Studies on bending limitations for the optimal fit of orthopaedic bone plates

Distal tibial fractures are now commonly treated via intermedullary plate fixation due to higher rates of union and lower rates of postoperative complications. However, patient specific bone morphology demands manual deformation of the plate to ensure appropriate fit along the bone Distal tibial fractures are now commonly treated via intermedullary plate fixation due to higher rates of union and lower rates of postoperative complications. However, patient specific bone morphology demands manual deformation of the plate to ensure appropriate fit along the bone contours, and depending on the material of the plate, different outcomes have been reported along with postoperative complications. A comparative analysis of Stainless Steel 316L and Ti-6Al-4V alloys was carried to estimate the safe bending limit for appropriate fits. The results from the ANSYS FEA simulations were validated with experiments based on ASTM F382-99. It is found that SS316L is better suited for large deformations (up to 16˚ in proximal tip and 7.5˚ in distal end) and Ti for smaller deformation contours (up to 3˚ in proximal tip and 1.8˚ in distal end). The results of this study have profound implications for the choice of plates based on preliminary radiographical fracture examinations to ensure better fixation and higher rates of union of distal tibial fractures.

Bi-2212/Ag laminated tapes: Bending and joining effects

Superconducting composite Bi-2212/Ag tapes and their joints are fabricated by a combination of dip-coating and partial melt processing. The heat treated tapes have a critical current (Ic) between 8 and 26A, depending on tape thickness and the number of Bi-2212 layers. Current transmissions between 80% and 100% have been achieved through the joints of tapes. Different types of HTS joints of Bi-2212/Ag laminated tapes are made and their transport properties during winding operations are investigated. Irreversible strain values (ε irrev) for laminated tapes and their joints are determined and it is found that the degradation of Ic during tape bending depends on the type of joint.

Bi-2212/Ag tapes and laminates : effects of bending

Superconducting Bi-2212 tapes and laminates are fabricated by a combination of dip-coating and partial melt processing. The heat treated tapes have critical current densities (Jc) up to 11 kAcm -2. We investigate the degradation of critical current (Ic) during bending experiments for both single tapes and tapes with laminate structure. Although degradation of Ic is observed in both forms, the characteristics of the degradation differ. It is determined that laminated tapes perform better than single tapes when critical current is measured against bending radius, and laminated tapes tolerate a higher strain for a given reduction in critical current. It is found that increasing the number of Bi-2212 layers increases the total Ic of the laminated tape, but degradation of critical current is more pronounced during bending because of the increased total thickness of the laminate structure. It is also found that addition of silver to the Bi-2212 layers reduces critical current degradation during bending for both tapes and laminates.

Cohesive zone modelling of mineralized collagen fibril arrays in bending

Hard biological materials such as bone possess superior material properties of high stiffness and toughness. Two unique characteristics of bone microstructure are a large aspect ratio of mineralized collagen fibrils (MCF), and an extremely thin and large area of extrafibrillar protein matrix located between the MCF. The objective of this study is to investigate the effects of: (1) MCF aspect ratio, and (2) energy dissipation in extrafibrillar protein matrix on the mechanical behaviour of MCF arrays. In this study, notched specimens of MCF arrays in extrafibrillar protein matrix are subjected to bending. Cohesive zone model was implemented to simulate the failure of extrafibrillar protein matrix. The study reveals that the MCF array with a higher MCF aspect ratio and the MCF array with a higher protein energy dissipation in the interface direction are able to sustain a higher bending force and dissipate higher energy.

