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Concept: Torsion


Classic beam theory is frequently used in biomechanics to model the stress behaviour of vertebrate long bones, particularly when creating intraspecific scaling models. Although methodologically straightforward, classic beam theory requires complex irregular bones to be approximated as slender beams, and the errors associated with simplifying complex organic structures to such an extent are unknown. Alternative approaches, such as finite element analysis (FEA), while much more time-consuming to perform, require no such assumptions. This study compares the results obtained using classic beam theory with those from FEA to quantify the beam theory errors and to provide recommendations about when a full FEA is essential for reasonable biomechanical predictions. High-resolution computed tomographic scans of eight vertebrate long bones were used to calculate diaphyseal stress owing to various loading regimes. Under compression, FEA values of minimum principal stress (σ(min)) were on average 142 per cent (±28% s.e.) larger than those predicted by beam theory, with deviation between the two models correlated to shaft curvature (two-tailed p = 0.03, r(2) = 0.56). Under bending, FEA values of maximum principal stress (σ(max)) and beam theory values differed on average by 12 per cent (±4% s.e.), with deviation between the models significantly correlated to cross-sectional asymmetry at midshaft (two-tailed p = 0.02, r(2) = 0.62). In torsion, assuming maximum stress values occurred at the location of minimum cortical thickness brought beam theory and FEA values closest in line, and in this case FEA values of τ(torsion) were on average 14 per cent (±5% s.e.) higher than beam theory. Therefore, FEA is the preferred modelling solution when estimates of absolute diaphyseal stress are required, although values calculated by beam theory for bending may be acceptable in some situations.

Concepts: Interval finite element, Finite element method, Model, Biomechanics, Solid mechanics, Beam, Torsion, Structural analysis


To validate torsional analysis, based on finite elements, of WaveOne instruments against in vitro tests and to model the effects of different nickel titanium materials METHODOLOGY: WaveOne reciprocating instruments (Small, Primary and Large, n=8 each, M-Wire) were tested under torsion according to standard ISO 3630-1. Torsional profiles including torque and angle at fracture were determined. Test conditions were reproduced through Finite Element Analysis (FEA) simulations based on micro CT scans at 10μm resolution; results were compared to experimental data using analysis of variance and two-sided one sample t-tests. The same simulation was performed on virtual instruments with identical geometry and load condition, based on M-Wire or conventional NiTi alloy.

Concepts: Engineering, Finite element method, Hilbert space, Normal distribution, Analysis of variance, Standard, Partial differential equation, Torsion


Open reduction internal fixation technique has been generally accepted for treatment of midshaft clavicle fractures. Both superior and anterior clavicle plates have been reported in clinical or biomechanical researches, while presently the spiral clavicle plate design has been introduced improved biomechanical behavior over conventional designs. In order to objectively realize the multi-directional biomechanical performances among the three geometries for clavicle plate designs, a current conceptual finite element study has been conducted with identical cross-sectional features for clavicle plates. The conceptual superior, anterior, and spiral clavicle plate models were constructed for virtual reduction and fixation to an OTA 15-B1.3 midshaft transverse fracture of clavicle. Mechanical load cases including cantilever bending, axial compression, inferior bending, and axial torsion have been applied for confirming the multi-directional structural stability and implant safety in biomechanical perspective. Results revealed that the anterior clavicle plate model represented lowest plate stress under all loading cases. The superior clavicle plate model showed greater axial compressive stiffness, while the anterior clavicle plate model performed greater rigidity under cantilever bending load. Three model represented similar structural stiffness under axial torsion. Played as a transition structure between superior and anterior clavicle plate, the spiral clavicle plate model revealed comparable results with acceptable multi-directional biomechanical behavior. The concept of spiral clavicle plate design is worth considering in practical application in clinics. Implant safety should be further investigated by evidences in future mechanical tests and clinical observations.

Concepts: Bone fracture, Fracture, Orthopedic surgery, Clavicle fracture, Elasticity, Clavicle, Torsion, Superiority complex


Almost all species of modern birds are capable of flight; the mechanical competency of their wings and the rigidity of their skeletal system evolved to enable this outstanding feat. One of the most interesting examples of structural adaptation in birds is the internal structure of their wing bones. In flying birds, bones need to be sufficiently strong and stiff to withstand forces during takeoff, flight, and landing, with a minimum of weight. The cross-sectional morphology and presence of reinforcing structures (struts and ridges) found within bird wing bones vary from species to species, depending on how the wings are utilized. It is shown that both morphology and internal features increases the resistance to flexure and torsion with a minimum weight penalty. Prototypes of reinforcing struts fabricated by 3D printing were tested in diametral compression and torsion to validate the concept. In compression, the ovalization decreased through the insertion of struts, while they had no effect on torsional resistance. An elastic model of a circular ring reinforced by horizontal and vertical struts is developed to explain the compressive stiffening response of the ring caused by differently oriented struts.

Concepts: Structure, Bird, Reinforcement, Flight, Wing, Flying and gliding animals, Torsion, Bird flight


Insight into crumpling or compaction of one-dimensional objects is important for understanding biopolymer packaging and designing innovative technological devices. By compacting various types of wires in rigid confinements and characterizing the morphology of the resulting crumpled structures, here, we report how friction, plasticity and torsion enhance disorder, leading to a transition from coiled to folded morphologies. In the latter case, where folding dominates the crumpling process, we find that reducing the relative wire thickness counter-intuitively causes the maximum packing density to decrease. The segment size distribution gradually becomes more asymmetric during compaction, reflecting an increase of spatial correlations. We introduce a self-avoiding random walk model and verify that the cumulative injected wire length follows a universal dependence on segment size, allowing for the prediction of the efficiency of compaction as a function of material properties, container size and injection force.

