual stresses beneath the surface. However, such components often contain surface or subsurface geometrical defects that can reduce fatigue life. Accurate understanding of the resulting residual mechanical fields near these defects is essential for integrating shot-peening into the design process and accurately predicting the fatigue life. This study investigates the evolution of residual mechanical fields both near and far from an artificial hole (800 μm in diameter and 400 μm in depth), as well as the associated edge-hole distortion after shot-peening. A finite element framework was employed to compare two approaches: a multi-impact shot-peening model and an eigenstrain reconstruction method incorporating elastoplastic behavior. Both approaches were applied to TRIP780 steel, using experimental material parameters as inputs and experimental residual stress profiles for validation. Results showed that the multi-impact shot-peening model successfully simulated the localized plastic deformation adjacent to the hole, where strain concentration and distortion extended up to 200 μm from the edge. Although the eigenstrain method could not reproduce the edge-hole distortion, it generated comparatively similar localized plastic deformation near the hole and provided accurate residual stress predictions at distances beyond 200 μm from the hole, owing to inputs from the multi-impact shot-peening model. Both approaches indicated that the radial stresses were more influenced by the hole than the tangential ones.</div></div>","PeriodicalId":50483,"journal":{"name":"European Journal of Mechanics A-Solids","volume":"117 ","pages":"Article 106018"},"PeriodicalIF":4.2,"publicationDate":"2026-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146038062","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}