Global Bending Research Articles

Bending and twisting with a pinch: Shape morphing of creased sheets

In this letter, we introduce a unique behavior seen in creased sheets where localized changes in the folding (i.e., a pinch) result in global bending and twisting deformations. Using isometric deformation theory, we identify the connections between pinching, crease curvature, and crease torsion that begin to explain the shape-morphing behavior. Given the limitations of isometric deformations, we expand our understanding of the behavior using a mechanics-based bar and hinge model of creased sheets, where the sheet is allowed to stretch. With this tool, we found that the increase in crease curvature and torsion due to pinching are proportional to the curvature of the crease before folding and that curved creases facilitate the bending and twisting. Additionally, we explored the bending and twisting of sheets with more than one crease. We found that sheets with an even number of creases generate more intense twisting than those with an odd number of creases and experience twisting even when the creases are straight. The number of creases had little effect on the pinch-induced bending of the origami. The stiffness of the sheets had little effect on the amount of bending and twisting, but greater spacing between the creases resulted in more bending with little effect on the twisting. Based on these results, we created a framework to design crease patterns to have desirable bending and twisting that can be coupled or not, and demonstrated this programmability with simulations and by pinching physical prototypes. Our findings enable shape morphing of creased sheets with a low-complexity input and a versatile output.

Longitudinal bending of corrugated sandwich panels with cores of various shapes

The mechanical response of aluminium corrugated sandwich panels with cores of different shapes subjected to longitudinal three-point bending is investigated experimentally and numerically in this paper. The shapes of the core are sinusoid, triangle, trapezoid, and rectangle, respectively. The experimental and simulated results match well with each other. Subsequently, numerical models with specific boundary conditions are developed to simulate the corrugate sandwich panels with an infinite number of core cells. Parametric studies are conducted using these numerical models. The effects of core web thickness, core length, and corrugation angle are investigated numerically. Two deformation modes (Mode I and Mode II) are observed. The panels that deform in Mode I have a larger indentation area and minor global bending. Mode I tends to happen in panels with weaker core webs. Finally, the multiobjective Bayesian optimization method based on lower confidence bound (LCB) criterion is adopted to optimize the geometry of trapezoidal corrugated sandwich panels to improve the specific energy absorption (SEA) and reduce the intrusion depth during the bending.

Competition between Mullins and curvature effects in the wrinkling of stretched soft shells

A highly stretched hyperelastic shell exhibits a coupling behavior of local wrinkling and global bending within the stability boundary, and curvature resists and can even suppress surface wrinkles beyond a critical threshold. Here, we report a novel phenomenon that smooth surface maintains upon stretching a soft shell, while wrinkles emerge upon unloading, which implies a nonlinear interplay between curvature and Mullins (stress softening and residual strain) effects in the entire loading–unloading cycle. To quantitatively account for such material damage (Mullins effect) and explore the underlying mechanism, we develop a finite-strain pseudo-elastic shell model that can predict the entire post-buckling morphology evolution. Results reveal three representative scenarios of morphology evolution of stretched soft shells. For shells within a certain range of aspect ratios and curvatures, no wrinkle appears upon loading while wrinkling occurs during the unloading process. For shells with smaller curvature, wrinkles exist during loading and unloading, while the shells with larger curvature remain constantly smooth in the loading–unloading process. The Mullins effect advances wrinkle formation, while curvature resists instability occurrence. Understanding such coupling effects between material and curvature on morphological evolution is critical for wrinkle-tunable design of functional surfaces.

