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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


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


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


The present contribution focuses on the application of the multiscale finite element method to the modeling of actin networks which are embedded in the cytosol. These cell components are of particular importance with regard to the cell response to external stimuli. The homogenization strategy chosen uses the Hill-Mandel macro-homogeneity condition for bridging two scales: the macroscopic scale which is related to the cell level, and the microscopic scale related to the representative volume element. For the modeling of filaments, the Holzapfel-Ogden β-model is applied. It provides a relationship between the tensile force and the caused stretches, serves as the basis for the derivation of the stress and elasticity tensors and enables a novel finite element implementation. The elements with the neo-Hookean constitutive law are applied for the simulation of the cytosol. The results presented corroborate the main advantage of the concept, namely its flexibility with regard to the choice of the representative volume element as well as of macroscopic tests. The focus is particularly placed on the study of the filament orientation and of its influence on the effective behavior. This article is protected by copyright. All rights reserved.

Concepts: Fundamental physics concepts, Engineering, Finite element method, Elasticity, Abstraction, All rights reserved, Copyright, Structural analysis


This work deals with the structural analysis of screw clamps for external fixator devices. Screw clamps are widely used in external fixators as a means to connect the half-pins to the fixator body. The analysis is carried out by both numerical and experimental techniques, based on the case study of a clamp produced by Citieffe (Bologna, Italy). As a preliminary activity, the tribological parameters involved in the screw-clamp interaction have been characterized by means of a mixed finite element analysis and experimental procedure. Then, an assessment of the current design of the clamp has been carried out. A re-design has been proposed, which, based on some targeted geometrical modifications, allows achieving higher strength requirements with the same overall dimensions and type of materials. A higher load-bearing capability for a given size may allow the fixator to be used on a broader population. Finally, a list of good practices for the design of this kind of clamps has been proposed.

Concepts: Evaluation methods, Finite element method, Hilbert space, Partial differential equation, Numerical analysis, Finite element method in structural mechanics, External fixation, Structural analysis


Material properties of the human tongue tissue have a significant role in understanding its function in speech, respiration, suckling, and swallowing. Tongue as a combination of various muscles is surrounded by the mucous membrane and is a complicated architecture to study. As a first step before the quantitative mechanical characterization of human tongue tissues, the passive biomechanical properties in the superior longitudinal muscle (SLM) and the mucous tissues of a bovine tongue have been measured. Since the rate of loading has a sizeable contribution to the resultant stress of soft tissues, the rate dependent behavior of tongue tissues has been investigated via uniaxial tension tests (UTTs). A method to determine the mechanical properties of transversely isotropic tissues using UTTs and inverse finite element (FE) method has been proposed. Assuming the strain energy as a general nonlinear relationship with respect to the stretch and the rate of stretch, two visco-hyperelastic constitutive laws (CLs) have been proposed for isotropic and transversely isotropic soft tissues to model their stress-stretch behavior. Both of them have been implemented in ABAQUS explicit through coding a user-defined material subroutine called VUMAT and the experimental stress-stretch points have been well tracked by the results of FE analyses. It has been demonstrated that the proposed laws make a good description of the viscous nature of tongue tissues. Reliability of the proposed models has been compared with similar nonlinear visco-hyperelastic CLs.

Concepts: Oral mucosa, Mouth, Tissues, Materials science, Elasticity, Taste bud, Structural analysis, Constitutive equation