To enhance the bending resistance of bellows,an environmentally friendly electric pulse heat treatment(EPHT)method was used.The strengthening mechanism was systematically studied by microstructure characterization,fin...To enhance the bending resistance of bellows,an environmentally friendly electric pulse heat treatment(EPHT)method was used.The strengthening mechanism was systematically studied by microstructure characterization,finite element simulation and bending test.The results showed that during EPHT process,the cross-sectional area of the trough was small,so that the current density was large,which made the temperature of the trough significantly higher than those of other regions.The temperature difference between the peak and the trough was most influenced by frequency.Empirical formulas were derived to predict the temperature and current density of the trough under varying parameters.The dislocation elimination and grain growth of the trough achieved the optimal balance at 800℃and 7 A/mm2,obtaining the best bending resistance.Bellows prepared by general heat treatment process(GHTP)had coarse grains and local high dislocation density areas.In contrast,the grains of EPHT bellows were fine,the dislocations were eliminated completely and uniformly,and the crack propagation path was more tortuous.Compared with GHTP,EPHT significantly reduced the dislocation density and eliminated oxide inclusions.This microstructural optimization altered the crack propagation behavior from simultaneous bidirectional growth(initiating from both high-strain surfaces and wall center)to unidirectional propagation(surface to center)of GHTP,thereby greatly reducing the crack propagation rate.Notably,the fracture mechanism changed from quasi-cleavage to ductile fracture.Compared with GHTP,the number of bending cycles of EPHT bellows increased by about 200%before fracture.展开更多
The structure profile of magnesium alloy tube is difficult to control for complex microstructural evolution under the asymmetric loading of tension and compression induced during tube bending.This study investigates t...The structure profile of magnesium alloy tube is difficult to control for complex microstructural evolution under the asymmetric loading of tension and compression induced during tube bending.This study investigates the electro-assisted bending of extruded AZ61(Mg-6Al-1Zn)magnesium alloy tubes,with particular focus on the influence of pulsed current on microstructure evolution and plastic deformation mechanisms under varying degrees of deformation.The results indicate that pulsed current increases the fraction of{1012}tensile twins and effectively regulates twin nucleation positions along the tangential cross-sections on both sides of the bending head.The initially disordered twin distribution is transformed into a more ordered arrangement,thereby enhancing radial microstructural uniformity during bending.The thermal and electromagnetic energy generated by the current promotes the alignment or polarization of twins and dislocations along specific directions.This phenomenon suggests that pulsed current can improve the formability of magnesium alloy tubes through distinctive microstructural modifications.These findings offer valuable insights into microstructure control and bending ability enhancement of magnesium alloy tube.展开更多
This study comprehensively investigates the bending behavior of 3D star-shaped auxetic(3D-SAU)metamaterials,which exhibit a distinctive negative Poisson's ratio(NPR)effect along three orthogonal spatial directions...This study comprehensively investigates the bending behavior of 3D star-shaped auxetic(3D-SAU)metamaterials,which exhibit a distinctive negative Poisson's ratio(NPR)effect along three orthogonal spatial directions.Parametric analysis reveals that the out-of-plane NPR effect is significantly enhanced by increasing the hexagon side length(l),whereas reduced by increasing the offset angle(α)or interlayer spacing(h).Results extracted from experimental and numerical three-point bending tests indicate that auxetic(3D-SAU and 3D-RE)metamaterials exhibit 3.5 times to 10.7 times higher bending compliance than the traditional BCC one,due to their distinct deformation modes under bending loads.Notably,the architecture of the 3D-SAU unit cell,featuring reversely staggered star-shaped frames,facilitates a unique deformation mechanism dominated by rod rotation,thereby ensuring the metamaterial's superior structural compliance under bending loads.Furthermore,the potential application is explored by integrating 3D-SAU metamaterials into morphing airfoils actuated by shape memory alloy(SMA)skins.A functionally-graded design for the unit cell'sα,has been introduced to enable controllable and localized deformation of the airfoil profile.Through a combined experimental and numerical approach,it is found that the 3D-SAU metamaterials not only achieve exceptional deformability but also effectively reduce stress concentration through its tailored compliance.This study establishes a novel design framework for high-performance morphing airfoils that achieves a synergy between large,controllable shape adaptation with inherent impact-resistance for advanced aerospace applications.展开更多
To enhance the bending mechanical properties of fiber-reinforced plastics(FRP)and address rapid damage repair under multiple bending loads,an improved shape memory alloy hybrid composite(ISMAHC)was developed by embedd...To enhance the bending mechanical properties of fiber-reinforced plastics(FRP)and address rapid damage repair under multiple bending loads,an improved shape memory alloy hybrid composite(ISMAHC)was developed by embedding layered orthogonal shape memory alloy(SMA)wires into FRP.Three-point bending and water bath recovery tests were performed on traditional single-layer unidirectional SMA hybrid composites(SMAHC),ISMAHC and FRP.The effects of layered orthogonal SMA configuration on stiffness,strength,and recovery capability were compared and investigated.Results demonstrate that SMA wires form a coupling effect with FRP,increasing the bending modulus.Furthermore,ISMAHC has higher stiffness due to its orthogonal architecture.The water bath recovery tests indicate that SMAHC and ISMAHC possess good deflection recoverability and mechanical property recoverability after multiple bending loadings.The deflection recovery rate of the first bending test is greater than 60%,and that of the second bending test is greater than 30%.Additionally,the bending modulus and bending strength recover more than 30%,with ISMAHC showing superior recoverability.展开更多
This research encompasses three-point bending based on artificial neural networks(ANNs)for a simple accurate process design.Uniaxial tensile tests are carried out for 22 steel and aluminum sheet metals with different ...This research encompasses three-point bending based on artificial neural networks(ANNs)for a simple accurate process design.Uniaxial tensile tests are carried out for 22 steel and aluminum sheet metals with different thicknesses to characterize their mechanical properties,such as the Young’s modulus,yield stress,strength,strain hardening,etc.Approximately 20-30 three-point bending tests are conducted for each sheet metal with different gaps and punch strokes to obtain different bending angles before and after spring-back ranging from 60°to 165°.The angles after spring-back are modeled by an ANN as the output.The inputs for the ANN model include the mechanical properties obtained from uniaxial tensile tests,as well as gap and punch stroke used in three-point bending.The angles after spring-back predicted by the ANN model trained by 22 materials are compared with experimental results to evaluate its performance.The comparison shows that the trained ANN model can precisely predict the angle after spring-back with a maximum error of less than 3.7%.The trained ANN model is also tested for unseen gap and stroke,to design the processing parameters in three-point bending of advanced high-strength steel(DP980)and an aluminum alloy(AA6K21-T4).The application demonstrates that the trained ANN model can design the process parameters with high accuracy even for unseen data.This study shows that the ANN model is strongly suggested to be used in process and tool design/optimization of metal forming processes to achieve high accuracy and generalizability.展开更多
