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Concept: Finite element method


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


Soft actuators made from elastomeric active materials can find widespread potential implementation in a variety of applications ranging from assistive wearable technologies targeted at biomedical rehabilitation or assistance with activities of daily living, bioinspired and biomimetic systems, to gripping and manipulating fragile objects, and adaptable locomotion. In this manuscript, we propose a novel two-component soft actuator design and design tool that produces actuators targeted towards these applications with enhanced mechanical performance and manufacturability. Our numerical models developed using the finite element method can predict the actuator behavior at large mechanical strains to allow efficient design iterations for system optimization. Based on two distinctive actuator prototypes' (linear and bending actuators) experimental results that include free displacement and blocked-forces, we have validated the efficacy of the numerical models. The presented extensive investigation of mechanical performance for soft actuators with varying geometric parameters demonstrates the practical application of the design tool, and the robustness of the actuator hardware design, towards diverse soft robotic systems for a wide set of assistive wearable technologies, including replicating the motion of several parts of the human body.

Concepts: Failure assessment, Linear actuator, Continuum mechanics, Human body, Numerical analysis, Design, Finite element method, Engineering


Silks are remarkable materials with desirable mechanical properties, yet the fine details of natural production remain elusive and subsequently inaccessible to biomimetic strategies. Improved knowledge of the natural processes could therefore unlock development of a host of bio inspired fibre spinning systems. Here, we use the Chinese silkworm Bombyx mori to review the pressure requirements for natural spinning and discuss the limits of a biological extrusion domain. This provides a target for finite element analysis of the flow of silk proteins, with the aim of bringing the simulated and natural domains into closer alignment. Supported by two parallel routes of experimental validation, our results indicate that natural spinning is achieved, not by extruding the feedstock, but by the pulling of nascent silk fibres. This helps unravel the oft-debated question of whether silk is pushed or pulled from the animal, and provides impetus to the development of pultrusion-based biomimetic spinning devices.The natural production of silks remains elusive and subsequently inaccessible to biomimetic strategies. Here the authors show that silks cannot be spun by pushing alone, and that natural spinning is dominated by pultrusion, which provides design guidelines for future biomimetic spinning systems.

Concepts: Sericulture, Bombyx mandarina, Bombyx, Bombycidae, Finite element method, Engineering, Silk, Bombyx mori


Sintering of nanoparticle inks over large area-substrates is a key enabler for scalable fabrication of patterned and continuous films, with multiple emerging applications. The high speed and ambient condition operation of photonic sintering has elicited significant interest for this purpose. In this work, we experimentally characterize the temperature evolution and densification in photonic sintering of silver nanoparticle inks, as a function of nanoparticle size. It is shown that smaller nanoparticles result in faster densification, with lower temperatures during sintering, as compared to larger nanoparticles. Further, high densification can be achieved even without nanoparticle melting. Electromagnetic Finite Element Analysis of photonic heating is coupled to an analytical sintering model, to examine the role of interparticle neck growth in photonic sintering. It is shown that photonic sintering is an inherently self-damping process, i.e., the progress of densification reduces the magnitude of subsequent photonic heating even before full density is reached. By accounting for this phenomenon, the developed coupled model better captures the experimentally observed sintering temperature and densification as compared to conventional photonic sintering models. Further, this model is used to uncover the reason behind the experimentally observed increase in densification with increasing weight ratio of smaller to larger nanoparticles.

Concepts: Gold, Silicon, Temperature, Ceramic engineering, Heat, Finite element method, Liquid, Nanoparticle


The most stable pattern of internal fixation for fractures of the mandibular condyle is a matter for ongoing discussion. In this study we investigated the stability of three commonly used patterns of plate fixation, and constructed finite element models of a simulated mandibular condylar fracture. The completed models were heterogeneous in the distribution of bony material properties, contained about 1.2 million elements, and incorporated simulated jaw-adducting musculature. Models were run assuming linear elasticity and isotropic material properties for bone. This model was considerably larger and more complex than previous finite element models that have been used to analyse the biomechanical behaviour of differing plating techniques. The use of two parallel 2.0 titanium miniplates gave a more stable configuration with lower mean element stresses and displacements over the use of a single miniplate. In addition, a parallel orientation of two miniplates resulted in lower stresses and displacements than did the use of two miniplates in an offset pattern. The use of two parallel titanium plates resulted in a superior biomechanical result as defined by mean element stresses and relative movement between the fractured fragments in these finite element models.

Concepts: Mathematics, Materials science, Finite element method in structural mechanics, Bone fracture, Finite element method, Elasticity, Orientation, Fracture


To improve understanding of the internal structure of the proximal phalanx (P1), response of the bone to load and possible relation to the pathogenesis of fractures in P1.

Concepts: Finite element method in structural mechanics, Discrete mathematics, Set theory, Hilbert space, Partial differential equation, Finite element method


Finite element analysis is frequently used in several fields such as automotive simulations or biomechanics. It helps researchers and engineers to understand the mechanical behaviour of complex structures. The development of computer science brought the possibility to develop realistic computational models which can behave like physical ones, avoiding the difficulties and costs of experimental tests. In the framework of biomechanics, lots of FE models have been developed in the last few decades, enabling the investigation of the behaviour of the human body submitted to heavy damage such as in road traffic accidents or in ballistic impact. In both cases, the thorax/abdomen/pelvis system is frequently injured. The understanding of the behaviour of this complex system is of extreme importance. In order to explore the dynamic response of this system to impact loading, a finite element model of the human thorax/abdomen/pelvis system has, therefore, been developed including the main organs: heart, lungs, kidneys, liver, spleen, the skeleton (with vertebrae, intervertebral discs, ribs), stomach, intestines, muscles, and skin. The FE model is based on a 3D reconstruction, which has been made from medical records of anonymous patients, who have had medical scans with no relation to the present study. Several scans have been analyzed, and specific attention has been paid to the anthropometry of the reconstructed model, which can be considered as a 50th percentile male model. The biometric parameters and laws have been implemented in the dynamic FE code (Radioss, Altair Hyperworks 11©) used for dynamic simulations. Then the 50th percentile model was validated against experimental data available in the literature, in terms of deflection, force, whose curve must be in experimental corridors. However, for other anthropometries (small male or large male models) question about the validation and results of numerical accident replications can be raised.