Bending behavior of 3D printed mechanically robust tubular lattice metamaterials

Tubular lattice structures have gained tremendous attention due to their lightweight and excellent mechanical properties. In this work, we designed a new type of tubular lattice architecture by rolling up planar lattice structures with a negative Poisson’s ratio, and then fabricated samples using a material jetting 3D printing technique. We investigated their bending behavior under large deformation using a combined experimental and numerical approach. It was found that the proposed auxetic tubular lattice (ATL) structure exhibits a more compliant behavior, and the ductility increased by up to 85.4% compared to that of a conventional diamond tubular lattice (DTL) structure. Meanwhile, the ATL structure is characterized by a local bending behavior due to the auxetic effect, while the DTL structure is featured with global bending mode. Finite element simulations further reveal that the stress on the ATL structure distributes locally around the indenter. In contrast, stress on the DTL structure distributes much more uniformly across the span. As such, the ATL structures exhibit excellent global stability compared to the DTL structure. Our parametric study shows that bending stiffness, maximum load, and ductility of the proposed ATL structure are mainly controlled by beam depth, due to its large exponential contribution to the moment of inertia. Increasing beam depth leads to a more desirable ductility than increasing beam thickness. The beam amplitude and tubular curvature have minor effects on the bending performance compared to other geometric parameters. The findings reported in this work can guide designing and optimizing mechanically robust tubular lattice metamaterials for applications in tissue engineering, biomedical devices, and robotics engineering.

Full scale structural, mechanical and dynamical properties of HIV-1 liposomes.

Enveloped viruses are enclosed by a lipid membrane inside of which are all of the components necessary for the virus life cycle; viral proteins, the viral genome and metabolites. Viral envelopes are lipid bilayers that adopt morphologies ranging from spheres to tubes. The envelope is derived from the host cell during viral replication. Thus, the composition of the bilayer depends on the complex constitution of lipids from the host-cell’s organelle(s) where assembly and/or budding of the viral particle occurs. Here, molecular dynamics (MD) simulations of authentic, asymmetric HIV-1 liposomes are used to derive a unique level of resolution of its full-scale structure, mechanics and dynamics. Analysis of the structural properties reveal the distribution of thicknesses of the bilayers over the entire liposome as well as its global fluctuations. Moreover, full-scale mechanical analyses are employed to derive the global bending rigidity of HIV-1 liposomes. Finally, dynamical properties of the lipid molecules reveal important relationships between their 3D diffusion, the location of lipid-rafts and the asymmetrical composition of the envelope. Overall, our simulations reveal complex relationships between the rich lipid composition of the HIV-1 liposome and its structural, mechanical and dynamical properties with critical consequences to different stages of HIV-1’s life cycle.

Experimental and numerical simulation of dynamic response of U-type corrugated sandwich panels under low-velocity impact

U-type corrugated sandwich panels exhibit excellent mechanical properties, and their application in the design of ship structures meets the requirements of the future development of ship and ocean engineering structures. In this study, the dynamic response of U-type corrugated sandwich panels under low-velocity impact using a drop-weight apparatus at the impact velocity of 4.43 m/s was measured and compared with finite element predictions. Moreover, the effect of impact velocity and location were evaluated. Both the experimental and simulation results indicated that the deformation modes of the front face were localized indentation, membrane stretching and wrinkle formation around the contact area between the front face and indenter, however the deformation modes of the corrugated cores were indentation and global bending. The dynamic responses of the sandwich panel determined through experiment and numerical simulation were consistent, revealing that the numerical simulation demonstrated reasonable accuracy. When the impact velocity increased from 2.8 to 4.85 m/s, the loading process and deformation modes of the sandwich panel were mainly influenced by the properties of the structure. The transverse impact resistance performance of the U-type corrugated sandwich panel was better than the longitudinal performance, owing to the higher number of core cells involved in deformation and energy absorption.

Nonlinear Stability Analysis of Elastic High Strength Steel Tubes Under Global Bending

A recent computational study has found unique zones of stability behaviour in elastic High-strength steel tubes under global bending with different geometrical lengths. A situation under which the most compressed fiber approaches the buckling stress for uniform axial compression is the initial estimation of elastic buckling strength in bending. Cylinders with sufficient length develop a fully developed ovalization of the cross-section and fail by local buckling around the Brazier prediction. Under global bending regimes, typical buckles are fairly modest and extend across a very tiny region, accompanied by global bending extending the crucial value. The situation under which the major compressed fiber approaches the buckling stress for compression bending is the initial estimate of the elastic buckling strength in bending. In this study, the nonlinear behavior of short to long tubes under global bending is studied, with specific and different dimensions, radius-to-thickness ratios, and boundary conditions according to Europe an Standard 1993-1-6. Both the crucial buckling Eigenmode and the geometrically nonlinear elastic analysis are investigated. Because of a buckling stress state dominated by local harmony bending, it is confirmed that the cylinder length takes part in a crucial part in finding this behavior. A failure behavior of this type of material is then going to be investigated.

