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Concept: Polar moment of inertia


The combined influence of cyclic fatigue and torsional stress on rotary nickel-titanium instruments has been little investigated. The aim of this study was to determine possible differences in the fracture point of rotary nickel-titanium instruments depending on the application of cyclic fatigue only (CO) or in combination with torsional stress (CT).

Concepts: Fracture mechanics, Elasticity, Mechanics, Polar moment of inertia


We developed an innovative non-fusion correction system (XS LATOR) consisting of two individual implants that are extendable and extremely flexible. One implant, the XS LAT, generates a lateral, bending moment and one implant, the XS TOR, generates a torsion moment. Two ‘inverse’ implants were developed for generating torsion and lateral bending in a porcine model was tested for force delivery. An in vitro experiment was set up to describe the mechanical behavior of both implants.

Concepts: Torque, Force, In vitro, Group, Second moment of area, Polar moment of inertia


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


In aggressive battles, the extremely large male stag beetle jaws have to withstand strongly elevated bite forces. We found several adaptations of the male Cyclommatus metallifer jaw morphology for enhanced robustness that conspecific females lack. As a result, males improve their grip on opponents and they maintain their safety factor (5.2-7.2) at the same level as that of females (6.8), despite their strongly elevated bite muscle force (3.9 times stronger). Males have a higher second moment of area and torsion constant than females, owing to an enhanced cross-sectional area and shape. These parameters also increase faster with increasing bending moment towards the jaw base in males than in females. Male jaws are more bending resistant against the bite reaction force than against perpendicular forces (which remain lower in battles). Because of the triangular cross section of the male jaw base, it twists more easily than it bends. This torsional flexibility creates a safety system against overload that, at the same time, secures a firm grip on rivals. We found no structural mechanical function of the large teeth halfway along the male jaws. Therefore, it appears that the main purpose of these teeth is a further improvement of grip on rivals.

Concepts: Physics, Torque, Force, Classical mechanics, Reaction, Second moment of area, Polar moment of inertia, Stag beetle


Cortical bone porosity and specifically the orientation of vascular canals is an area of growing interest in biomedical research and comparative/paleontological anatomy. The potential to explain microstructural adaptation is of great interest. However, the determinants of the development of canal orientation remain unclear. Previous studies of birds have shown higher proportions of circumferential canals (called laminarity) in flight bones than in hindlimb bones, and interpreted this as a sign that circumferential canals are a feature for resistance to the torsional loading created by flight. We defined the laminarity index as the percentage of circumferential canal length out of the total canal length. In this study we examined the vascular canal network in the humerus and femur of a sample of 31 bird and 24 bat species using synchrotron micro-computed tomography (micro-CT) to look for a connection between canal orientation and functional loading. The use of micro-CT provides a full three-dimensional (3D) map of the vascular canal network and provides measurements of the 3D orientation of each canal in the whole cross-section of the bone cortex. We measured several cross-sectional geometric parameters and strength indices including principal and polar area moments of inertia, principal and polar section moduli, circularity, buckling ratio, and a weighted cortical thickness index. We found that bat cortices are relatively thicker and poorly vascularized, whereas those of birds are thinner and more highly vascularized, and that according to our cross-sectional geometric parameters, bird bones have a greater resistance to torsional stress than the bats; in particular, the humerus in birds is more adapted to resist torsional stresses than the femur. Our results show that birds have a significantly (P = 0.031) higher laminarity index than bats, with birds having a mean laminarity index of 0.183 in the humerus and 0.232 in the femur, and bats having a mean laminarity index of 0.118 in the humerus and 0.119 in the femur. Counter to our expectation, the birds had a significantly higher laminarity index in the femur than in the humerus (P = 0.035). To evaluate whether this discrepancy was a consequence of methodology we conducted a comparison between our 3D method and an analogue to two-dimensional (2D) histological measurements. This comparison revealed that 2D methods significantly underestimate (P < 0.001) the amount of longitudinal canals by an average of 20% and significantly overestimate (P < 0.001) the laminarity index by an average of 7.7%, systematically mis-estimating indices of vascular canal orientations. In comparison with our 3D results, our approximated 2D measurement had the same results for comparisons between the birds and bats but found significant differences only in the longitudinal index between the humerus and the femur for both groups. The differences between our 3D and pseudo-2D results indicate that differences between our findings and the literature may be partially based in methodology. Overall, our results do not support the hypothesis that the bones of flight are more laminar, suggesting a complex relation between functional loading and microstructural adaptation.