Bending is a crucial operation in the sheet forming of Mg alloys for automotive and aerospace applications.In this work,three kinds of sheets from an AZ31 rolled plate,sheared at 0°(S0),45°(S45),and 90°...Bending is a crucial operation in the sheet forming of Mg alloys for automotive and aerospace applications.In this work,three kinds of sheets from an AZ31 rolled plate,sheared at 0°(S0),45°(S45),and 90°(S90)to the rolling direction,were subjected to three-point bending tests.In-situ digital image correlation(DIC)system was employed to capture the strain fields.Electron backscatter diffraction(EBSD)was used to examine the through-thickness microstructures.A crystal plasticity finite element method(CPFEM)incorporating twinning and slip mechanisms was developed to simulate the bending deformation.The texture effect on the neutral layer shift and twinning behaviors was systematically investigated in terms of both experiments and simulations.The results show that CPFEM effectively simulated the texturedependent shifting behaviors of neutral layer and the associated twinning behaviors.Particularly,the spatial distributions of neutral layer across the entire bent plates were captured by both DIC and CPFEM.Additionally,some unusual twinning behaviors were analyzed in depth,such as the{10-12}-{10-12}secondary twins in S90,localized twin bands in S0,and the twin traces difference in S45.These findings reveal a close relationship between the neutral layer shift and twinning activity induced by the initial texture and strain levels.This work provides valuable insights into the bending deformation mechanisms of Mg alloys and has important implications for improving their formability and controlling springback.展开更多
Shale deformation is crucial in various geological processes.To investigate the effect of deformation on pore characteristics for highly compacted shale,the macro tectonic strain and micro pore structure were analyzed...Shale deformation is crucial in various geological processes.To investigate the effect of deformation on pore characteristics for highly compacted shale,the macro tectonic strain and micro pore structure were analyzed in the deeply buried Wufeng-Longmaxi shale of the Eastern Fold Belt of the Sichuan Basin.Despite similarities in their X-ray diffraction mineral compositions,significant differences in pore properties were observed between the shale samples from weak and strong curved synclines.Pore shapes identified from scanning electron microscopy and the covariation between total organic carbon(TOC)content and porosity suggest that organic pores predominantly contribute to total porosity.However,samples from weak-curved synclines exhibit porosities~2%higher than samples from strongcurved synclines,even with similar TOC contents.Compared to the weak-curved syncline samples,the strong-curved syncline samples show a transformation in organic pore morphology from spherical to elliptical with an increasing aspect ratio and reduced dominant pore size from 1-1000 nm to 1-100 nm due to pore collapse in the organic matrix.The porosities simulated using a syncline bending ductile strain model align well with the measured porosities,indicating that the porosity changes were induced by heterogeneous ductile strain during detachment folding.Strain heterogeneity also triggered tectonic stress heterogeneity,causing clockwise rotation of the principal stress orientation from weak to strong curved synclines.This study improves our understanding of the variations in pore system with syncline deformation strain,providing a theoretical basis for subsequent shale hydrocarbon exploration and resource assessment in complex tectonic zones.展开更多
Manufacturing sound thin-walled metallic tubes via Free Bending Forming(FBF)technology depends on a geometric relationship involving the eccentricity of the bending die,rotation angle,deformation zone length,and bendi...Manufacturing sound thin-walled metallic tubes via Free Bending Forming(FBF)technology depends on a geometric relationship involving the eccentricity of the bending die,rotation angle,deformation zone length,and bending radius.This accuracy of relationship relies ideally on the bending die rotating,maintaining tangency with the tube.Nevertheless,if the die deviates from this ideal rotation owing to material properties,the interaction between the die and tube occurs,leading to inaccuracies in the geometric relationship.Thus,investigating the influence of the non-ideal rotation of the bending die on thin-walled metallic tubes during the FBF process is essential.A new theoretical model is proposed to determine and study the forces acting on the tube during non-ideal die rotation,which is divided into bending outer and inner forces.The proposed model examines the force directions in three forms,over-rotation,under-rotation,and ideal rotation,to explain the changes in the internal forces within the cross-section and bending radius of tube.In addition,it determines the unit squeezing force on the tubes during non-ideal rotation.To validate the proposed theoretical model,Finite Element Modeling(FEM)and actual forming experiments were conducted to investigate the influence of forces acting on the tube during non-ideal die rotation and analyze the tube stresses under the three rotation forms.The FEM and experimental results strongly correlate with the theoretical analysis,confirming the accuracy of model in predicting tube behavior under varying bending die conditions.展开更多
This paper introduces a novel gradient-enhanced physics-informed neural network(gPINN)framework for analyzing Kirchhoff-Love plate bending under diverse boundary conditions.The approach marks a significant advancement...This paper introduces a novel gradient-enhanced physics-informed neural network(gPINN)framework for analyzing Kirchhoff-Love plate bending under diverse boundary conditions.The approach marks a significant advancement in physicsinformed machine learning by offering three key innovations:(1)a gradient-regularized loss function that enforces the biharmonic equation and boundary constraints concurrently;(2)a modular neural architecture featuring interconnected subnets for transverse and in-plane displacements;(3)an adaptive training algorithm with physics-informed sampling strategies.The proposed technical framework integrates several pioneering elements.It augments the strain energy functional with higher-order gradient terms to accurately capture curvature effects near plate boundaries.Furthermore,it introduces edge-specific penalty functions that automatically accommodate various support conditions,such as clamped,simply supported,and free edges,without requiring geometric remeshing.The network design further integrates dedicated submodules for displacement gradients,utilizing shared weights for mixed partial derivatives critical to the bending moment formulation.Numerical validations across three benchmark cases(complex boundary conditions)highlight the framework’s superiority over traditional PINNs.Notable outcomes include:(I)a 72%average reduction in relative error at boundary transitions(p<0.01);(II)convergence to engineering accuracy(<%error)in 38%fewer iterations;(III)robust generalization to untested boundary condition combinations.The gPINN solutions align closely with finite element benchmarks while eliminating meshing dependencies,demonstrating particular strength in high-stress concentration zones.This study sets a new benchmark for physics-informed deep learning in plate mechanics,offering immediate relevance for designing aerospace components,marine structures,and other thin-walled structures where precise deformation prediction under complex constraints is essential.The gradient enhancement methodology provides a scalable blueprint for applying physics-aware machine learning to other fourth-order boundary value problems in solid mechanics.展开更多