Elastic-plastic Buckling Analysis of Q690 High Strength Steel Tubes Under Global Bending

In recent years, high-strength steel has been used extensively for infrastructures because of its many advantages, such as its ductility and strain-hardening properties, which are inferior to those of ordinary structural steel, and the small dimensions of the structural elements, which lead to greater freedom and elegance in design, resulting in lighter structures. In practice, imperfections such as residual stresses due to the welding process and pre-buckling mode imperfections are inevitable in cylindrical structures made of high-strength steel. A small imperfection amplitude can lead to a disproportionate reduction in buckling strength. Therefore, imperfection sensitivity should be considered when studying the buckling behaviour of the shell. The influence of the combined residual stress and pre-buckling mode imperfection on the buckling behaviour of Q690 high strength steel cylindrical shell under global bending has not yet been investigated and described for all dimensions. In this paper, the combined imperfections influences on the buckling behaviour of high-strength steel cylindrical shell in global bending in the elastic-plastic range are investigated. Using the ABAQUS fine elements software, perfect cylinders with a constant length to thickness ratio equal to 7 and a radius to thickness ratio in the range 10≤ r/t ≤700 were considered to perform the linear bifurcation analysis (LBA) and the geometric nonlinear analysis (GNA). The non-linear analysis with imperfections (GNIA) and the geometric and material non-linear analysis with imperfections (GMNIA) were then performed considering imperfection amplitudes between 0.01 and 2 to derive the critical buckling loads known as bifurcation point for the models with different aspect ratio. The influences of the combined imperfections show that moderately and very thin cylinders are very sensitive to the increase of the pre-buckling mode imperfection amplitude and their buckling strength is insensitive to plasticity. For thick cylinders, the effect of plasticity is more consistent, while the buckling strength is not significantly affected by the increase in pre-buckling mode imperfection amplitude. The main objective is to predict the buckling sensitivity of cylinders under the influence of combined residual stress and pre-buckling mode imperfection. The obtained results, comments and conclusions intend to allow for safer.

Towards Realistic Vibration Testing of Large Floor Batteries for Battery Electric Vehicles (BEV)

This contribution shows an analysis of vibration measurement on large floor-mounted traction batteries of Battery Electric Vehicles (BEV). The focus lies on the requirements for a realistic replication of the mechanical environments in a testing laboratory. Especially the analysis on global bending transfer functions and local corner bending coherence indicate that neither a fully stiff fixation of the battery nor a completely independent movement on the four corners yields a realistic and conservative test scenario. The contribution will further show what implication these findings have on future vibration & shock testing equipment for large traction batteries. Additionally, it will cover an outlook on how vibration behavior of highly integrated approaches (cell2car) changes the mechanical loads on the cells.

Paper tube-guided blast response of sandwich panels with auxetic re-entrant and regular hexagonal honeycomb cores – An experimental study

Auxetic honeycomb structures have drawn increasing attention for impact/blast protection purposes owing to their superior indentation resistance and energy absorption capability. However, few comparative study on the blast performance among sandwich structures with different auxetic and non-auxetic cores has been performed to date. In this paper, the dynamic behaviors of metallic sandwich panels with auxetic re-entrant and regular hexagonal honeycomb cores (i.e. RHSPs and HHSPs) under the paper tube-guided explosions were investigated by a series of blast tests. The failure modes and underlying mechanisms of the target panels with different core relative densities under different impulse levels were classified and analyzed in detail. The panel blast resistance was evaluated by means of the back-face maximum permanent deflections, introducing the testing results of double arrowhead honeycomb sandwich panels (DAHSPs) in a separate paper. It indicates that the introduction of the paper tube achieved the concentration of shock energy, thus aggravating the panel central damage levels remarkably. For the RHSPs with NPR effect, the predominated failure modes of front faces transitioned essentially from the complete petal-like tearing to a local inner dome as the blast impulse decreased. The ones for the back faces ranged from partial tearing to pure global bending deformation, while the core failure modes tuned from central crushing and peripheral buckling to global compression deformation with central shrinkage and boundary adduction. Relative to the RHSPs, the equivalent HHSPs with a higher compressive strength were less insensitive to the blast intensity. Within the scope of present study, the DAHSPs could experience lower back face deflections than those of RHSPs regardless of core relative density. The auxetic honeycomb sandwich panels not always exhibited better over the non-auxetic HHSPs, which depended greatly on the blast impulse and core density level. This comparative research provides a useful reference for the auxetic sandwich honeycomb core design in protection applications.