Concepts: Heart, Computer graphics, Accidents, Human body, Engineering, Intervertebral disc, Tram accident, Finite element method


We evaluated both the outcome of using a locking plate as a definitive external fixator for treating open tibial fractures and, using finite element analysis, the biomechanical performance of external and internal metaphyseal locked plates in treating proximal tibial fractures. Eight open tibial patients were treated using a metaphyseal locked plate as a low-profile definitive external fixator. Then, finite element models of internal (IPF) as well as two different external plate fixations (EPFs) for proximal tibial fractures were reconstructed. The offset distances from the bone surface to the EPFs were 6cm and 10cm. Both axial stiffness and angular stiffness were calculated to evaluate the biomechanical performance of these three models. The mean follow-up period was 31 months (range, 18-43 months). All the fractures united and the mean bone healing time was 37.5 weeks (range, 20-52 weeks). All patients had excellent or good functional results and were walking freely at the final follow-up. The finite element finding revealed that axial stiffness and angular stiffness decreased as the offset distance from the bone surface increased. Compared to the IPF models, in the two EPF models, axial stiffness decreased by 84-94%, whereas the angular stiffness decreased by 12-21%. The locking plate used as a definitive external fixator provided a high rate of union. While the locking plate is not totally rigid, it is clinically stable and may be advisable for stiffness reduction of plating constructs, thus promoting fracture healing by callus formation. Our patients experienced a comfortable clinical course, excellent knee and ankle joint motion, satisfactory functional results and an acceptable complication rate.

Concepts: Periosteum, Direct stiffness method, Fracture, Finite element method in structural mechanics, Finite element method, Bone healing, Bone, Bone fracture


OBJECTIVES: It is still unclear whether the inlay thickness is an important factor influencing the fracture risk of ceramic inlays. As high tensile stresses increase the fracture risk of ceramic inlays, the objective of the present finite element method (FEM) study was to biomechanically analyze the correlation between inlay thickness (T) and the induced first principal stress. METHODS: 14 ceramic inlay models with varying thickness (0.7 - 2.0mm) were generated. All inlays were combined with a CAD model of a first mandibular molar (tooth 46), including the PDL and a mandibular segment which was created by means of the CT data of an anatomical specimen. Two materials were defined for the ceramic inlays (e.max(®) or empress(®)) and an occlusal force of 100N was applied. The first principal stress was measured within each inlay and the peak values were considered and statistically analyzed. RESULTS: The stress medians ranged from 20.7MPa to 22.1MPa in e.max(®) and from 27.6MPa to 29.2MPa in empress(®) inlays. A relevant correlation between the first principal stress and thickness (T) could not be detected, neither for e.max(®) (Spearman: r=0.028, p=0.001), nor for empress(®) (Spearman: r=0.010, p=0.221). In contrast, a very significant difference (p<0.001) between the two inlay materials (M) was verified. CONCLUSIONS: Under the conditions of the present FEM study, the inlay thickness does not seem to be an important factor influencing the fracture risk of ceramic inlays. However, further studies are necessary to confirm this.

Concepts: Inlay, Correlation does not imply causation, Factor analysis, Materials science, Statistics, Spearman's rank correlation coefficient, Teeth, Finite element method


ObjectivesLoosening and loss rates of monocortical mini-implants are relatively high, therefore the following null hypothesis was tested: ‘The local bone stress in mono and bicortically-anchored mini-implants is identical’.Material and MethodsAnisotropic Finite Element Method (FEM) models of the mandibular bone, including teeth, periodontal ligaments, orthodontic braces, and mini-implants of varying length, were created. The morphology was based on the Computed Tomography data of an anatomical preparation. All mini-implants with varying insertion depths (monocortical short, monocortical long, bicortical) were typically loaded, and the induced effective stress was calculated in the cervical area of the cortical bone. The obtained values were subsequently analysed descriptively and exploratively using the SPSS 19.0 software.ResultsThe null hypothesis was rejected, since the stress values of each anchorage type differed significantly (Kruskal-Wallis Test, P < 0.001). Therefore, the lowest effective stress values were induced in bicortical anchorage (mean = 0.65MPa, SD = 0.06MPa) and the highest were induced in monocortical (short) anchorage of the mini-implants (mean = 1.79MPa, SD = 0.29MPa). The Spearman rank correlation was 0.821 (P < 0.001).ConclusionsThe deeper the mini-implant was anchored, the lower were the effective stress values in the cervical region of the cortical bone. Bicortical implant anchorage is biomechanically more favourable than monocortical anchorage; therefore, bicortical anchorage should be especially considered in challenging clinical situations requiring heavy anchorage.

Concepts: Finite element method in structural mechanics, Orthodontics, Statistical tests, Null hypothesis, Spearman's rank correlation coefficient, Non-parametric statistics, Finite element method