Stiffness Of Sheets Research Articles

Triangular graphene nanosheets, structures with extraordinary bending behavior.

Sometimes, manipulating the geometry or creating a defect can help the engineering of the nanostructured properties, such as increasing the frequency sensitivity of graphene nanosheets as a mass sensor by changing the geometry of the structure in a triangular shape and also by creating a vacancy or making nanodiodes in a triangular shape, which restricts the flow of heat in one direction and expands it in another direction. Then, the mechanical properties of the triangular geometry of graphene nanosheets have an excellent value for future devices. The results of the molecular dynamics study can illustrate the mechanical properties of graphene sheets well, which is particularly important. In this study, using molecular dynamics (MD) simulation, the bending stiffness of triangular graphene sheets was investigated to present a broader view of engineering applications of graphene sheets. Analyzing stress-displacement results of triangular graphene sheets in both zigzag and armchair directions under bending load reveals the effect of the directions of sheets on their bending stiffness. Also, comparing the bending stiffness of pristine and defective sheets showed that bending stiffness was decreased when an atom was removed from the middle of a sheet and made a single vacancy defected sheet. Obtained results suggest that triangular graphene nanosheets with higher bending stiffness, compared to rectangular sheets with the same number of atoms, are better for applications requiring higher bending properties, such as nanoelectromechanical devices. The reported results of this work provide an overall viewpoint concerning the geometry and defect effects on the graphene nanosheets' mechanical properties. The bending stiffness of triangular sheets was 20 and 10 times that of intrinsic and defective rectangular sheets, respectively.

Mesh Layer Jamming to Cover and Secure Curved Surfaces without Wrinkles

Layer jamming technologies, which can alter the stiffness of layered sheets enveloped in an elastic bag via internal vacuum pressure, have typically been used for wearable robots. However, wrinkles on the layer jamming element covering the body impair the feeling of wear and are undesirable. Aligning curved surfaces using sheets without wrinkling requires the sheets to be sufficiently elastic, which reduces the stiffness when used for layer jamming. Mesh sheets (i.e., woven fabrics) cannot elongate along the fibers; however, they can elongate and contract in the diagonal direction by changing their shape. This study proposes using mesh sheets for layer jamming and analytically and experimentally demonstrates their ability to fit curved surfaces without wrinkling. The layer jamming element using mesh sheets changes the bending stiffness in proportion to the internal vacuum pressure and the number of sheets, as in conventional layer jamming. The simple structure and flexibility of the mesh layer jamming are not only suitable for fixing a body or fragile objects but also extend the range of applications using layer jamming technologies. This study also provides a foundation for investigating the wrinkle formation associated with curved surface deformation unique to flexible robots.

Buckling and Wrinkling of Sandwich Structures Reinforced by Functionally Graded Carbon Nanotubes

Soft-core sandwich structures subjected to coplanar compression loading might exhibit wrinkling behaviors, which will reduce significantly the support capability of the structure. In order to prevent the wrinkling behaviors of sandwich structures, this work attempts to improve stiffness of face sheets reinforced by carbon nanotubes (CNTs). To achieve such a goal, the following work is to be required. First, an equivalent single-layer model will be proposed to accurately analyze the wrinkling behaviors of sandwich structures because only layerwise models possess the capability to accurately predict wrinkling behaviors of sandwich structures, but these models are often computationally expensive. Second, the influence of distributions of the CNTs through thickness on the buckling and wrinkling behaviors for the sandwich beams will be investigated in detail. Moreover, the translation mechanism between the buckling deformation and the wrinkling deformation has been also explored. The proposed model has been verified by using the quasi three-dimensional (3D) elasticity solutions and the 3D finite-element results (3D-FEM). Third, by selecting the proper distributions of the CNTs through the thickness of sandwich structures, the wrinkling behaviors of sandwich structures can be effectively prevented. Thus, a scheme resisting wrinkling deformation of sandwich structures has been proposed, which can provide a reference for other investigators.