A New Stress Intensity Factor Solution Based on the Response Surface Method for Nozzle Corner Cracks in Nuclear Reactor for Thermal Energy Generation

As considered carbon-free, the use of nuclear energy for thermal energy generation may expand in the future, with the guarantee of safe operation of the nuclear reactor. In a nuclear reactor pressure vessel (RPV), the nozzle area is an important part of the safe operation. It bears internal pressure, axial force, and overall moment, and at the same time bears higher stress than the rest of the vessel. To assess the integrity of the nozzle structure with a crack under combined load, an accurate solution of stress intensity factors (SIF) along the crack front is necessary. To obtain the SIF, this paper proposes a solution method that uses the stress on the crack surface and the response surface method to fit the stress under the framework of the linear superposition technique. This method is the first choice to determine a series of influence coefficients under unit pressure load. Then, one can estimate the SIFs by superposition method for an arbitrary stress distribution resulted from combined loads. The proposed solution is verified for a typical RPV with cracks under internal pressure, axial force, and global bending moment. The results reveal that the proposed solution is in good agreement with the existing solutions under internal pressure. Therefore, it can be obtained that this solution can be effectively used for the structural integrity assessment of RPV with nozzle corner cracks.

Influences on the structural response of beams in drop tower experiments

AbstractDrop tower tests on beam specimens were carried out to evaluate the influence of different geometric features and different loading velocities on the beams' response. Tested geometric characteristics are stirrup reinforcement in addition to longitudinal reinforcement, and notches. The goal is to quantify the differences in the global behavior and the amount of strains and strain rates measured at different positions on the reinforcement. This gives an insight into strain distributions along the rebars from which bond stresses can be derived. It can be stated that stirrup reinforcement kept the specimens together and thus increased the impact resistance. That was seen in the deflection and acceleration measurements, but it was also suggested by strain measurements, especially looking at residual strains. The maximum strains are generally more affected by global bending of the specimens than by the formation of a localized punching cone, which was the main failure mode.

Limit load for cylinders with axial internal surface cracks under combined internal pressure and global bending moment

The global and local limit loads for cylinders with axial internal surface cracks under combined internal pressure and global bending moment are investigated using the elastic-perfectly plastic finite element (FE) method. An ellipse function is recommended to describe the relationship between the normalised global limit pressure and normalised global limit bending moment. The predictions using the ellipse function are conservative compared with the global FE results except for the cases with bending moment dominance, where the predictions may be slightly non-conservative. The investigation shows that the local limit load FE results can be well described by the local limit load model recommended by Lei and the predictions are all reasonably conservative except for cases with very long and deep cracks. Further work is required to validate the recommended global and local limit load solutions for J predictions when they are used in the reference stress J scheme.

