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Concept: Beam


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


The mathematical modelling of column buckling or beam bending under an axial or transverse load is well established. However, the existent models generally assume a high degree of symmetry in the structure of the column and minor longitudinal and transverse displacements. The situation when the column is made of several components with different mechanical properties asymmetrically distributed in the transverse section, semi-rigid, and subjected to multiple axial loads with significant longitudinal and transverse displacements through compression and bending has not been well characterised. A more comprehensive theoretical model allowing for these possibilities and assuming a circular arc contour for the bend is developed, and used to establish the bending axes, balance between compression and bending, and equivalent stiffness of the column. In certain situations, such as with pull cable catheters commonly used for minimally invasive surgical procedures, the compression loads are applied via cables running through channels inside a semi-rigid column. The model predicts the mathematical relationships between the radius of curvature of the bend and the tension in and normal force exerted by such cables. Conjugate extension with reciprocal compression-bending is a special structural arrangement for a semi-rigid column such that extension of one segment is linked to compression-bending of another by inextensible cables running between them. Leads are cords containing insulated electrical conductor coil and cables between the heart muscle and cardiac implantable electronic devices. Leads can behave like pull cable catheters through differential component pulling, providing a possible mechanism for inside-out abrasion and conductor cable externalisation. Certain design features may predispose to this mode of structural failure.

Concepts: Force, Structural engineering, Beam, Column, Bending, Buckling, Skin effect, Truss


Microcantilever biosensors in the static operation mode translate molecular recognition into a surface stress signal. Surface stress is derived from the nanomechanical cantilever bending by applying Stoney’s equation, derived more than 100 years ago. This equation ignores the clamping effect on the cantilever deformation, which induces significant errors in the quantification of the biosensing response. This leads to discrepancies in the surface stress induced by biomolecular interactions in measurements with cantilevers with different sizes and geometries. So far, more accurate solutions have been precluded by the formidable complexity of the theoretical problem that involves solving the two-dimensional biharmonic equation. In this paper, we present an accurate and simple analytical expression to quantify the response of microcantilever biosensors. The equation exhibits an excellent agreement with finite element simulations and DNA immobilization experiments on gold-coated microcantilevers.

Concepts: Linear elasticity, Cantilever, Beam, Cantilever bridge, Fallingwater


RGO flakes are homogeneously dispersed in a Cu matrix through a molecular-level mixing process. This novel fabrication process prevents the agglomeration of the RGO and enhances adhesion between the RGO and the Cu. The yield strength of the 2.5 vol% RGO/Cu nanocomposite is 1.8 times higher than that of pure Cu. The strengthening mechanism of the RGO is investigated by a double cantilever beam test using the graphene/Cu model structure.

Concepts: Tensile strength, Solid mechanics, Cantilever, Beam, Ultimate failure


This paper presents a platform combining an inverse electromagnetic design computational method with additive manufacturing to design and fabricate all-dielectric metadevices. As opposed to conventional flat metasurface-based devices that are composed of resonant building blocks resulting in narrow band operation, the proposed design approach creates non-resonant, broadband (Δλ/λ up to >50%) metadevices based on low-index dielectric materials. High-efficiency (transmission >60%), thin (≤2λ) metadevices capable of polarization splitting, beam bending, and focusing are proposed. Experimental demonstrations are performed at millimeter-wave frequencies using 3D-printed devices. The proposed platform can be readily applied to the design and fabrication of electromagnetic and photonic metadevices spanning microwave to optical frequencies.

Concepts: Optics, Fundamental physics concepts, Electromagnetic radiation, Maxwell's equations, Metamaterial, Radio, Beam, Dielectric


Flexoelectricity allows a dielectric material to polarize in response to a mechanical bending moment and, conversely, to bend in response to an electric field. Compared with piezoelectricity, flexoelectricity is a weak effect of little practical significance in bulk materials. However, the roles can be reversed at the nanoscale. Here, we demonstrate that flexoelectricity is a viable route to lead-free microelectromechanical and nanoelectromechanical systems. Specifically, we have fabricated a silicon-compatible thin-film cantilever actuator with a single flexoelectrically active layer of strontium titanate with a figure of merit (curvature divided by electric field) of 3.33 MV(-1), comparable to that of state-of-the-art piezoelectric bimorph cantilevers.