Mechanical Behavior of Blisters Spontaneously Formed by Multilayer 2D Materials

AbstractBlisters can form spontaneously when transferring 2D materials on a substrate because of the small molecules trapped at the interface. Though extensive works have revealed a characteristic aspect ratio of these blisters by neglecting the bending effect of the layer, how the bending comes into play as the layer number increases has not been fully understood. Here, by simply measuring the profiles of blisters formed by transferred multilayer graphene and MoS2 sheets, the variable profiles of blisters and the transition of their characteristic shape from a constant aspect ratio to a constant dome curvature are observed. Taking variable profiles of blisters and different characteristics of the interface into consideration, a theoretical model is established, and the mechanism of such transition is further analytically unveiled. In addition, based on this theory, the bending stiffness of sheets and the adhesion energy between sheets and substrates can be obtained simultaneously. This method is simple but robust, providing a new experimental way to explore the mechanical behavior of 2D material structures.

Bending Stiffness of Circular Multilayer van der Waals Material Sheets

Abstract We study the bending stiffness of symmetrically bent circular multilayer van der Waals (vdW) material sheets, which correspond to the nonisometric configuration in bulge tests. Frenkel sinusoidal function is employed to describe the periodic interlayer tractions due to the lattice structure nature and the bending stiffness of sheets is theoretically extracted via an energetic consideration. Our quantitative prediction shows good agreement with recent experimental results, where the bending stiffness of different types of sheets with the comparable thickness could follow a trend opposite to their Young’s moduli. On the basis of our model, we propose that this trend may experience a transition as the thickness decreases. Apart from the apparent effects of Young’s modulus and interlayer shear strength, the interlayer distance is also found to have an important impact on the bending stiffness. In addition, according to our analysis on the size effect, the bending stiffness of such symmetrically bent circular sheets can steadily own a relatively large value, in contrast to the cases of isometric deformations.

Performance of RC beams externally strengthened with hybrid CFRP and PET-FRP laminates

The use of fiber-reinforced polymers (FRP) composite materials in strengthening applications of reinforced concrete (RC) structures has been gaining wide popularity in recent decades. This is due to its superior properties such as high strength to weight ratio, durability, and versatility. In fact, it is well established that bonding FRP materials to the soffit of RC beams enhances the flexural capacity of such beams. However, the non-yielding characteristic of FRP materials is a major concern, and often results in sudden and brittle failure mode of the strengthened member. To encounter this issue, a new type of FRP materials composed from polyethylene terephthalate (PET) fibers have been developed. Compared to conventional FRPs, PET-FRP have large deformability and possess a nonlinear stress-strain relationship. Employing PET-FRP in the retrofitting industry reduces construction waste, enhances the capacity of structures and provides a solution that encourages the concept of sustainability. However, these types of large rupture strain (LRS) FRPs have lower stiffness and tensile strengths than conventional FRPs. Therefore, the main aim of this study is to combine the lower stiffness and large rupture strain of PET-FRP sheets with that of the higher stiffness and strength of carbon FRP (CFRP) sheets resulting in a new hybrid composite system. The research program consists of four RC beams externally strengthened with CFRP, PET-FRP, and their hybrid combinations, in addition to a control unstrengthened beam specimen. The beams are tested under four-point bending and load-displacement curves along with the failure modes, strength, strain in the FRP, and ductility of the beam specimens are examined. Test results indicate that strengthening with PET-FRP laminates significantly enhances the deformation capacity of the strengthened specimens compared to that with CFRP. In addition, the hybrid mix between CFRP and PET-FRPs resulted in 46-48% strength improvement compared to the unstrengthened control beam. However, the effectiveness of the hybrid system was not pronounced in terms of ductility due to the premature debonding of the concrete cover that occurred before utilizing the full strain of the hybrid system. Hence, it is advised for future research studies to anchor the hybrid sheets by means of end U-wraps or FRP spike anchors to delay the debonding failure and to exploit the benefits of the proposed hybrid system.