Since the view that the localized rail third-order bending mode can cause high-order polygonization(mainly 18-23)of high-speed train wheels was put forward in 2017,many scholars have attempted to link a connection bet...Since the view that the localized rail third-order bending mode can cause high-order polygonization(mainly 18-23)of high-speed train wheels was put forward in 2017,many scholars have attempted to link a connection between the localized rail bending modes and wheel polygonization phenomenon and polygonal wheel passing frequency.This paper first establishes a flexible track model considering the structural and parametric characteristics of fasteners,verifies the model by using vehicle tracking test data,then investigates the influence of fastener parameter matching on the localized rail bending modes,and obtains the following conclusions:(1)There is nearly a 1:1 mapping relationship between the localized rail bending modal frequency and polygonal wheel passing(PWP)frequency,which supports that the localized rail bending mode is one of the causes of wheel polygonization.(2)The iron plate of the fastener system plays a role of dynamic vibration absorber in the vehicle-rail coupled system,and the fastener parameters significantly influence the localized rail bending modal vibration.Finally,this paper proposes a design principle of a high-frequency vibration-absorbing fastener,which provides a feasible solution to mitigate the localized rail bending modal vibration and high-order wheel polygonization.Meanwhile,it points out that this measure may induce other high-frequency vibration problems,e.g.,aggravating modal vibration above 800 Hz.Further,this paper proposes a concept of differentiated arrangement of fasteners,suggesting that different high-frequency vibration-absorbing fasteners be installed in different sections of the whole line to make the localized rail bending modal frequency of the whole line disordered,thus disrupting and further mitigating the development of the wheel polygonization.展开更多
Percutaneous coronary intervention(PCI)via the transradial route is now standard practice,particularly in elderly patients,owing to its lower bleeding risk and early ambulation.However,agerelated vascular changes such...Percutaneous coronary intervention(PCI)via the transradial route is now standard practice,particularly in elderly patients,owing to its lower bleeding risk and early ambulation.However,agerelated vascular changes such as radial and subclavian tortuosity,elongation,and reduced arterial compliance can pose unique procedural challenges.One such challenge is catheter kinking,which can impede the smooth delivery of stents.展开更多
Functionally graded material(FGM)plates are widely used in various engineering structures owing to their tailor-made mechanical properties,whereas cracked homogeneous plates constitute a canonical setting in fracture ...Functionally graded material(FGM)plates are widely used in various engineering structures owing to their tailor-made mechanical properties,whereas cracked homogeneous plates constitute a canonical setting in fracture mechanics analysis.These two classes of problems respectively embody material non-uniformity and geometric discontinuity,thereby imposing more stringent requirements on numerical methods in terms of high-order field continuity and accurate defect representation.Based on the classical Kirchhoff-Love plate theory,a numerical manifold method(MLS-NMM)incorporating moving least squares(MLS)interpolation is developed for bending analysis of FGM plates and fracture simulation of homogeneous plates with defects.The method constructs an H2-regular approximation with high-order continuous weighting functions and,combined with the separation of mathematical and physical covers,establishes a unified framework that accurately handles material gradients and cracks without mesh reconstruction.For the crack tip,a singular physical cover incorporating the Williams asymptotic field is introduced to achieve local enrichment,enabling the natural capture of displacement discontinuity and stress singularity.Stress intensity factors are extracted using the interaction integral method,and the dimensionless J-integral shows a maximum relative error below 1.2%compared with the reference solution.Numerical results indicate that MLS-NMM exhibits excellent convergence performance:using 676 mathematical nodes,the nondimensional central deflection of both FGM and homogeneous plates agrees with reference solutions with a maximum relative error below 0.81%,and no shear locking occurs.A systematic analysis reveals that for a simply supported on all four edges(SSSS)FGM square plate with a/h=10,the nondimensional central deflection increases by 212%as the gradient index nrises from 0 to 5.For a homogeneous plate containing a central crack with c/a=0.6,the nondimensional central deflection increases by approximately 46%compared with the intact plate.Under weak boundary constraints(e.g.,SFSF),the deformation is markedly amplified,with the deflection reaching more than three times that under strong constraints(SCSC).The proposed method provides an efficient,reconstruction-free numerical tool for high-accuracy bending and fracture analyses of FGM and cracked thin-plate structures.展开更多
Investigating the deformation behavior of graphene-reinforced composite structures holds significant engineering implications,while the rapid advancement of machine learning has introduced new technical approaches to ...Investigating the deformation behavior of graphene-reinforced composite structures holds significant engineering implications,while the rapid advancement of machine learning has introduced new technical approaches to structural bending analysis.In this study,we investigate the mechanical bending behavior of graphene origami(GOri)-enabled auxetic metamaterial beams using a physics-informed neural network(PINN).GOri-enabled auxetic metamaterials represent an innovative composite system characterized by a negative Poisson’s ratio(NPR)and superior mechanical performance.Here,we propose a composite beam model incorporating the modified coupled stress theory(MCST)and employing the PINN method to solve higher-order bending governing equations.Compared to the analytical solution,the accuracy and effectiveness of the PINN framework as a meshless solver for higher-order partial differential equations are verified.The bending properties of metamaterial beams are studied by considering the mechanical properties and size effect of metamaterials.It was found that the length scale parameters,more graphene platelets,and a higher folding degree have the best reinforcement effect on composite beams.By systematically varying the GOri folding parameters and graphene content,we demonstrate the robustness of the PINN methodology in resolving microscale beam bending phenomena,particularly in capturing complex size-effect interactions.展开更多
The stimulated Brillouin scattering(SBS)of heavy germania-doped few-mode fiber(HG-FMF)up to 98 mol%and its dependence on temperature,strain,and bending are studied in this paper,respectively.Two widely located individ...The stimulated Brillouin scattering(SBS)of heavy germania-doped few-mode fiber(HG-FMF)up to 98 mol%and its dependence on temperature,strain,and bending are studied in this paper,respectively.Two widely located individual Brillouin gain spectra(BGS),whose central peaks are 8.151 GHz and 8.862 GHz,are found in HG-FMF,respectively.These two BGS are generated by the interaction between the fundamental and higher-order acoustic wave modes,which match well with the numerical simulation.The heavy germania-doping induced a large refractive index difference between the core and cladding that strongly confined the optical field in the fiber core and modified its Brillouin parameter.This fact also leads to the bending resistance of HG-FMF,in the bending radii from 0.3 cm to 2 cm,in contrast to traditional FMFs,and suppressed the temperature and strain sensitivity of the two BGS to 213 k Hz/℃,342 k Hz/℃and 20.5 k Hz/μɛ,21.4 k Hz/μɛ,respectively.These advances of HG-FMF could be potentially used for bending-resistant distributed multi-parameter sensing.展开更多