Dynamic responses of metal foam sandwich beams to repeated impacts

The phenomena of repeated impacts are very common, especial in the field of ship and ocean engineering. When the ship structures suffering from repeated impact loadings, the deformation and damages will accumulate, leading to failure even damage of the structures, which may cause serious accident. In order to study the dynamic behaviors of metal foam sandwich beams (MFSBs) under repeated impact loadings, the nonlinear finite element model was established based on the material model of crushable foam by using Abaqus-Explicit, and the approach to achieve repeated impacts in the software was proposed. The accuracy of the numerical simulation was verified by comparing the permanent deflections of front and back face sheets. Based on the results of the numerical simulations, the deformation modes, loading and unloading process as well as the energy absorption behavior of the MFSBs under repeated impacts were analyzed. Results show that during repeated impacts, the deformation of the MFSBs is accumulated gradually, the front face sheet mainly experiences global bending and local indentation, and the metal foam core suffers from local compression, while the back face sheet is subjected to global bending. During the repeated impacts, the loading and unloading stiffness increases with the impact number. The energy absorption of front face is larger than that of back face and metal foam core in all the impacts. As the impact number increases, the energy absorbed by front face sheet and foam core declines gradually, while that of the back face sheet increases, approaching a constant value. The plastic deformation energy of the MFSBs decreases with the impact number, on the opposite, the rebound energy of the MFSBs increases gradually with the impact number, while both of them trends to be stable. The proposed finite element method can be applied to accurately predict the dynamic responses of the MFSBs suffering from repeated impact loadings, and provide technical supports for the anti-impact design of metal foam sandwich structures.

Multi-scale analysis of the flexural behaviour of 3D printed cellular polymer materials: Comparison between morphing and sandwich beams

Cellular materials with tailorable properties are increasingly being used as a controllable morphing mechanism in airfoils. Nonetheless, the flexural properties of this mechanism change depending on the configuration. Thus, the aim of this paper is to identify and analyse parameters tailoring these properties. A multi-scale analysis that models reliably the behaviour of 3D printed structures is developed. Three scales are considered. The microscopic scale, where the properties of the 3D-printed material are measured. The mesoscopic scale, where mechanical properties of four different patterns, selected for their current use in morphing applications, are estimated via numerical homogenisation. The macroscopic scale, where the global bending behaviour of cellular beams is studied. Then, the mechanical behaviour of cantilever cellular beams is studied while varying their skin rigidity. Results indicate that the skin rigidity is a critical parameter tailoring the core’s behaviour. Rigid skins force the morphing airfoil to behave like a sandwich structure, while compliant skins induce a more complex behaviour.

Non-linear dynamics of hydrodynamic tori as a model of oscillations and bending waves in astrophysical discs

ABSTRACT Understanding oscillations and waves in astrophysical fluid bodies helps to elucidate their observed variability and the underlying physical mechanisms. Indeed, global oscillations and bending modes of accretion discs or tori may be relevant to quasi-periodicity and warped structures around compact objects. While most studies rely on linear theory, observationally significant, non-linear dynamics is still poorly understood, especially in Keplerian discs for which resonances typically demand a separate treatment. In this work, we introduce a novel analytical model which exactly solves the ideal, compressible fluid equations for a non-self-gravitating elliptical cylinder within a local shearing sheet. The aspect ratio of the ring is an adjustable parameter, allowing a continuum of models ranging from a torus of circular cross-section to a thin ring. We restrict attention to flow fields which are a linear function of the coordinates, capturing the lowest order global motions and reducing the dynamics to a set of coupled ordinary differential equations (ODEs). This system acts as a framework for exploring a rich range of hydrodynamic phenomena in both the large amplitude and Keplerian regimes. We demonstrate the connection between tilting tori and warped discs within this model, showing that the linear modes of the ring correspond to oppositely precessing global bending modes. These are further confirmed within a numerical grid based simulation. Crucially, the ODE system developed here allows for a more tractable investigation of non-linear dynamics. This will be demonstrated in a subsequent paper which evidences mode coupling between warping and vertical motions in thin tilted rings.

Fatigue behavior of steel fiber reinforced concrete composite girder under high cycle negative bending action

Tensile concrete crack is a critical factor in the negative flexural region of a steel–concrete composite girder, which could influence the entire structural safety and durability dramatically. The steel fiber reinforced concrete (SFRC) has been utilized for constraining these cracks because of its good tensile performance and low cost in practice. But the practical application of SFRC is still hindered by the unclear fatigue performance of SFRC composite girder. To this end, four 3.3 m-long composite girder tests were executed for investigating the static and cyclic effects of SFRC and connector arrangement. About 3 million load cycles with a monolithic ultimate loading process were applied on each specimen. Generally, the fatigue load cycles in tests resulted in about 10–30% reduction of girders’ global bending stiffness without interlay bonding, and the effect of SFRC on it was not obvious. Even though there were more fatigue load induced cracks found on SFRC slabs than on the normal concrete slabs during loading, the SFRC crack width was smaller. Moreover, the steel–concrete interlayer slip development was found to be slower in SFRC composite girders, while arranging stud connectors in groups resulted in faster slip development. In addition, the test simulation and parametric analysis with material damage plasticity models were carried out, which showed a higher longitudinal reinforcement ratio in SFRC could further reduce fatigue damage on concrete.