SHEAR BEHAVIOR AND MECHANICAL MODEL FOR SELF-DRILLING SCREW CONNECTIONS BETWEEN THIN STEEL SHEETS

Self-drilling screw connections between thin steel sheets were tested under shearing forces, and the impacts of the sheet thickness and the screw diameter on the shear behavior of the connections were investigated. It has been indicated that: the obtained three typical failure modes including bearing failure of steel sheets, pull-out failure and shear failure of screw, depend on the ratio between the screw diameter and the thickness of the sheet adjacent to the screw head. The shear resistance of each connection is positively correlated with the sheet thickness and the screw diameter, and the initial stiffness and the ductility of the connections are also related to these two parameters. Elaborated finite element (FE) models for the self-drilling screw connections were developed by introducing the Johnson-Cook damage constitutive model and the linear damage accumulation rule, and by considering the geometric characteristics of screw threads. The developed FE models were validated against the obtained test results, which provide accurate simulations of shear behavior of self-drilling screw connections. By using the calculation formulas for the shear resistance of self-drilling screw connections in the Chinese code GB 50018−2002, a new three-stage simplified mechanical model was proposed herein by considering the impacts of the compressive stiffness of steel sheets and of the shear stiffness of screw, as well as of the multi-screws effect, which has been further verified for accurately predicting the shear force versus deformation relationships of self-drilling screw connections.

Poking and bulging of suspended thin sheets: Slippage, instabilities, and metrology

Measurement of in-plane elasticity of thin sheets often leverages out-of-plane poking or bulging, also known as indentation or bulge tests. For linear elastic sheets, a load-cubic deflection relation has been frequently assumed so that the stiffness of the sheet could be readily extracted. However, we find that recent results of indentation and bulge tests on 2D materials do not support the assumption, which can be attributed to the slippage of 2D materials against their supporting substrates. Besides, the interfacial slippage could cause instabilities in the sheet such as radial wrinkles in suspended region, with finite lengths. To gain a quantitative understanding, we assume constant interfacial shear traction and study the wrinkling extent and the effective stiffness of thin sheets upon poking and bulging. We identify a single dimensionless parameter governing these mechanical responses—the sliding number—defined by comparing the sheet tension (that drives the slippage) with the interfacial traction (that resists the slippage). We discuss several useful asymptotic behaviors emerging at small and large sliding numbers. These understandings inspire when the effect of the interfacial slippage (as well as other substrate-associated subtleties) can be neglected in these tests. For instance, traditional bulge and indentation tests suffer from complexities caused by the slippage, pretension, Poisson's ratio, substrate roughness, and various interfacial traction-separation laws. Based on such understandings, we propose a simple poking/bulging methodology immune to all of these complexities, enabling an alternative way to measure the sheet stiffness.

The Brain is Not Flat: Conformal Electrode Arrays Diminish Complications of Subdural Electrode Implantation, A Series of 117 Cases

Intracranial recordings are integral to evaluating patients with pharmacoresistant epilepsy whom noninvasive testing fails to localize seizure focus. Although stereo-electroencephalography is the preferred method of intracranial recordings in most centers, subdural electrode (SDE) implantation is necessary in selected cases. To identify imaging correlates that predict SDE complications (extra-axial fluid collections [EFCs]), and determine if modifications that diminish stiffness of electrode sheets reduce complications. A prospective epilepsy surgery database was used to identify adults undergoing craniotomy for SDE implantation over a 14-year period. EFCs and midline shift were measured via magnetic resonance imaging and computed tomography imaging. Correlation analyses and multivariable logistic regression explored associations between use of conformal arrays, serial order of patients, previous ipsilateral intracranial surgery, midline shift, number of SDEs, and neurologic complications. A total of 111 consecutive patients (59 female) underwent 117 craniotomies (mean, 115 electrode contacts) for SDE implantation. There were 8 surgical complications, 3 in the first 17 (17.7%). and 5 (after electrode modifications) in a subsequent 100 craniotomies (5.0%). We noted an increase in electrode numbers implanted over time (P < 0.001) and decreased midline shift with conformal grids (ρ= - 0.32; P < 0.001). A multivariable regression showed that midline shift correlated with complications (odds ratio, 2.32; 95% confidence interval, 1.12-4.78; P= 0.023). Hemorrhagic complications after SDE implantation are difficult to detect because of artifact from electrodes, but predictable by prominent midline shift (>4 mm). Risks inherent to SDE implantation may be minimized using conformal grids. With symptomatic EFCs, a single electrode cable exit site allows hematoma evacuation without terminating intracranial recordings.