The bending behavior of microbeams in micro-nano devices exhibits significant size effects,making accurate prediction of their mechanical behaviors crucial for device reliability.This paper employs the modified couple...The bending behavior of microbeams in micro-nano devices exhibits significant size effects,making accurate prediction of their mechanical behaviors crucial for device reliability.This paper employs the modified couple stress theory(MCST)and derives the governing equations for the Reddy beam theory(RBT)via the principle of virtual work.By considering the load equivalence,the analytical solutions for the bending problem are derived and expressed as the functional relations based on the Euler-Bernoulli beam model.Once the Euler-Bernoulli beam solution is obtained,the exact solution for the corresponding Reddy beam can be directly determined through these functional relations and boundary conditions.Analytical solutions for the doubly simply-supported(S-S),clamped-free(C-F),and clamped-clamped(C-C)boundary conditions are derived and validated through comparison with the results of previous studies.This study clarifies the analytical relationship between the two beam theories at the micro-scale,enabling exact mechanical solutions for higher-order shear deformation beams without solving complex higher-order governing equations.展开更多
The bending collapse and energy absorption of 7003 aluminum alloy bumper beams under four aging conditions(pre-aging,under-aging,peak-aging,and over-aging)were investigated through three-point bending tests.Microstruc...The bending collapse and energy absorption of 7003 aluminum alloy bumper beams under four aging conditions(pre-aging,under-aging,peak-aging,and over-aging)were investigated through three-point bending tests.Microstructural characterization was performed using scanning electron microscopy and transmission electron microscopy.Based on the Swift−Hockett−Sherby constitutive model combined with the Gurson−Tvergaard−Needleman damage model,the plastic response and fracture behavior of the 7003 aluminum alloy under uniaxial tension and three-point bending were accurately predicted.The results showed that the peak bending force of the beams was proportional to the strength under different aging states,while stress triaxiality governed the cracking failure.Pre-aged and under-aged beams resisted cracking until reaching 250 mm displacement due to stress transition from tensile to compression on the bottom surface.The under-aged beam exhibited optimal energy absorption(7.86 kJ)and a higher peak force(38.75 kN).展开更多
Piezoelectric ceramic bending actuators play a pivotal role in various high-tech applications.As a new strategy for fabricating bending actuators,constructing defect dipole concentration gradient has emerged as an eff...Piezoelectric ceramic bending actuators play a pivotal role in various high-tech applications.As a new strategy for fabricating bending actuators,constructing defect dipole concentration gradient has emerged as an effective strategy for boosting electro-bending displacement,yet achieving reproducibility remains challenging due to the uncontrollable alkali volatilization.Herein we propose a new strategy to fabricate barium-doped(K,Na)NbO3 piezoelectric bending actuators with controllable gradient distribution of highly stable-oriented(VK/Na'-VO··)defect dipoles,achieving a centimeter-level displacement performance of 1.2 cm under±200 V sinusoidal AC excitations.Samples with defect gradient design but lower oxygen vacancy content exhibit larger bending displacement and excellent fatigue stability without leakage conduction,confirming that the defect dipole concentration gradient,rather than oxygen vacancy migration drives the large bending deformation.Experimental analysis combined with phase-field simulations uncovers that the delicate concentration design of-oriented defect dipoles within orthorhombic stripe domains plays crucial roles in controllable and stable displacement output.We validate the feasibility of the bending actuators in piezoelectric haptic feedback and piezoelectric micro-pump applications,providing new insights into the design of piezoceramic actuators.展开更多
Flexoelectricity refers to the link between electrical polarization and strain gradient fields in piezoelectric materials,particularly at the nano-scale.The present investigation aims to comprehensively focus on the s...Flexoelectricity refers to the link between electrical polarization and strain gradient fields in piezoelectric materials,particularly at the nano-scale.The present investigation aims to comprehensively focus on the static bending analysis of a piezoelectric sandwich functionally graded porous(FGP)double-curved shallow nanoshell based on the flexoelectric effect and nonlocal strain gradient theory.Two coefficients that reduce or increase the stiffness of the nanoshell,including nonlocal and length-scale parameters,are considered to change along the nanoshell thickness direction,and three different porosity rules are novel points in this study.The nanoshell structure is placed on a Pasternak elastic foundation and is made up of three separate layers of material.The outermost layers consist of piezoelectric smart material with flexoelectric effects,while the core layer is composed of FGP material.Hamilton’s principle was used in conjunction with a unique refined higher-order shear deformation theory to derive general equilibrium equations that provide more precise outcomes.The Navier and Galerkin-Vlasov methodology is used to get the static bending characteristics of nanoshells that have various boundary conditions.The program’s correctness is assessed by comparison with published dependable findings in specific instances of the model described in the article.In addition,the influence of parameters such as flexoelectric effect,nonlocal and length scale parameters,elastic foundation stiffness coefficient,porosity coefficient,and boundary conditions on the static bending response of the nanoshell is detected and comprehensively studied.The findings of this study have practical implications for the efficient design and control of comparable systems,such as micro-electromechanical and nano-electromechanical devices.展开更多
The relatively insufficient knowledge of the deformation behavior has limited the wide application of the lightest structure material-Mg alloys.Among others,bending behavior is of great importance because it is unavoi...The relatively insufficient knowledge of the deformation behavior has limited the wide application of the lightest structure material-Mg alloys.Among others,bending behavior is of great importance because it is unavoidably involved in various forming processes,such as folding,stamping,etc.The hexagonal close-packed structure makes it even a strong texture-dependent behavior and even hard to capture and predict.In this regard,the bending behaviors are investigated in terms of both experiments and simulations in the current work.Bending samples with longitudinal directions inclined from the transverse direction by different angles have been prepared from an extruded AZ31 plate,respectively.The moment-curvature curves and strain distribution have been recorded in the four-point bending tests assisted with an in-situ digital image correlation(DIC)system.A crystal-plasticity-based bending-specific approach named EVPSC-BEND was applied to bridge the mechanical response to the microstructure evolution and underlying deformation mechanisms.The flow stress,texture,twin volume fraction,stress distribution,and strain distribution evolve differently from sample to sample,manifesting strong texture-dependent bending behaviors.The underlying mechanisms associated with this texture dependency,especially the occurrence of both twinning and detwinning during the monotonic bending,are carefully discussed.Besides,the simulation has been conducted to reveal the moment-inclination angle relation of the investigated AZ31 extruded plate in terms of the polar coordinate,which intuitively shows the texture-dependent behaviors.Specifically,the samples with longitudinal directions parallel to the extruded direction bear the biggest initial yielding moment.展开更多
基金financial supports from the National Natural Science Foundation of China(Nos.52204406 and 52375390)the Science and Technology Program of Hebei Province,China(Nos.E2025203087,E2024203229 and E2023203260)the Key S&T Special Projects of Xingtai City(No.2023ZZ017).
