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Concept: Structural analysis


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 mechanical properties of individual multiwall boron nitride nanotubes (MWBNNTs) synthesized by a growth-vapor-trapping chemical vapor deposition method are investigated by a three-point bending technique via atomic force microscopy. Multiple locations on suspended tubes are probed in order to determine the boundary conditions of the supported tube ends. The bending moduli (E(B)) calculated for 20 tubes with diameters ranging from 18 to 58 nm confirm the exceptional mechanical properties of MWBNNTs, with an average E(B) of 760 ± 30 GPa. For the first time, the bending moduli of MWBNNTs are observed to increase with decreasing diameter, ranging from 100 ± 20 GPa to as high as 1800 ± 300 GPa. This diameter dependence is evaluated by Timoshenko beam theory. The Young’s modulus and shear modulus were determined to be 1800 ± 300 and 7 ± 1 GPa, respectively, for a trimmed data set of 16 tubes. The low shear modulus of MWBNNTs is the reason for the detected diameter-dependent bending modulus and is likely due to the presence of interwall shearing between the crystalline and faceted helical nanotube structures of MWBNNTs.

Concepts: Continuum mechanics, Shear stress, Chemical vapor deposition, Young's modulus, Elasticity, Shear strength, Boron nitride, Structural analysis


BACKGROUND: This study aims to clarify the effect of various designs of reverse shoulder prosthesis (RSP) on stress variation of its glenoid component using 2-dimensional (2D) finite element analysis (FEA). This FEA study provides future reference for the optimal design of glenoid component of RSP. MATERIALS AND METHODS: In this study, a 2D finite element (FE) model of human shoulder with implementation of RSP was developed by commercial FE software. The proper material properties were adopted in our model. Various design factors were simulated and all the mechanical profile data were investigated by FEA. RESULTS: Both distal placement and increased lateral offset of glenosphere induce higher stress over glenoid-baseplate junction. Increased thickness of graft, inferiorly tilting of the baseplate, and adoption of BIO-RSA (bony increased-offset reverse shoulder arthroplasty) incur higher stresses over glenoid screws. The inferior screw attains more stress than superior screw. Maximum stress occurs at the base of inferior screw. CONCLUSION: Increased eccentric offset and lateral offset of glenosphere, although being able to reduce notching, may pay the penalty of significant stress concentration over glenoid and its subsequent loosening. Maximum stress occurs at the base of inferior screw elucidate the direct contact failure mode at the middle of inferior screw. This study provides an alternative tool for the optimal design of glenoid component of RSP in the future.

Concepts: Engineering, Finite element method, Hilbert space, Shoulder, Partial differential equation, Finite element method in structural mechanics, Structural analysis


Surgical replacement of the pulmonary valve (PV) is a common treatment option for congenital pulmonary valve defects. Engineered tissue approaches to develop novel PV replacements are intrinsically complex, and will require methodical approaches for their development. Single leaflet replacement utilizing an ovine model is an attractive approach in that candidate materials can be evaluated under valve level stresses in blood contact without the confounding effects of a particular valve design. In the present study an approach for optimal leaflet shape design based on finite element (FE) simulation of a mechanically anisotropic, elastomeric scaffold for PV replacement is presented. The scaffold was modeled as an orthotropic hyperelastic material using a generalized Fung-type constitutive model. The optimal shape of the fully loaded PV replacement leaflet was systematically determined by minimizing the difference between the deformed shape obtained from FE simulation and an ex-vivo microCT scan of a native ovine PV leaflet. Effects of material anisotropy, dimensional changes of PV root, and fiber orientation on the resulting leaflet deformation were investigated. In-situ validation demonstrated that the approach could guide the design of the leaflet shape for PV replacement surgery.

Concepts: Blood, Engineering, Continuum mechanics, Materials science, Young's modulus, Valves, Structural analysis, Constitutive equation


Mechanobiology relates cellular processes to mechanical signals, such as determining the effect of variations in matrix stiffness with cell tractions. Cell traction recorded via traction force microscopy (TFM) commonly takes place on materials such as polyacrylamide- and polyethylene glycol-based gels. Such experiments remain limited in physiological relevance because cells natively migrate within complex tissue microenvironments that are spatially heterogeneous and hierarchical. Yet, TFM requires determination of the matrix constitutive law (stress-strain relationship), which is not always readily available. In addition, the currently achievable displacement resolution limits the accuracy of TFM for relatively small cells. To overcome these limitations, and increase the physiological relevance of in vitro experimental design, we present a new approach and a set of associated biomechanical signatures that are based purely on measurements of the matrix’s displacements without requiring any knowledge of its constitutive laws. We show that our mean deformation metrics (MDM) approach can provide significant biophysical information without the need to explicitly determine cell tractions. In the process of demonstrating the use of our MDM approach, we succeeded in expanding the capability of our displacement measurement technique such that it can now measure the 3D deformations around relatively small cells (∼10 micrometers), such as neutrophils. Furthermore, we also report previously unseen deformation patterns generated by motile neutrophils in 3D collagen gels.