Bending properties of Ag nanowires with pre-existing surface defects

Materials used in the engineering always contain imperfections or defects which significantly affect their performances. Based on the large-scale molecular dynamics simulation and the Euler–Bernoulli beam theory, the influence from different pre-existing surface defects on the bending properties of Ag nanowires (NWs) is studied in this paper. It is found that the nonlinear-elastic deformation, as well as the flexural rigidity of the NW is insensitive to different surface defects for the studied defects in this paper. On the contrary, an evident decrease of the yield strength is observed due to the existence of defects. In-depth inspection of the deformation process reveals that, at the onset of plastic deformation, dislocation embryos initiate from the locations of surface defects, and the plastic deformation is dominated by the nucleation and propagation of partial dislocations under the considered temperature. Particularly, the generation of stair-rod partial dislocations and Lomer–Cottrell lock are normally observed for both perfect and defected NWs. The generation of these structures has thwarted attempts of the NW to an early yielding, which leads to the phenomenon that more defects does not necessarily mean a lower critical force.

Experimental studies of hollow flange channel beams subject to combined bending and shear actions

This paper presents the details of an experimental study of a cold-formed steel hollow flange channel beam known as LiteSteel Beam (LSB) subject to combined bending and shear actions. The LSB sections are produced by a patented manufacturing process involving simultaneous cold-forming and electric resistance welding. Due to the geometry of the LSB, as well as its unique residual stress characteristics and initial geometric imperfections resultant of manufacturing processes, much of the existing research for common cold-formed steel sections is not directly applicable to LSB. Experimental and numerical studies have been carried out to evaluate the behaviour and design of LSBs subject to pure bending actions and predominant shear actions. To date, however, no investigation has been conducted into the strength of LSB sections under combined bending and shear actions. Combined bending and shear is especially prevalent at the supports of continuous span and cantilever beams, where the interaction of high shear force and bending moment can reduce the capacity of a section to well below that for the same section subject only to pure shear or moment. Hence experimental studies were conducted to assess the combined bending and shear behaviour and strengths of LSBs. Eighteen tests were conducted and the results were compared with current AS/NZS 4600 and AS 4100 design rules. AS/NZS 4600 design rules were shown to grossly underestimate the combined bending and shear capacities of LSBs and hence two lower bound design equations were proposed based on experimental results. Use of these equations will significantly improve the confidence and cost-effectiveness of designing LSBs for combined bending and shear actions.

Material yielding by both axial and bending spring stiffness at elevated temperature

Material yielding is typically modeled either by plastic zone or plastic hinge methods under the context of geometric and material nonlinear finite element methods. In fire analysis of steel structures, the plastic zone method is widely used, but it requires extensively more computational efforts. The objective of this paper is to develop the nonlinear material model allowing for interaction of both axial force and bending moment, which relies on the plastic hinge method to achieve numerical efficiency and reduce computational effort. The biggest advantage of the plastic-hinge approach is its computational efficiency and easy verification by the design code formulae of the axial force–moment interaction yield criterion for beam–column members. Further, the method is reliable and robust when used in analysis of practical and large structures. In order to allow for the effect of catenary action, axial thermal expansion is considered in the axial restraint equations. The yield function for material yielding incorporated in the stiffness formulation, which allows for both axial force and bending moment effects, is more accurate and rational to predict the behaviour of the frames under fire. In the present fire analysis, the mechanical properties at elevated temperatures follow mainly the Eurocode 3 [Design of steel structures, Part 1.2: Structural fire design. European Committee for Standisation; 2003]. Example of a tension member at a steady state heating condition is modeled to verify the proposed spring formulation and to compare with results by others. The behaviour of a heated member in a highly redundant structure is also studied by the present approach.

Numerical studies and design of hollow flange channel beams subject to combined bending and shear actions

LiteSteel beam (LSB) is a cold-formed steel hollow flange channel section produced using a patented manufacturing process involving simultaneous cold-forming and dual electric resistance welding. It is commonly used as floor joists and bearers in residential, industrial and commercial buildings. Design of the LSB is governed by the Australian cold-formed steel structures code, AS/NZS 4600. Due to the geometry of the LSB, as well as its unique residual stress characteristics and initial geometric imperfections resultant of manufacturing processes, currently available design equations for common cold-formed sections are not directly applicable to the LSB. Many research studies have been carried out to evaluate the behaviour and design of LSBs subject to pure bending actions and predominant shear actions. To date, however, no investigation has been conducted into the strength of LSB sections under combined bending and shear actions. Hence experimental and numerical studies were conducted to assess the combined bending and shear behaviour of LSBs. Finite element models of LSBs were developed to simulate their combined bending and shear behaviour and strength of LSBs. They were then validated by comparing the results with available experimental test results and used in a detailed parametric study. The results from experimental and finite element analyses were compared with current AS/NZS 4600 and AS 4100 design rules. Both experimental and numerical studies show that the AS/NZS 4600 design rule based on circular interaction equation is conservative in predicting the combined bending and shear capacities of LSBs. This paper presents the details of the numerical studies of LSBs and the results. In response to the inadequacies of current approaches to designing LSBs for combined bending and shear, two lower bound design equations are proposed in this paper.