摘要To enhance the bending resistance of bellows,an environmentally friendly electric pulse heat treatment(EPHT)method was used.The strengthening mechanism was systematically studied by microstructure characterization,finite element simulation and bending test.The results showed that during EPHT process,the cross-sectional area of the trough was small,so that the current density was large,which made the temperature of the trough significantly higher than those of other regions.The temperature difference between the peak and the trough was most influenced by frequency.Empirical formulas were derived to predict the temperature and current density of the trough under varying parameters.The dislocation elimination and grain growth of the trough achieved the optimal balance at 800℃and 7 A/mm2,obtaining the best bending resistance.Bellows prepared by general heat treatment process(GHTP)had coarse grains and local high dislocation density areas.In contrast,the grains of EPHT bellows were fine,the dislocations were eliminated completely and uniformly,and the crack propagation path was more tortuous.Compared with GHTP,EPHT significantly reduced the dislocation density and eliminated oxide inclusions.This microstructural optimization altered the crack propagation behavior from simultaneous bidirectional growth(initiating from both high-strain surfaces and wall center)to unidirectional propagation(surface to center)of GHTP,thereby greatly reducing the crack propagation rate.Notably,the fracture mechanism changed from quasi-cleavage to ductile fracture.Compared with GHTP,the number of bending cycles of EPHT bellows increased by about 200%before fracture.
基金funded by Graduate Student Research Innovation Capability Enhancement Project of Jilin Province (No. JJKH20250105BS)the National Natural Science Foundation of China (No. 52201120)
摘要The structure profile of magnesium alloy tube is difficult to control for complex microstructural evolution under the asymmetric loading of tension and compression induced during tube bending.This study investigates the electro-assisted bending of extruded AZ61(Mg-6Al-1Zn)magnesium alloy tubes,with particular focus on the influence of pulsed current on microstructure evolution and plastic deformation mechanisms under varying degrees of deformation.The results indicate that pulsed current increases the fraction of{1012}tensile twins and effectively regulates twin nucleation positions along the tangential cross-sections on both sides of the bending head.The initially disordered twin distribution is transformed into a more ordered arrangement,thereby enhancing radial microstructural uniformity during bending.The thermal and electromagnetic energy generated by the current promotes the alignment or polarization of twins and dislocations along specific directions.This phenomenon suggests that pulsed current can improve the formability of magnesium alloy tubes through distinctive microstructural modifications.These findings offer valuable insights into microstructure control and bending ability enhancement of magnesium alloy tube.
基金financial supports from National Natural Science Foundation of China(Grant Nos.52575321,52375245,and 12572140)。
摘要This study comprehensively investigates the bending behavior of 3D star-shaped auxetic(3D-SAU)metamaterials,which exhibit a distinctive negative Poisson's ratio(NPR)effect along three orthogonal spatial directions.Parametric analysis reveals that the out-of-plane NPR effect is significantly enhanced by increasing the hexagon side length(l),whereas reduced by increasing the offset angle(α)or interlayer spacing(h).Results extracted from experimental and numerical three-point bending tests indicate that auxetic(3D-SAU and 3D-RE)metamaterials exhibit 3.5 times to 10.7 times higher bending compliance than the traditional BCC one,due to their distinct deformation modes under bending loads.Notably,the architecture of the 3D-SAU unit cell,featuring reversely staggered star-shaped frames,facilitates a unique deformation mechanism dominated by rod rotation,thereby ensuring the metamaterial's superior structural compliance under bending loads.Furthermore,the potential application is explored by integrating 3D-SAU metamaterials into morphing airfoils actuated by shape memory alloy(SMA)skins.A functionally-graded design for the unit cell'sα,has been introduced to enable controllable and localized deformation of the airfoil profile.Through a combined experimental and numerical approach,it is found that the 3D-SAU metamaterials not only achieve exceptional deformability but also effectively reduce stress concentration through its tailored compliance.This study establishes a novel design framework for high-performance morphing airfoils that achieves a synergy between large,controllable shape adaptation with inherent impact-resistance for advanced aerospace applications.
摘要To enhance the bending mechanical properties of fiber-reinforced plastics(FRP)and address rapid damage repair under multiple bending loads,an improved shape memory alloy hybrid composite(ISMAHC)was developed by embedding layered orthogonal shape memory alloy(SMA)wires into FRP.Three-point bending and water bath recovery tests were performed on traditional single-layer unidirectional SMA hybrid composites(SMAHC),ISMAHC and FRP.The effects of layered orthogonal SMA configuration on stiffness,strength,and recovery capability were compared and investigated.Results demonstrate that SMA wires form a coupling effect with FRP,increasing the bending modulus.Furthermore,ISMAHC has higher stiffness due to its orthogonal architecture.The water bath recovery tests indicate that SMAHC and ISMAHC possess good deflection recoverability and mechanical property recoverability after multiple bending loadings.The deflection recovery rate of the first bending test is greater than 60%,and that of the second bending test is greater than 30%.Additionally,the bending modulus and bending strength recover more than 30%,with ISMAHC showing superior recoverability.
基金supported by the National Natural Science Foundation of China(Grant Nos.52075423 and U2141214)the Fundamental Research Funds for the Central Universities(Grant Nos.xtr012019004 and zrzd2017027)the National Science and Technology Major Project of China(Grant No.J2019-III-0008-0051).
摘要This research encompasses three-point bending based on artificial neural networks(ANNs)for a simple accurate process design.Uniaxial tensile tests are carried out for 22 steel and aluminum sheet metals with different thicknesses to characterize their mechanical properties,such as the Young’s modulus,yield stress,strength,strain hardening,etc.Approximately 20-30 three-point bending tests are conducted for each sheet metal with different gaps and punch strokes to obtain different bending angles before and after spring-back ranging from 60°to 165°.The angles after spring-back are modeled by an ANN as the output.The inputs for the ANN model include the mechanical properties obtained from uniaxial tensile tests,as well as gap and punch stroke used in three-point bending.The angles after spring-back predicted by the ANN model trained by 22 materials are compared with experimental results to evaluate its performance.The comparison shows that the trained ANN model can precisely predict the angle after spring-back with a maximum error of less than 3.7%.The trained ANN model is also tested for unseen gap and stroke,to design the processing parameters in three-point bending of advanced high-strength steel(DP980)and an aluminum alloy(AA6K21-T4).The application demonstrates that the trained ANN model can design the process parameters with high accuracy even for unseen data.This study shows that the ANN model is strongly suggested to be used in process and tool design/optimization of metal forming processes to achieve high accuracy and generalizability.