Concepts: Nanotechnology, Materials science, Atomic force microscopy, Microelectromechanical systems, Piezoelectricity, Beam, Second moment of area, Nanoelectromechanical systems


Engineered cartilage is a promising option for auricular reconstruction. We have previously demonstrated that a titanium wire framework within a composite collagen ear-shaped scaffold helped to maintain the gross dimensions of the engineered ear after implantation, resisting the deformation forces encountered during neocartilage maturation and wound healing. The ear geometry was redesigned to achieve a more accurate aesthetic result when implanted subcutaneously in a nude rat model. A non-invasive method was developed to assess size and shape changes of the engineered ear in three dimensions. Computer models of the titanium framework were obtained from CT scans before and after implantation. Several parameters were measured including the overall length, width and depth, the minimum intrahelical distance and overall curvature values for each beam section within the framework. Local curvature values were measured to gain understanding of the bending forces experienced by the framework structure in situ. Length and width changed by less than 2%, whereas the depth decreased by approximately 8% and the minimum intrahelical distance changed by approximately 12%. Overall curvature changes identified regions most susceptible to deformation. Eighty-nine per cent of local curvature measurements experienced a bending moment less than 50 µN-m owing to deformation forces during implantation. These quantitative shape analysis results have identified opportunities to improve shape fidelity of engineered ear constructs.

Concepts: Dimension, Euclidean space, Depth perception, Units of measurement, Height, Length, Distance, Beam


In this paper, we present a technique for increasing the strength of thermoplastic fused deposition manufactured printed parts while retaining the benefits of the process such as ease, speed of implementation, and complex part geometries. By carefully placing voids in the printed parts and filling them with high-strength resins, we can improve the overall part strength and stiffness by up to 45% and 25%, respectively. We discuss the process parameters necessary to use this strengthening technique and the theoretically possible strength improvements to bending beam members. We then show three-point bend testing data comparing solid printed ABS samples with those strengthened through the fill compositing process, as well as examples of 3D printed parts used in real-world applications.

Concepts: Elasticity, Solid mechanics, Beam, Second moment of area, Bending, Statics, Buckling, Truss


We explore and exploit diffraction effects that have been previously neglected when modelling optical measurement techniques for the bending of micro-mechanical transducers such as cantilevers for atomic force microscopy. The illumination of a cantilever edge causes an asymmetric diffraction pattern at the photo-detector affecting the calibration of the measured signal in the popular optical beam deflection technique (OBDT). The conditions that avoid such detection artefacts conflict with the use of smaller cantilevers. Embracing diffraction patterns as data yields a potent detection technique that decouples tilt and curvature and simultaneously relaxes the requirements on the illumination alignment and detector position through a measurable which is invariant to translation and rotation. We show analytical results, numerical simulations and physiologically relevant experimental data demonstrating the utility of the diffraction patterns. We offer experimental design guidelines and quantify possible sources of systematic error in OBDT. We demonstrate a new nanometre resolution detection method that can replace OBDT, where diffraction effects from finite sized or patterned cantilevers are exploited. Such effects are readily generalized to cantilever arrays, and allow transmission detection of mechanical curvature, enabling instrumentation with simpler geometry. We highlight the comparative advantages over OBDT by detecting molecular activity of antibiotic Vancomycin.

Concepts: Diffraction, Optics, Measurement, Wavelength, Pattern, Atomic force microscopy, Cantilever, Beam


Fifth metatarsal base fractures of the metaphyseal-diaphyseal watershed junction (Jones fracture) are commonly treated with surgical fixation in athletes. Intramedullary screw fixation remains the most utilized construct, although plantar-lateral plating is an alternative. Purpose/Hypothesis: The purpose was to compare the mechanical strength of fracture fixation between an intramedullary screw and plantar-lateral plating. The hypothesis was that plantar-lateral plate fixation would allow for more cycles and higher peak loads before failure, as well as less fracture gapping, than would an intramedullary screw in cadaveric foot specimens with simulated Jones fractures exposed to cantilever bending.

Concepts: Bone, Fracture mechanics, Materials science, Solid mechanics, Forensic engineering, Beam, Statics, Buckling