Mechanical bending properties of sodium titanate (Na2Ti3O7) nanowires

We report on the mechanical properties of sodium titanate nanowires (Na2Ti3O7 NW) through a combination of bending experiments and theoretical analysis. Na2Ti3O7 NWs with lateral dimensions ranging from 20–700 nm were synthesized by a hydrothermal approach. A focused ion beam (FIB) was used to manipulate the selected Na2Ti3O7 NW over a hole drilled in an indium tin oxide substrate. After welding the nanowire, a series of bending tests was performed. It was observed that the Na2Ti3O7 NW exhibits a brittle behavior, and a nonlinear elastic deformation was observed before failure. By using the modified Euler–Bernoulli beam theory, such nonlinear elastic deformation is found to originate from a combination of surface effects and axial elongation (arising from the bending deformation). The effective Young's modulus of the Na2Ti3O7 NW was found to be independent of the wire length, and ranges from 21.4 GPa to 45.5 GPa, with an average value of 33 ± 7 GPa. The yield strength of the Na2Ti3O7 NW is measured at 2.7 ± 0.7 GPa.

Development of a new ultrasound-based system for tracking motion of the human lumbar spine: Reliability, stability and repeatability during forward bending movement trials

The aim of this study was to develop a new method for quantifying intersegmental motion of the spine in an instrumented motion segment L4–L5 model using ultrasound image post-processing combined with an electromagnetic device. A prospective test–retest design was employed, combined with an evaluation of stability and within- and between-day intra-tester reliability during forward bending by 15 healthy male patients. The accuracy of the measurement system using the model was calculated to be ± 0.9° (standard deviation = 0.43) over a 40° range and ± 0.4 cm (standard deviation = 0.28) over 1.5 cm. The mean composite range of forward bending was 15.5 ± 2.04° during a single trial (standard error of the mean = 0.54, coefficient of variation = 4.18). Reliability (intra-class correlation coefficient = 2.1) was found to be excellent for both within-day measures (0.995–0.999) and between-day measures (0.996–0.999). Further work is necessary to explore the use of this approach in the evaluation of biomechanics, clinical assessments and interventions.

Behaviour and strength of hollow flange channel sections under torsion and bending

Hollow flange channel section is a cold-formed high-strength and thin-walled steel section with a unique shape including two rectangular hollow flanges and a slender web. Due to its mono-symmetric characteristics, it will also be subjected to torsion when subjected to transverse loads in practical applications. Past research on steel beams subject to torsion has concentrated on open sections while very few steel design standards give suitable design rules for torsion design. Since the hollow flange channel section is different from conventional open sections, its torsional behaviour remains unknown to researchers. Therefore the elastic behaviour of hollow flange channel sections subject to uniform and non-uniform torsion, and combined torsion and bending was investigated using the solutions of appropriate differential equilibrium equations. The section torsion shear flow, warping normal stress distribution, and section constants including torsion constant and warping constant were obtained. The results were compared with those from finite element analyses that verified the accuracy of analytical solutions. Parametric studies were undertaken for simply supported beams subject to a uniformly distributed torque and a uniformly distributed transverse load applied away from the shear centre. This paper presents the details of this research into the elastic behaviour and strength of hollow flange channel sections subject to torsion and bending and the results.