基金supported by the National Natural Science Foundation of China(No.52371004,52201144,52071040,U20A20230).
摘要Bending is a crucial operation in the sheet forming of Mg alloys for automotive and aerospace applications.In this work,three kinds of sheets from an AZ31 rolled plate,sheared at 0°(S0),45°(S45),and 90°(S90)to the rolling direction,were subjected to three-point bending tests.In-situ digital image correlation(DIC)system was employed to capture the strain fields.Electron backscatter diffraction(EBSD)was used to examine the through-thickness microstructures.A crystal plasticity finite element method(CPFEM)incorporating twinning and slip mechanisms was developed to simulate the bending deformation.The texture effect on the neutral layer shift and twinning behaviors was systematically investigated in terms of both experiments and simulations.The results show that CPFEM effectively simulated the texturedependent shifting behaviors of neutral layer and the associated twinning behaviors.Particularly,the spatial distributions of neutral layer across the entire bent plates were captured by both DIC and CPFEM.Additionally,some unusual twinning behaviors were analyzed in depth,such as the{10-12}-{10-12}secondary twins in S90,localized twin bands in S0,and the twin traces difference in S45.These findings reveal a close relationship between the neutral layer shift and twinning activity induced by the initial texture and strain levels.This work provides valuable insights into the bending deformation mechanisms of Mg alloys and has important implications for improving their formability and controlling springback.
基金supported by the National Natural Science Foundation of China(No.42072184,41702157)the Science and Technology Cooperation Project of the CNPC-SWPU Innovation Alliance(No.2020CX010302)。
摘要Shale deformation is crucial in various geological processes.To investigate the effect of deformation on pore characteristics for highly compacted shale,the macro tectonic strain and micro pore structure were analyzed in the deeply buried Wufeng-Longmaxi shale of the Eastern Fold Belt of the Sichuan Basin.Despite similarities in their X-ray diffraction mineral compositions,significant differences in pore properties were observed between the shale samples from weak and strong curved synclines.Pore shapes identified from scanning electron microscopy and the covariation between total organic carbon(TOC)content and porosity suggest that organic pores predominantly contribute to total porosity.However,samples from weak-curved synclines exhibit porosities~2%higher than samples from strongcurved synclines,even with similar TOC contents.Compared to the weak-curved syncline samples,the strong-curved syncline samples show a transformation in organic pore morphology from spherical to elliptical with an increasing aspect ratio and reduced dominant pore size from 1-1000 nm to 1-100 nm due to pore collapse in the organic matrix.The porosities simulated using a syncline bending ductile strain model align well with the measured porosities,indicating that the porosity changes were induced by heterogeneous ductile strain during detachment folding.Strain heterogeneity also triggered tectonic stress heterogeneity,causing clockwise rotation of the principal stress orientation from weak to strong curved synclines.This study improves our understanding of the variations in pore system with syncline deformation strain,providing a theoretical basis for subsequent shale hydrocarbon exploration and resource assessment in complex tectonic zones.
基金the National Center of Technology Innovation for Advanced Aviation Equipment Science Foundation,China,the Aeronautical Science Foundation of China(No.2024M047052002)the National Natural Science Foundation of China(Nos.52175328,52105360)+1 种基金the Postgraduate Research and Practice Innovation Program of Jiangsu Province,China(No.KYCX23_0370)funding for this research was provided by the Prince Sattam bin Abdulaziz University(No.PSAU/2024/R/1445)。
摘要Manufacturing sound thin-walled metallic tubes via Free Bending Forming(FBF)technology depends on a geometric relationship involving the eccentricity of the bending die,rotation angle,deformation zone length,and bending radius.This accuracy of relationship relies ideally on the bending die rotating,maintaining tangency with the tube.Nevertheless,if the die deviates from this ideal rotation owing to material properties,the interaction between the die and tube occurs,leading to inaccuracies in the geometric relationship.Thus,investigating the influence of the non-ideal rotation of the bending die on thin-walled metallic tubes during the FBF process is essential.A new theoretical model is proposed to determine and study the forces acting on the tube during non-ideal die rotation,which is divided into bending outer and inner forces.The proposed model examines the force directions in three forms,over-rotation,under-rotation,and ideal rotation,to explain the changes in the internal forces within the cross-section and bending radius of tube.In addition,it determines the unit squeezing force on the tubes during non-ideal rotation.To validate the proposed theoretical model,Finite Element Modeling(FEM)and actual forming experiments were conducted to investigate the influence of forces acting on the tube during non-ideal die rotation and analyze the tube stresses under the three rotation forms.The FEM and experimental results strongly correlate with the theoretical analysis,confirming the accuracy of model in predicting tube behavior under varying bending die conditions.
基金supported by the Deanship of Graduate Studies and Scientific Research,Jazan University,Saudi Arabia(Grant No.JU-202503221-DGSSR-RP-2025).
摘要This paper introduces a novel gradient-enhanced physics-informed neural network(gPINN)framework for analyzing Kirchhoff-Love plate bending under diverse boundary conditions.The approach marks a significant advancement in physicsinformed machine learning by offering three key innovations:(1)a gradient-regularized loss function that enforces the biharmonic equation and boundary constraints concurrently;(2)a modular neural architecture featuring interconnected subnets for transverse and in-plane displacements;(3)an adaptive training algorithm with physics-informed sampling strategies.The proposed technical framework integrates several pioneering elements.It augments the strain energy functional with higher-order gradient terms to accurately capture curvature effects near plate boundaries.Furthermore,it introduces edge-specific penalty functions that automatically accommodate various support conditions,such as clamped,simply supported,and free edges,without requiring geometric remeshing.The network design further integrates dedicated submodules for displacement gradients,utilizing shared weights for mixed partial derivatives critical to the bending moment formulation.Numerical validations across three benchmark cases(complex boundary conditions)highlight the framework’s superiority over traditional PINNs.Notable outcomes include:(I)a 72%average reduction in relative error at boundary transitions(p<0.01);(II)convergence to engineering accuracy(<%error)in 38%fewer iterations;(III)robust generalization to untested boundary condition combinations.The gPINN solutions align closely with finite element benchmarks while eliminating meshing dependencies,demonstrating particular strength in high-stress concentration zones.This study sets a new benchmark for physics-informed deep learning in plate mechanics,offering immediate relevance for designing aerospace components,marine structures,and other thin-walled structures where precise deformation prediction under complex constraints is essential.The gradient enhancement methodology provides a scalable blueprint for applying physics-aware machine learning to other fourth-order boundary value problems in solid mechanics.