Concepts: Bone, Measurement, Cerebral cortex, Cortical bone, Bat, Flying and gliding animals, Canals of the United Kingdom, Polar moment of inertia


In order to solve the supporting problem in underground engineering with high stress, square steel confined concrete (SQCC) supporting method is adopted to enhance the control on surrounding rocks, and the control effect is remarkable. The commonly used cross section shapes of confined concrete arch are square and circular. At present, designers have no consensus on which kind is more proper. To search for the answer, this paper makes an analysis on the mechanical properties of the two shapes of the cross-sections. A full-scale indoor comparative test was carried out on the commonly used straight-wall semi-circular SQCC arch and circular steel confined concrete arch (CCC arch). This test is based on self-developed full-scale test system for confined concrete arch. Our research, combining with the numerical analysis, shows: (1) SQCC arch is consistent with CCC arch in the deformation and failure mode. The largest damages parts are at the legs of both of them. (2) The SQCC arch’s bearing capability is 1286.9 kN, and the CCC arch’s ultimate bearing capability is 1072.4kN. Thus, the SQCC arch’s bearing capability is 1.2 times that of the CCC arch. (3) The arches are subjected to combined compression and bending, bending moment is the main reason for the arch failure. The section moment of inertia of SQCC arch is 1.26 times of that of CCC arch, and the former is better than the latter in bending performance. The ultimate bearing capacity is positively correlated with the size of the moment of inertia. Based on the above research, the engineering suggestions are as follows: (1) To improve the bearing capacity of the arch, the cross-sectional shape of the chamber should be optimized and the arch bearing mode changed accordingly. (2) The key damaged positions, such as the arch leg, should be reinforced, optimizing the state of force on the arch. SQCC arches should be used for supporting in underground engineering, which is under stronger influence of the bending moment and non-uniform load on the supporting arches. The research results could provide a theoretical basis for the design of confined concrete support in underground engineering.

Concepts: Torque, Force, Moment of inertia, Second moment of area, Inertia, Arch, Polar moment of inertia, Bearing capacity


During walking, the friction between the foot and the ground surface causes a free moment (FM), which influences the torsional stress on the lower extremity. However, few studies have investigated the FM during natural walking. The main aim of this study was to examine the relationship between the FM and the absolute and relative rotation angles of the foot and pelvis.

Concepts: Angular momentum, Torque, Group, Classical mechanics, Metaphysics, Mechanics, Theology, Polar moment of inertia


Unlike conventional steel strands, the smart strand supports strain-measuring function and adopts different materials for its core wire and helical wires. This study intends to analytically derive the nonlinear stress-strain model of this strand made of two materials. The effect of the bending moment and torsional moment of the helical wires on the overall load within the range of geometric shapes shown by actually used strands is verified to be negligible and is thus ignored in order to simplify the analytical model. Moreover, the slight difference between the actual and analytic behaviors, which only appears in the slope varying part in the case of bilinear behavior, such as that of steel, is also ignored. The proposed constitutive model of the smart strand obtained by introducing the experimental stress-strain relation between the carbon fiber reinforced polymer core wire and the helical steel wires is in good agreement with the experimental data. The previous analytical models are applicable only to strands made of a unique linear material, whereas the model proposed in this study is also applicable to strands in which the core wire and the helical wires are made of two different materials, exhibiting nonlinear behavior.

Concepts: Function, Torque, Elasticity, Wire, Second moment of area, Analytic philosophy, Polar moment of inertia, Analytic


The objectives of this study were to describe fracture morphology resulting from common loading mechanisms such as bending and torsion in immature bone and to identify differences in the energy required to produce various fracture types under these two loading mechanisms using an immature porcine animal model.

Concepts: Bone, Hip fracture, Torque, Mechanics, Torsion, Polar moment of inertia


High failure rates of Peripheral Arterial Disease (PAD) stenting appear to be associated with the inability of certain stent designs to accommodate severe biomechanical environment of the femoropopliteal artery (FPA) that bends, twists, and axially compresses during limb flexion. Twelve Nitinol stents (Absolute Pro, Supera, Lifestent, Innova, Zilver, Smart Control, Smart Flex, EverFlex, Viabahn, Tigris, Misago, and Complete SE) were quasi-statically tested under bench-top axial and radial compression, axial tension, bending, and torsional deformations. Stents were compared in terms of force-strain behavior, stiffness, and geometrical shape under each deformation mode. Tigris was the least stiff stent under axial compression (6.6N/m axial stiffness) and bending (0.1N/m) deformations, while Smart Control was the stiffest (575.3N/m and 105.4N/m, respectively). Under radial compression Complete SE was the stiffest (892.8N/m), while Smart Control had the lowest radial stiffness (211.0N/m). Viabahn and Supera had the lowest and highest torsional stiffness (2.2μNm/° and 959.2μNm/°), respectively. None of the 12 PAD stents demonstrated superior characteristics under all deformation modes and many experienced global buckling and diameter pinching. Though it is yet to be determined which of these deformation modes might have greater clinical impact, results of the current analysis may help guide development of new stents with improved mechanical characteristics.

Concepts: Cardiology, Stent, Young's modulus, Elasticity, Solid mechanics, Stiffness, Deformation, Polar moment of inertia