RC columns longitudinally strengthened via novel EBRIOG technique

AbstractCarbon fiber reinforced polymer (CFRP) composites are materials that have been acceptably used for the external reinforcement of structural load carrying elements such as reinforced concrete (RC) columns. When subjected to axial compression loads, columns longitudinally strengthened with CFRP sheets undergo buckling and debonding of their longitudinal CFRP strips as their failure modes. The present study investigates the efficiency of the new technique called “externally bonded reinforcement in/on grooves” (EBRIOG) on square RC columns strengthened with longitudinal FRP composites when subjected to cyclic axial compression loading, and examines whether EBRIOG delays the buckling and debonding of longitudinal CFRP sheets. Another aspect of the study involves investigation of the influence of the recently developed corner strip‐batten (CSB) technique on confining specimens. In the CSB technique, CFRP battens used for transverse strengthening tend to stretch as entirely straight sheets like what occurs with flat coupons, as they do not tolerate any curvature. In order to compare the above‐mentioned techniques and the conventional ones, 12 square column specimens (150 × 150 × 900 mm3) are subjected to cyclic axial compression. The experiment parameters consist of the method used for longitudinal strengthening and the technique utilized for confining the specimens. The results exhibit improved efficiency of square RC columns (as realized by their peak load, ductility indices, energy dissipation, equivalent damping factor, secant stiffness, and average compressive stress of longitudinal composite sheets) when the EBRIOG and CSB techniques are employed simultaneously. For instance, the column strengthened through the CSB and EBRIOG method exhibits increases of 192 and 72% in its ductility and load carrying capacity, respectively, compared to those of the unstrengthened one.

Wet-end addition of nanofibrillated cellulose pretreated with cationic starch to achieve paper strength with less refining and higher bulk

Nanofibrillated cellulose (NFC) treated with cationic starch was evaluated as a bonding system to permit lower degrees of refining and lower apparent density of high-mass handsheets made from bleached kraft pulp. Mixed pulp (70% hardwood, 30% softwood) was formed into sheets with the optional addition of 5% by dry mass of NFC. The default addition of NFC was compared with a system in which the NFC had been pretreated either with cationic starch (at various levels) or optionally followed by colloidal silica. Comparative tests also were carried out with separate addition of cationic starch to the main furnish. Unrefined fibers (514 mL CSF) were compared with low-refined (473 mL CSF) and high-refined (283 mL CSF) pulp mixtures. The NFC that had been pretreated with cationic starch at a high level was especially effective at boosting the tensile strength and stiffness of sheets prepared from pulp that had been refined at a low level, thus achieving improved strength at relatively low apparent density (high bulk) of the handsheets. The results support a strategy, for applicable grades of paper, of using cationic starchpretreated NFC in place of refining energy applied to the main fiber furnish. It was further established that colloidal silica can be employed as a further pretreatment of the cationic starch–treated NFC as a means of promoting dewatering in the combined system.

Thickening process of concave edge for increasing stiffness and fatigue strength of ultra-high strength steel sheets

A thickening process was applied for the concave edge to increase the stiffness and fatigue strength of the ultra-high strength steel sheets. In the thickening process, the sheet was trimmed under the tension between the taper punch and the step die. The trimmed edge was bent by the taper of the punch into the corner step of the die and the surface of the sheared edge was ironed. After filling into the corner step, the excessive material was sheared. The effect of the step shape in the die on the stiffness and fatigue strength in the bending and tensile tests was investigated. The stiffness of the thickened edge was larger than that without thickening in both the bending and tensile tests. The fatigue strength of the thickened edge was higher than that without thickening in the bending test, whereas, the strength in the tensile test was lower in certain conditions due to stress concentration. It was found that thickening in the concave edge of the ultra-high strength steel sheets is effective in the increase of the stiffness and fatigue strength of the part.