基金supported by the National Natural Science Foundation of China(Grant Nos.:52202423,U2268211,and 52475136)the China Postdoctoral Science Foundation(Grant Nos.:2022M712636 and 2023T160546)+1 种基金the Natural Science Foundation of Sichuan Province(Grant No.:2025ZNSFSC0398)the Independent R&D Project of the State Key Laboratory of Traction Power(Grant No.:2023TPL-T14).
摘要Since the view that the localized rail third-order bending mode can cause high-order polygonization(mainly 18-23)of high-speed train wheels was put forward in 2017,many scholars have attempted to link a connection between the localized rail bending modes and wheel polygonization phenomenon and polygonal wheel passing frequency.This paper first establishes a flexible track model considering the structural and parametric characteristics of fasteners,verifies the model by using vehicle tracking test data,then investigates the influence of fastener parameter matching on the localized rail bending modes,and obtains the following conclusions:(1)There is nearly a 1:1 mapping relationship between the localized rail bending modal frequency and polygonal wheel passing(PWP)frequency,which supports that the localized rail bending mode is one of the causes of wheel polygonization.(2)The iron plate of the fastener system plays a role of dynamic vibration absorber in the vehicle-rail coupled system,and the fastener parameters significantly influence the localized rail bending modal vibration.Finally,this paper proposes a design principle of a high-frequency vibration-absorbing fastener,which provides a feasible solution to mitigate the localized rail bending modal vibration and high-order wheel polygonization.Meanwhile,it points out that this measure may induce other high-frequency vibration problems,e.g.,aggravating modal vibration above 800 Hz.Further,this paper proposes a concept of differentiated arrangement of fasteners,suggesting that different high-frequency vibration-absorbing fasteners be installed in different sections of the whole line to make the localized rail bending modal frequency of the whole line disordered,thus disrupting and further mitigating the development of the wheel polygonization.
摘要Percutaneous coronary intervention(PCI)via the transradial route is now standard practice,particularly in elderly patients,owing to its lower bleeding risk and early ambulation.However,agerelated vascular changes such as radial and subclavian tortuosity,elongation,and reduced arterial compliance can pose unique procedural challenges.One such challenge is catheter kinking,which can impede the smooth delivery of stents.
基金supported by Beijing Natural Science Foundation(L233025)。
摘要Functionally graded material(FGM)plates are widely used in various engineering structures owing to their tailor-made mechanical properties,whereas cracked homogeneous plates constitute a canonical setting in fracture mechanics analysis.These two classes of problems respectively embody material non-uniformity and geometric discontinuity,thereby imposing more stringent requirements on numerical methods in terms of high-order field continuity and accurate defect representation.Based on the classical Kirchhoff-Love plate theory,a numerical manifold method(MLS-NMM)incorporating moving least squares(MLS)interpolation is developed for bending analysis of FGM plates and fracture simulation of homogeneous plates with defects.The method constructs an H2-regular approximation with high-order continuous weighting functions and,combined with the separation of mathematical and physical covers,establishes a unified framework that accurately handles material gradients and cracks without mesh reconstruction.For the crack tip,a singular physical cover incorporating the Williams asymptotic field is introduced to achieve local enrichment,enabling the natural capture of displacement discontinuity and stress singularity.Stress intensity factors are extracted using the interaction integral method,and the dimensionless J-integral shows a maximum relative error below 1.2%compared with the reference solution.Numerical results indicate that MLS-NMM exhibits excellent convergence performance:using 676 mathematical nodes,the nondimensional central deflection of both FGM and homogeneous plates agrees with reference solutions with a maximum relative error below 0.81%,and no shear locking occurs.A systematic analysis reveals that for a simply supported on all four edges(SSSS)FGM square plate with a/h=10,the nondimensional central deflection increases by 212%as the gradient index nrises from 0 to 5.For a homogeneous plate containing a central crack with c/a=0.6,the nondimensional central deflection increases by approximately 46%compared with the intact plate.Under weak boundary constraints(e.g.,SFSF),the deformation is markedly amplified,with the deflection reaching more than three times that under strong constraints(SCSC).The proposed method provides an efficient,reconstruction-free numerical tool for high-accuracy bending and fracture analyses of FGM and cracked thin-plate structures.
基金supported by the Natural Science Foundation of Henan(252300420935)Young Backbone Teacher Training Program of Zhengzhou Normal University(QNGG-232300)+1 种基金Zhengzhou Normal University Undergraduate Innovation and Entrepreneurship Training Program Project(DCY2024011)Scientific Research Starting Foundation of Zhengzhou Normal University(2021-702442).
摘要Investigating the deformation behavior of graphene-reinforced composite structures holds significant engineering implications,while the rapid advancement of machine learning has introduced new technical approaches to structural bending analysis.In this study,we investigate the mechanical bending behavior of graphene origami(GOri)-enabled auxetic metamaterial beams using a physics-informed neural network(PINN).GOri-enabled auxetic metamaterials represent an innovative composite system characterized by a negative Poisson’s ratio(NPR)and superior mechanical performance.Here,we propose a composite beam model incorporating the modified coupled stress theory(MCST)and employing the PINN method to solve higher-order bending governing equations.Compared to the analytical solution,the accuracy and effectiveness of the PINN framework as a meshless solver for higher-order partial differential equations are verified.The bending properties of metamaterial beams are studied by considering the mechanical properties and size effect of metamaterials.It was found that the length scale parameters,more graphene platelets,and a higher folding degree have the best reinforcement effect on composite beams.By systematically varying the GOri folding parameters and graphene content,we demonstrate the robustness of the PINN methodology in resolving microscale beam bending phenomena,particularly in capturing complex size-effect interactions.
基金supported in part by the Guangdong Introducing Innovative and Entrepreneurial Teams of“the Pearl River Talent Recruitment Program”(No.2019ZT08X340)the National Natural Science Foundation of China(No.62475052)。
摘要The stimulated Brillouin scattering(SBS)of heavy germania-doped few-mode fiber(HG-FMF)up to 98 mol%and its dependence on temperature,strain,and bending are studied in this paper,respectively.Two widely located individual Brillouin gain spectra(BGS),whose central peaks are 8.151 GHz and 8.862 GHz,are found in HG-FMF,respectively.These two BGS are generated by the interaction between the fundamental and higher-order acoustic wave modes,which match well with the numerical simulation.The heavy germania-doping induced a large refractive index difference between the core and cladding that strongly confined the optical field in the fiber core and modified its Brillouin parameter.This fact also leads to the bending resistance of HG-FMF,in the bending radii from 0.3 cm to 2 cm,in contrast to traditional FMFs,and suppressed the temperature and strain sensitivity of the two BGS to 213 k Hz/℃,342 k Hz/℃and 20.5 k Hz/μɛ,21.4 k Hz/μɛ,respectively.These advances of HG-FMF could be potentially used for bending-resistant distributed multi-parameter sensing.