Concepts: Fundamental physics concepts, Force, Space, Materials science, Classical mechanics, Point, Wire, Torsion


Fractures of bone account 25% of all paediatric injuries (Cooper et al. in J Bone Miner Res 19:1976-1981, 2004. ). These can be broadly categorised into accidental or inflicted injuries. The current clinical approach to distinguish between these two is based on the clinician’s judgment, which can be subjective. Furthermore, there is a lack of studies on paediatric bone to provide evidence-based information on bone strength, mainly due to the difficulties of obtaining paediatric bone samples. There is a need to investigate the behaviour of children’s bones under external loading. Such data will critically enhance our understanding of injury tolerance of paediatric bones under various loading conditions, related to injuries, such as bending and torsional loads. The aim of this study is therefore to investigate the response of paediatric femora under two types of loading conditions, bending and torsion, using a CT-based finite element approach, and to determine a relationship between bone strength and age/body mass of the child. Thirty post-mortem CT scans of children aged between 0 and 3 years old were used in this study. Two different boundary conditions were defined to represent four-point bending and pure torsional loads. The principal strain criterion was used to estimate the failure moment for both loading conditions. The results showed that failure moment of the bone increases with the age and mass of the child. The predicted failure moment for bending, external and internal torsions were 0.8-27.9, 1.0-31.4 and 1.0-30.7 Nm, respectively. To the authors' knowledge, this is the first report on infant bone strength in relation to age/mass using models developed from modern medical images. This technology may in future help advance the design of child, car restrain system, and more accurate computer models of children.

Concepts: Bone, Torque, Finite element method, Continuum mechanics, Elliptic boundary value problem, Mechanics, Torsion, Polar moment of inertia


Soft bioelectronic devices provide new opportunities for next-generation implantable devices owing to their soft mechanical nature that leads to minimal tissue damages and immune responses. However, a soft form of the implantable optoelectronic device for optical sensing and retinal stimulation has not been developed yet because of the bulkiness and rigidity of conventional imaging modules and their composing materials. Here, we describe a high-density and hemispherically curved image sensor array that leverages the atomically thin MoS2-graphene heterostructure and strain-releasing device designs. The hemispherically curved image sensor array exhibits infrared blindness and successfully acquires pixelated optical signals. We corroborate the validity of the proposed soft materials and ultrathin device designs through theoretical modeling and finite element analysis. Then, we propose the ultrathin hemispherically curved image sensor array as a promising imaging element in the soft retinal implant. The CurvIS array is applied as a human eye-inspired soft implantable optoelectronic device that can detect optical signals and apply programmed electrical stimulation to optic nerves with minimum mechanical side effects to the retina.

Concepts: Photon, Optics, Engineering, Finite element method, Retina, Optic nerve, Photonics, Torsion


The mechanical flexibility of coordination frameworks can lead to a range of highly anomalous structural behaviours. Here, we demonstrate the extreme compressibility of the LnFe(CN)6 frameworks (Ln = Ho, Lu or Y), which reversibly compress by 20% in volume under the relatively low pressure of 1 GPa, one of the largest known pressure responses for any crystalline material. We delineate in detail the mechanism for this high compressibility, where the LnN6 units act like torsion springs synchronized by rigid Fe(CN)6 units performing the role of gears. The materials also show significant negative linear compressibility via a cam-like effect. The torsional mechanism is fundamentally distinct from the deformation mechanisms prevalent in other flexible solids and relies on competition between locally unstable metal coordination geometries and the constraints of the framework connectivity, a discovery that has implications for the strategic design of new materials with exceptional mechanical properties.

Concepts: Crystal, Torque, Thermodynamics, Metal, Materials science, Pressure, Torsion, Torsion spring


Football turf is increasingly used in European soccer competition. Little is known on the rotational torque that players experience on these fields. High rotational torques between the shoe outsole and the sports surface has been correlated with torsional injuries of the lower limb and knee.

Concepts: Angular momentum, Torque, Rotation, Shoe, Moment of inertia, Artificial turf, Torsion, Torque tester


In this paper, a support stiffness monitoring scheme based on torsional guided waves for detecting loss of rigidity in a support of cylindrical structures is presented. Poor support performance in cylindrical specimens such as a pipeline setup located in a sloping terrain may produce a risky operation condition in terms of the installation integrity and the possibility of human casualties. The effects of changing the contact forces between support and the waveguide have been investigated by considering variations in the load between them. Fundamental torsional T ( 0 , 1 ) mode is produced and launched by a magnetostrictive collar in a pitch-catch configuration to study the support effect in the wavepacket propagation. Several scenarios are studied by emulating an abnormal condition in the support of a dedicated test bench. Numerical results revealed T ( 0 , 1 ) ultrasonic energy leakage in the form of S H 0 bulk waves when a mechanical coupling between the cylindrical waveguide and support is yielded. Experimental results showed that the rate of ultrasonic energy leakage depends on the magnitude of the reaction forces between pipe and support; so different levels of attenuation of T ( 0 , 1 ) mode will be produced with different mechanical contact conditions. Thus, it is possible to relate a measured attenuation to variations in the supports condition. Results of each scenarios are presented and discussed demonstrating the feasibility and potential of tracking of the amplitude of the T ( 0 , 1 ) as an indicator of abnormal conditions in simple supports.

Concepts: Quantum mechanics, Coupling, Torque, Force, Classical mechanics, Support, Torsion, Possibility