Elastic-plastic buckling analysis of stiffened panel subjected to global bending in forming process

A new method has been proposed in this study for the elastic-plastic buckling analysis of stiffened panels under global bending. In this method, a simplified model of the stiffened panels has been built with the application of two theories of plasticity, the incremental theory (IT) and the deformation theory (DT). The effect of transverse shear deformation through the stiffener thickness has been considered using the Mindlin-Reissner plate theory. The governing differential equations have been solved by the differential quadrature (DQ) method and an iteration process has been adopted due to the non-linearity of material properties in the elastic-plastic buckling analysis. Non-linear finite element (FE) modelling of elastic-plastic buckling analysis has been carried out, and the FE results are between those based on DT and IT in general. When the reciprocal of strain hardening exponent mt increases to 20, the FE results are in a good agreement with DT results. Based on the proposed method and FE simulations, the effect of geometric parameters of stiffened panels (stiffener thickness to height ratio, stiffened panel length to height ratio, width to height ratio, and skin thickness to stiffener thickness ratio) on buckling behaviour in the elastic-plastic region has been investigated and discussed. The proposed method provides an efficient way for parameter optimisation in the structure design of stiffened panels for the aerospace applications.

On the structural parameters of honeycomb-core sandwich panels against low-velocity impact

This paper presents a combined experimental and numerical study on the low-velocity impact behavior of honeycomb-core sandwich panels with different structural parameters, including facesheet thickness, core height, honeycomb cell size, and cell wall thickness. Impact tests were conducted at four different energies using a drop-weight impact facility, and the deformation and damage characteristics of the tested sandwich panels were analyzed by microscopic X-ray computed tomography. The experimental results revealed two distinct failure modes of sandwich panels: namely mode A, with localized damage in both facesheets and core, which is dominated by indentation; and mode B, which is characterized by global bending deflection of the facesheets and overall core crushing. It was found that a sandwich panel with thin facesheets and a high-density honeycomb core (e.g. with a small cell size and/or a thick cell wall) tended to fail in mode A, but core height did not influence the failure mechanism notably. Furthermore, finite element modeling was carried out to gain further understanding of the effects of these structural parameters. The perforation resistance and energy absorption capacity were significantly enhanced with increasing facesheet thickness. Whereas reducing the cell size and/or thickening the cell wall resulted in lower perforation resistance. When the total thickness of facesheets remained a constant, the impact behavior of the sandwich structure could be optimized by controlling the thickness ratio of the front to back facesheets. Finally, cost efficiency analysis was performed to achieve a rational design of the sandwich structure considering both the impact performance and cost.

Seismic responses of hyperbolic cooling towers under horizontal and vertical earthquake

Following the dynamic property analysis and elaboration, linear response spectrum analysis (RSA) and response history analysis (RHA) were conducted on a representative hyperbolic cooling towers (HCT) in present study. The seismic responses in tower shell were illustrated in detail, including the internal force amplitude, modal contribution, influence from damping ratio, comparison of results got from RSA and RHA and especially the latitude distributions of internal forces. The results show that the eigenmodes could be classified in a new method into four types according to their mode shapes and only the lateral bending modes and vertical stretching modes are meaningful for horizontal and vertical earthquake correspondingly. The bending modes and seismic deformation display the same feature which is global lateral bending accompanied by minute circular flow displacement of section. This feature also decides the latitude distributions of internal forces as sine or cosine. Moreover, the following method is also proposed for approximate estimation of internal force amplitudes without time-consuming response history analysis: getting the response spectrums of the selected ground accelerations and then comparing values of response spectrums at the natural period of first lateral bending mode because it is always prime dominant for horizontal seismic responses.