基金Project supported by the National Natural Science Foundation of China(No.52278531)the Education Department of Shaanxi Provincial Government of China(No.24JR093)the Ningxia Natural Science Foundation of China(No.2024AAC04004)。
摘要The bending behavior of microbeams in micro-nano devices exhibits significant size effects,making accurate prediction of their mechanical behaviors crucial for device reliability.This paper employs the modified couple stress theory(MCST)and derives the governing equations for the Reddy beam theory(RBT)via the principle of virtual work.By considering the load equivalence,the analytical solutions for the bending problem are derived and expressed as the functional relations based on the Euler-Bernoulli beam model.Once the Euler-Bernoulli beam solution is obtained,the exact solution for the corresponding Reddy beam can be directly determined through these functional relations and boundary conditions.Analytical solutions for the doubly simply-supported(S-S),clamped-free(C-F),and clamped-clamped(C-C)boundary conditions are derived and validated through comparison with the results of previous studies.This study clarifies the analytical relationship between the two beam theories at the micro-scale,enabling exact mechanical solutions for higher-order shear deformation beams without solving complex higher-order governing equations.
基金supported by the National Natural Science Foundation of China(Nos.52272362,U20A20275)the Technology Innovation and Application Development Special Key Project of Chongqing City,China(No.CSTB2022TIAD-KPX0035).
摘要The bending collapse and energy absorption of 7003 aluminum alloy bumper beams under four aging conditions(pre-aging,under-aging,peak-aging,and over-aging)were investigated through three-point bending tests.Microstructural characterization was performed using scanning electron microscopy and transmission electron microscopy.Based on the Swift−Hockett−Sherby constitutive model combined with the Gurson−Tvergaard−Needleman damage model,the plastic response and fracture behavior of the 7003 aluminum alloy under uniaxial tension and three-point bending were accurately predicted.The results showed that the peak bending force of the beams was proportional to the strength under different aging states,while stress triaxiality governed the cracking failure.Pre-aged and under-aged beams resisted cracking until reaching 250 mm displacement due to stress transition from tensile to compression on the bottom surface.The under-aged beam exhibited optimal energy absorption(7.86 kJ)and a higher peak force(38.75 kN).
基金financially supported by the National Natural Science Foundation of China(Nos.62474107 and 52032012)the National Key Research and Development Program of China(Nos.2022YFA1205300 and 2022YFA1205304).
摘要Piezoelectric ceramic bending actuators play a pivotal role in various high-tech applications.As a new strategy for fabricating bending actuators,constructing defect dipole concentration gradient has emerged as an effective strategy for boosting electro-bending displacement,yet achieving reproducibility remains challenging due to the uncontrollable alkali volatilization.Herein we propose a new strategy to fabricate barium-doped(K,Na)NbO3 piezoelectric bending actuators with controllable gradient distribution of highly stable-oriented(VK/Na'-VO··)defect dipoles,achieving a centimeter-level displacement performance of 1.2 cm under±200 V sinusoidal AC excitations.Samples with defect gradient design but lower oxygen vacancy content exhibit larger bending displacement and excellent fatigue stability without leakage conduction,confirming that the defect dipole concentration gradient,rather than oxygen vacancy migration drives the large bending deformation.Experimental analysis combined with phase-field simulations uncovers that the delicate concentration design of-oriented defect dipoles within orthorhombic stripe domains plays crucial roles in controllable and stable displacement output.We validate the feasibility of the bending actuators in piezoelectric haptic feedback and piezoelectric micro-pump applications,providing new insights into the design of piezoceramic actuators.
基金This work was supported by the Le Quy Don Technical University Research Fund(Grant No.23.1.11).
摘要Flexoelectricity refers to the link between electrical polarization and strain gradient fields in piezoelectric materials,particularly at the nano-scale.The present investigation aims to comprehensively focus on the static bending analysis of a piezoelectric sandwich functionally graded porous(FGP)double-curved shallow nanoshell based on the flexoelectric effect and nonlocal strain gradient theory.Two coefficients that reduce or increase the stiffness of the nanoshell,including nonlocal and length-scale parameters,are considered to change along the nanoshell thickness direction,and three different porosity rules are novel points in this study.The nanoshell structure is placed on a Pasternak elastic foundation and is made up of three separate layers of material.The outermost layers consist of piezoelectric smart material with flexoelectric effects,while the core layer is composed of FGP material.Hamilton’s principle was used in conjunction with a unique refined higher-order shear deformation theory to derive general equilibrium equations that provide more precise outcomes.The Navier and Galerkin-Vlasov methodology is used to get the static bending characteristics of nanoshells that have various boundary conditions.The program’s correctness is assessed by comparison with published dependable findings in specific instances of the model described in the article.In addition,the influence of parameters such as flexoelectric effect,nonlocal and length scale parameters,elastic foundation stiffness coefficient,porosity coefficient,and boundary conditions on the static bending response of the nanoshell is detected and comprehensively studied.The findings of this study have practical implications for the efficient design and control of comparable systems,such as micro-electromechanical and nano-electromechanical devices.
基金supported by State Key Laboratory for Geo Mechanics and Deep Underground Engineering,China University of Mining&Technology,Beijing(XD2021021)the National Natural Science Foundation of China(Nos.52075325,51975365,and 52011540403)。
摘要The relatively insufficient knowledge of the deformation behavior has limited the wide application of the lightest structure material-Mg alloys.Among others,bending behavior is of great importance because it is unavoidably involved in various forming processes,such as folding,stamping,etc.The hexagonal close-packed structure makes it even a strong texture-dependent behavior and even hard to capture and predict.In this regard,the bending behaviors are investigated in terms of both experiments and simulations in the current work.Bending samples with longitudinal directions inclined from the transverse direction by different angles have been prepared from an extruded AZ31 plate,respectively.The moment-curvature curves and strain distribution have been recorded in the four-point bending tests assisted with an in-situ digital image correlation(DIC)system.A crystal-plasticity-based bending-specific approach named EVPSC-BEND was applied to bridge the mechanical response to the microstructure evolution and underlying deformation mechanisms.The flow stress,texture,twin volume fraction,stress distribution,and strain distribution evolve differently from sample to sample,manifesting strong texture-dependent bending behaviors.The underlying mechanisms associated with this texture dependency,especially the occurrence of both twinning and detwinning during the monotonic bending,are carefully discussed.Besides,the simulation has been conducted to reveal the moment-inclination angle relation of the investigated AZ31 extruded plate in terms of the polar coordinate,which intuitively shows the texture-dependent behaviors.Specifically,the samples with longitudinal directions parallel to the extruded direction bear the biggest initial yielding moment.