Concepts: Protein, Measurement, Experiment, Young's modulus, Elasticity, Robert Hooke, Structural analysis, Constitutive equation


It has long been recognized that aortic root elasticity helps to ensure efficient aortic valve closure, but our understanding of the functional importance of the elasticity and geometry of the aortic root continues to e-volve as increasingly detailed in vivo imaging data become available. Herein, we describe a fluid-structure interaction model of the aortic root, including the aortic valve leaflets, the sinsuses of Valsalva, the aortic annulus, and the sinotubular junction, that employs a version of Peskin’s immersed boundary (IB) method with a finite element (FE) description of the structural elasticity. As in earlier work, we use a fiber-based model of the valve leaflets, but this study extends earlier IB models of the aortic root by employing an incompressible hyperelastic model of the mechanics of the sinuses and ascending aorta using a constitutive law fit to experimental data from human aortic root tissue. In vivo pressure loading is accounted for by a backward displacement method that determines the unloaded configurations of the root model. Our model yields realistic cardiac output at physiological pressures, with low transvalvular pressure differences during forward flow, minimal regurgitation during valve closure, and realistic pressure loads when the valve is closed during diastole. Further, results from high-resolution computations indicate that although the detailed leaflet and root kinematics show some grid sensitivity, our IB model of the aortic root nonetheless produces essentially grid-converged flow rates and pressures at practical grid spacings for the high-Reynolds number flows of the aortic root. These results thereby clarify minimum grid resolutions required by such models when used as stand-alone models of the aortic valve as well as when used to provide models of the outflow valves in models of left ventricular fluid dynamics.

Concepts: Heart, Fluid dynamics, Aorta, Ascending aorta, Left ventricle, Arteries of the thorax, Aortic valve, Structural analysis


Reducing the energetic cost of running seems the most feasible path to a sub-2-hour marathon. Footwear mass, cushioning, and bending stiffness each affect the energetic cost of running. Recently, prototype running shoes were developed that combine a new highly compliant and resilient midsole material with a stiff embedded plate.

Concepts: Classical mechanics, Elasticity, Elastic modulus, Shoe, Footwear, Hardness, Structural analysis, Athletic shoe


Assessing the condition of the alveolar bone before and after orthodontic treatment is important. Recently, cone-beam computed tomography has been widely accepted as a useful tool for orthodontic treatment. Moreover, using a three-dimensional (3D) structural analysis software enables gathering detailed information and quantifying data. The aim of this study was to introduce various quantitative analyses performed before and after orthodontic treatment by using a 3D structural analysis software for evaluating the morphological condition of the alveolar bone of a patient with gingival recession around the canines.

Concepts: Scientific method, Research methods, Mathematical analysis, Analysis, Orthodontics, Structural analysis


Quasi-one-dimensional microtubules (MTs) in cells enjoy high axial rigidity but large transverse flexibility due to the inter-protofilament (PF) sliding. This study aims to explore the structure-property relation for MTs and examine the relevance of the beam theories to their unique features. A molecular structural mechanics (MSM) model was used to identify the origin of the inter-PF sliding and its role in bending and vibration of MTs. The beam models were then fitted to the MSM to reveal how they cope with the distinct mechanical responses induced by the inter-PF sliding. Clear evidence showed that the inter-PF sliding is due to the soft inter-PF bonds and leads to the length-dependent bending stiffness. The Euler beam theory is found to adequately describe MT deformation when the inter-PF sliding is largely prohibited. Nevertheless, neither shear deformation nor the nonlocal effect considered in the ‘more accurate’ beam theories can fully capture the effect of the inter-PF sliding. This reflects the distinct deformation mechanisms between an MT and its equivalent continuous body.

Concepts: Continuum mechanics, Mechanical engineering, Elasticity, Solid mechanics, Mechanics, Beam, Deformation, Structural analysis


The momentum and heat transport in rarefied gas flows is known to deviate from the classical laws of Navier and Fourier in Navier-Stokes-Fourier (NSF) equations. A more sophisticated Nonlinear Coupled Constitutive Model (NCCM) has been derived from the Boltzmann equation to describe gaseous and thermal transport both in continuum and rarefied gas flows. We first develop a unified numerical framework for modeling continuum and rarefied flows based on the NCCM model both in two and three dimensions. Special treatment is given to the complex highly nonlinear transport equations for non-conserved variables that arise from the high degree of thermal nonequilibrium. For verification and validation, we apply the present scheme to a stiff problem of hypersonic gas flows around a 2D cylinder, a 3D sphere, and the Apollo configuration both in continuum and rarefied situations. The results show that the present unified framework yields solutions that are in better agreement with the benchmark and experimental data than are the NSF results in all studied cases of rarefied problems. Good agreement is observed between the present study and the NSF results for continuum cases. The results show that this study provides a unified framework for modeling continuum and rarefied gas flows.

Concepts: Fundamental physics concepts, Temperature, Thermodynamics, Classical mechanics, Equations, Structural analysis, Verification and validation