Relative planar strain control and minimizing deformation work in elastomeric sheets via reinforcing fiber arrays

This study investigates soft composite sheets that undergo significant deformations. The fiber reinforcement in these systems not only increases the stiffness of sheets like a traditional composite, but also controls the relationships between strains in orthogonal planar directions. Such an ability is useful in controlling the deformation of soft robots, and also enhancing the output of soft actuation techniques like electro-active polymer actuators (also called dielectric actuators). The inspiration for this work comes from squid mantle structures that couple orthogonal components of strain using helical fiber reinforcement. The resulting null space of deformations corresponding to the fiber restrictions creates a family of body deformations that optimize propulsion.The strain dynamics in the composite sheet are modeled geometrically from fiber orientations, assuming that the fibers are inextensible. After the strain dynamics have been determined, the stress/strain relationship is modeled by considering the matrix and reinforcing fibers to be two separate homogeneous systems interacting through local stresses. Both steps of this modeling technique are validated experimentally showing planar strains in a preferred direction to be as high as 16 times the resulting planar strain of an equivalent unreinforced sheet by forcing negative strains in the orthogonal planar directions. The work required for deformation is derived from the stress/strain relationship by calculating the strain energy stored in the material, and an optimal balance between increased planar strain output and increased material stiffness is analyzed. It is shown that for the specific materials used to create the soft composite sheets (thermoplastic elastomer with cotton fibers) optimal fiber angles lie between 15° and 25° to minimize work required for deformation, but this optimal range will increase with increasing ratio of fiber to matrix modulus.

How two-dimensional bending can extraordinarily stiffen thin sheets.

Curved thin sheets are ubiquitously found in nature and manmade structures from macro- to nanoscale. Within the framework of classical thin plate theory, the stiffness of thin sheets is independent of its bending state for small deflections. This assumption, however, goes against intuition. Simple experiments with a cantilever sheet made of paper show that the cantilever stiffness largely increases with small amounts of transversal curvature. We here demonstrate by using simple geometric arguments that thin sheets subject to two-dimensional bending necessarily develop internal stresses. The coupling between the internal stresses and the bending moments can increase the stiffness of the plate by several times. We develop a theory that describes the stiffness of curved thin sheets with simple equations in terms of the longitudinal and transversal curvatures. The theory predicts experimental results with a macroscopic cantilever sheet as well as numerical simulations by the finite element method. The results shed new light on plant and insect wing biomechanics and provide an easy route to engineer micro- and nanomechanical structures based on thin materials with extraordinary stiffness tunability.

Deformation mechanism of graphene in amorphous polyethylene: A molecular dynamics based study

The current paper focuses on investigating deformation mechanism of graphene sheets in a graphene reinforced polyethylene (Gn–PE) nanocomposite. Classical molecular dynamics (MD) simulation was conducted on large Gn–PE systems. Different spatial arrangements of graphene sheets were considered in order to study the effect of nonlocal interaction among the graphenes. In all the cases 5% weight concentration of graphene was considered in order to prepare atomistic models for Gn–PE. As expected, graphene seemed to enhance the overall Young’s modulus and tensile strength of the Gn–PE nanocomposite. Randomly oriented graphenes with strong nonlocal interaction were observed to be comparatively preferable than the other spatial arrangements of graphenes. The high strength and stiffness of graphene sheets can be properly utilized if the graphenes are randomly oriented and have strong long range interactions. Finally, the failure mechanism of the graphene and role of voids in the polymer were discussed both qualitatively and quantitatively. It was seen that the randomly oriented graphenes were firstly pulled out from the polyethylene matrix during deformation prior to breaking into pieces. This can explain the loss of stiffness and strength in graphene sheets embedded in the polymer matrix. From the current work it is clearly understood that the necessity of the long range graphene–graphene interaction is important in both elastic as well as plastic regime of the deformation.

Springback in stringer sheet stretch forming

Stringer sheets are sheet metal structures stiffened by bifurcations in the cross-section. In order to create spatially curved light-weight structures they may serve as preforms for sheet metal hydroforming. The stiffness of sheets altered by stringers is expected to affect the hydroforming results. In particular influences of the geometric inhomogeneity on the extent and orientation of springback are of interest. They are investigated by means of mathematical analysis and forming experiments. A modal analysis of formed stringer sheets is conducted in order to understand the different impacts of stringers on the elastic behaviour of parts and springback after forming.

