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The transient deformation of liquid capsules enclosed by elastic membranes in two-dimensional extensional flow is studied numerically, using an improved immersed boundary-lattice Boltzmann method. The purpose of the present study is to investigate the effect of interfacial bending stiffness on the deformation of such capsules, under the subcritical elasticity capillary number conditions. The present model can simulate flow-induced deformation of capsules with arbitrary resting shapes (concerning the in-plane tension) and bending-free configurations. The deformation of capsules with initially circular, elliptical, and biconcave resting shapes was investigated in the present study; the capsules' bending-free configurations were considered as either circular shapes or their initially resting shapes. The results show that for capsules with bending-free configuration as circles, membrane bending rigidity has significant rounding effect on the steady deformed profiles. For elliptical and biconcave capsules with resting shapes as the bending-free configurations, it is found that with the bending stiffness increasing, the capsules' steady shapes are more akin to their initial shapes.

This paper considers the discontinuous characteristics of a real aero-engine rotor system, that is, the existence of bolted connection characteristics, and establishes a new bolted connection rotor system model. Taking into account the bending stiffness and the nonlinear Hertzian contact force of the rolling bearing, the Newmark-$\beta$ numerical method is used to solve the system response, and the influence of the bending stiffness on the system is studied. Moreover, the effects of bending stiffness and eccentricity on the system dynamics are analyzed. The results show that the nonlinear phenomena of the system are more abundant and the critical speed of the system is higher when the bending stiffness is involved. With the increase of bending stiffness, the critical speed of the system increases, and the frequency component of the system becomes more complex. Then, the influence of eccentricity on the system is studied based on the bending stiffness. It is found that the greater the eccentricity, the greater the critical speed of the rotor and the greater the amplitude of the main frequency. In the case of the same eccentricity, the main frequency increases as the rotational speed increases, and the frequency doubling component appears in the 2-period motion. This paper provides a basis for predicting the nonlinear response of bolted rotor-bearing system.

This research study aimed to measure the bending stiffness of the lumbar spine when subjected to posteroanterior mobilization. The lumbar spine was modeled as an initially curved beam column supported over the rib cage and the pelvis. Together with the posteroanterior mobilization force acted on the spine formed the three-point bending of the beam. The bending stiffness of the spine was derived from the mobilization force and the change in curvature of the spine. The mobilization force was measured by mounting a force plate onto the mobilization couch, and electromagnetic sensors were used to measure the change in spinal curvature. The mean bending stiffness of the spine was found to be 38.5 Nm². The theoretical modelling suggested that the pelvic rotation produced by mobilization may be employed to provide an indicator of the magnitude of the mobilization force.

The bending stiffness of footwear impacts running efficiency and lower-limb work redistribution. However, studies integrating both aspects are scarce. This study aimed to examine the impact of footwear stiffness on lower-limb biomechanics, joint work, and overall metabolic efficiency. This study was performed on 12 male recreational runners to complete an experimental protocol while wearing two different running shoes with varying degrees of longitudinal bending stiffness. Paired-sample t tests were applied in this research. The stiffer footwear decreased the range of motion (ROM), angular velocity, negative and positive work of the metatarsophalangeal (MTP) joint, and ROM of the ankle joint. The running economy significantly improved with the stiffer footwear. However, no significant difference was observed in the joint work of other lower limbs. Shoes with increased bending stiffness significantly reduced the MTP joint ROM and angular velocity, thereby reducing negative power and work at the MTP joint and improving running economy for runners. This study provided relevant information for shoe designers, developers, and scientists conducting research on footwear midsole structures and designs.

Though biomechanical methods have been proposed to assess the healing status of fractured bones for more than two decades, the effective stiffnesses obtained theoretically never match the experimentally measured results for the healing progression. This paper proposed a novel numerical model, the simulation results of which are able to reflect the experimental observations. The callus is divided into 10 regions with different material properties and the gap-narrowing process of the fracture is simulated with the variations of the material properties during the healing progression. The variations of the effective bending stiffness and resonant frequency with the healing progression have been obtained. The bending stiffness and resonant frequency squared of the fractured bone show a substantial creeping part during gradual narrowing of the fracture gap. They start to increase rapidly during bridging of the fracture gap by a bony callus. When the Young’s modulus in the callus region calcified last (i.e., Region 10) reaches 5% that of the reference intact bone, the bending stiffness and resonant frequency squared rise up to 90% those of the reference intact bone. After that they increase slowly and get flat; they become less sensitive to bone growth in the late healing stages. It is the first time that the simulation results demonstrate three distinct stages like in the experimentally measured results. These results imply that the variations of the bending stiffness and resonant frequency squared are not linearly correlated with the healing progression; however, their fast growing phase does indicate bony bridging of the callus.

Interlaminar transverse shear stress plays a critical role in delamination and damage of laminated composite plates. As graphene platelets (GPLs) are piecewise distributed along the thickness to present gradient properties, fully assessing maximum values of transverse shear stress for functionally graded graphene-reinforced composite (FG-GRC) structures is necessary. This paper conducts a comprehensive analysis of transverse shear stress for FG-GRC sandwich plates. Nine different distribution patterns of GPLs covering three core types including softcore, hardcore and FG core are considered for the first time. To guarantee analysis accuracy of transverse shear stresses, a refined higher-order zigzag theory related with material heterogeneity in the framework of refined plate theory is presented. On this basis, governing equations for static analysis of GRC plates are formulated by employing the minimum potential energy principle, and analytical solutions are presented by the Navier method. Numerical cases well validate the accuracy of this model in predicting transverse shear stress fields by constitutive relations. Furthermore, numerical analysis and discussion demonstrate that the FG-GRC sandwich plate with GPL distribution pattern $\wedge -0-\vee$ shows the highest bending stiffness in most cases and the smallest value of maximum transverse shear stresses in GRC layers within full range of matrix modulus, core thickness, graphene weight ratio and side-to-thickness ratio.