Bending and torsion of hollow flange channel beams

The LiteSteel beam (LSB) is a cold-formed high strength steel channel section made of two torsionally rigid closed flanges and a slender web. Due to its mono-symmetric characteristics, its centroid and shear centre do not coincide. The LSBs can be used in floor systems as joists or bearers and in these applications they are often subjected to transverse loads that are applied away from the shear centre. Hence they are often subjected to combined bending and torsion actions. Previous researches on LSBs have concentrated on their bending or shear behaviour and strengths, and only limited research has been undertaken on their combined bending and torsion behaviour. Therefore in this research a series of nine experiments was first conducted on LSBs subject to combined bending and torsion. Three LSB sections were tested to failure under eccentric loading at mid-span, and appropriate results were obtained from seven tests. A special test rig was used to simulate two different eccentricities and to provide accurate simple boundary conditions at the supports. Finite element models of tested LSBs were developed using ANSYS, and the ultimate strengths, failure modes, and load–displacement curves were obtained and compared with corresponding test results. Finite element analyses agreed well with test results and hence the developed models were used in a parametric study to investigate the effects of load locations, eccentricities, and spans on the combined bending and torsion behaviour of LSBs. The interaction between the ultimate bending and torsional moment capacities was studied and a simple design rule was proposed. This paper presents the details of the tests, finite element analyses, and parametric study of LSBs subject to combined bending and torsion, and the results.

Molecular Origin of the Intrinsic Bending Force for Helical Morphology Observed in Chiral Amphiphilic Assemblies: Concentration and Size Dependence

The formation of the helical morphology in monolayers and bilayers of chiral amphiphilic assemblies is believed to be driven at least partly by the interactions at the chiral centers of the amphiphiles. However, a detailed microscopic understanding of these interactions and their relation with the helix formation is still not clear. In this article a study of the molecular origin of the chirality-driven helix formation is presented by calculating, for the first time, the effective pair potential between a pair of chiral molecules. This effective potential depends on the relative sizes of the groups attached to the two chiral centers, on the orientation of the amphiphile molecules, and also on the distance between them. We find that for the mirror-image isomers (in the racemic modification) the minimum energy conformation is a nearly parallel alignment of the molecules. On the other hand, the same for a pair of molecules of one kind of enantiomer favors a tilt angle between them, thus leading to the formation of a helical morphology of the aggregate. The tilt angle is determined by the size of the groups attached to the chiral centers of the pair of molecules considered and in many cases predicted it to be close to 45 degrees. The present study, therefore, provides a molecular origin of the intrinsic bending force, suggested by Helfrich (J. Chem. Phys. 1986, 85, 1085-1087), to be responsible for the formation of helical structure. This effective potential may explain many of the existing experimental results, such as the size and the concentration dependence of the formation of helical morphology. It is further found that the elastic forces can significantly modify the pitch predicted by the chiral interactions alone and that the modified real pitch is close to the experimentally observed value. The present study is expected to provide a starting point for future microscopic studies.

Bending Of Circular Plate On Elastic-Foundation

The governing differential equation of linear, elastic, thin, circular plate of uniform thickness, subjected to uniformly distributed load and resting on Winkler-Pasternak type foundation is solved using ``Chebyshev Polynomials''. Analysis is carried out using Lenczos' technique, both for simply supported and clamped plates. Numerical results thus obtained by perturbing the differential equation for plates without foundation are compared and are found to be in good agreement with the available results. The effect of foundation on central deflection of the plate is shown in the form of graphs.

Three-dimensional elastic analysis of cracked thick plates under bending fields

A three-dimensional analysis is presented for the bending problem of finite thick plates with through-the-thickness cracks. A general solution is obtained for Navier's equations of the theory of elasticity. It is found that the in-plane stresses and the transverse normal stress at the crack front are singular with an inverse square root singularity, while the transverse shear stresses are of the order of unity. Results from a numerical study indicate that the stress intensity factor, which varies across the thickness, is influenced by the thickness ratio in a significant manner. Results from a parametric study and those from a comparative study with existing finite element values are presented.