Elastic response of a grounded ice sheet coupled to a floating ice shelf

An ice sheet that spreads into an ocean is forced to bend owing to its buoyancy and detaches from the bedrock to form a floating ice shelf. The location of the transition between the grounded sheet and the floating shelf, defined as the grounding line, behaves as a free boundary. We develop a model of an elastic grounded sheet resting on a deformable elastic bed and coupled to an elastic floating shelf. We find that the grounding-line position is determined by the geometry of the bed and the bending-buoyancy length scale of the system. These two contributions depend on the reaction modulus of the bed in opposite ways. We show that the structure of the floating shelf depends on the bending-buoyancy length scale only, allowing us to calculate the bending stiffness of the elastic sheet independently of the properties of the bed. Relations between the structure of the floating shelf and the grounding-line position are also developed. Our theoretical predictions agree with laboratory experiments made using thick elastic sheets and a dense salt solution. Our findings may provide new insights into the dynamics near grounding lines, as well as methods to infer the bending stiffness of ice sheets and the grounding-line position from satellite altimetery that can be applied to elastic sheets in general.

Analytical Studies on Mixed-Mode Debonding along the FRP–Concrete Interface in the Peeling Test

The bonding of fiber reinforced polymer (FRP) strips and plates to the concrete structures has been found to be an effective technique for flexural strengthening. The FRP is then under both pulling and peeling forces, resulting in a combination of shear sliding and opening displacement along the FRP/concrete interface. A novel experimental set-up is studied that a peeling load is applied on the FRP sheet by a circular rod placed into the central notch of the beam. Based on the linear-elastic fracture mechanics approach, a theoretical analysis is conducted on specimens representing the peeling behavior. From the numerical analysis, the load–displacement curves, load–stiffness of FRP sheet curves, and load–fracture energy curves affected by different variables are discussed. The peel load is related to the FRP sheet stiffness and to the interfacial fracture energy. Therefore, only two material parameters, the interfacial fracture energy of FRP–concrete interface and stiffness of FRP sheets, are necessary to represent the interfacial fracture behavior. The theoretical load–deflection curves of specimens agree well with the corresponding experimental results in the literatures.

Correlation between stiffness of sheets prepared from cellulose whiskers and nanoparticles dimensions

Impressive mechanical properties of cellulose nanocrystals or whiskers have generated great interest from the scientific community as shown by the huge amount of recent literature in this field. It makes them ideal candidates for the processing of polymer nanocomposites. Their outstanding reinforcing capability is classically ascribed to a mechanical percolation phenomenon. At sufficiently high temperature, the stiffness of the materials depends only on the volume fraction of the percolating rigid phase and stiffness of the percolating network. The effect of the first parameter has been well investigated in the literature but surprisingly no report is found about the latter. Tensile tests were performed on films prepared by water evaporation of a series of cellulose whiskers suspensions. Interestingly, our experimental data show that a correlation exists between the stiffness of the films and aspect ratio of the constituent rod-like nanoparticles.

Peeling behavior and spalling resistance of CFRP sheets bonded to bent concrete surfaces

In this paper, the peeling behavior and the spalling resistance effect of carbon fiber reinforced polymer (CFRP) sheets externally bonded to bent concrete surfaces are firstly investigated experimentally. Twenty one curved specimens and seven plane specimens are studied in the paper, in which curved specimens with bonded CFRP sheets can simulate the concrete spalling in tunnel, culvert, arch bridge etc., whereas plane specimens with bonded CFRP sheets can simulate the concrete spalling in beam bridge, slab bridge and pedestrian bridge. Three kinds of curved specimens with different radii of curvature are chosen by referring to practical tunnel structures, and plane specimens are used for comparison with curved ones. A peeling load is applied on the FRP sheet by loading a circular steel tube placed into the central notch of beam to debond CFRP sheets from the bent concrete surface, meanwhile full-range load–deflection curves are recorded by a MTS 831.10 Elastomer Test System. Based on the experimental results, a theoretical analysis is also conducted for the specimens. Both theoretical and experimental results show that only two material parameters, the interfacial fracture energy of CFRP-concrete interface and the tensile stiffness of CFRP sheets, are needed for describing the interfacial spalling behavior. It is found that the radius of curvature has remarkable influence on peeling load–deflection curves. The test methods and test results given in the paper are helpful and available for reference to the designer of tunnel strengthening.