Shear Elastic Stiffness Research Articles

Apparent Flexural Rigidity of Single Flagella Depends on Inter-Doublet Shear Stiffness

Motile cilia and flagella are whip-like subcellular organelles that bend actively to propel cells or move fluids. Normal motile functions of cilia and flagella play a critical role in many developmental and physiological processes, while ciliary dysfunction is associated with a number of ciliopathies. Efficient bending deformation of cilia and flagella depends on coordinated interactions between active forces from an array of motor proteins and passive mechanical resistance from the complex cytoskeletal structure (the axoneme). However, details of this coordination, especially axonemal mechanics, remain unclear. We investigated two major biophysical parameters, flexural rigidity and inter-doublet shear stiffness, of single flagella in the unicellular alga Chlamydomonas reinhardtii. Combining theoretical analysis with optical tweezers and counterbend experiments, we demonstrated that the apparent flexural rigidity of the axoneme depends on both the intrinsic flexural rigidity and the elastic inter-doublet shear stiffness. By comparing wild-type flagella with specific structural mutants, we found that the lack of nexin-dynein regulatory complexes (N-DRC) or dynein arms significantly reduces inter-doublet shear stiffness. The quantitative understanding of axonemal mechanics will ultimately lead to the development of novel diagnostic and therapeutic methods for cilia-related disorders.

Evolution of stiffness anisotropy during creep of engineered silty sand in South Korea

The variation in elastic shear moduli measured through bender element tests and the nonlinear strains in the axial and radial directions of triaxial specimens during creep were experimentally investigated. To consider various conditions of different relative densities and different stress ratios, a number of triaxial specimens were prepared. The engineered silty sand reconstituted from weathered residual soil in South Korea was used as the testing material. Due to aging, the post-creep stress-strain curve exhibited a stiffer response compared to the pre-creep stress-strain curve. It was found that the variation in elastic shear stiffness and the nonlinear deformation during creep depends on the stress ratio and initial relative density. The continuous change in the stiffness anisotropy during creep was closely related to the creep deformation patterns.

Shear Deformations of RC Beams under Service Loads

AbstractShear deformations of reinforced concrete (RC) beams are not negligible after shear cracking. However, unlike the well-established procedure for calculating bending deformations of cracked beams, the calculation of shear deformations is still ignored in codes of practice due to a lack of practical models. This study aims to develop a practical approach for estimating instantaneous shear deformations of RC beams under service loads. Based on the truss analogy, an explicit equation for evaluating the yield shear stiffness of fully diagonally cracked beams is derived. It is discovered that the shear retention factor (ratio of the yield shear stiffness to the initial elastic shear stiffness) is approximately the cubic root of the shear-reinforcement ratio. An analytical approach for evaluating the degradation of effective shear stiffness and the development of shear deformation is proposed. Two restrained I-beams with thin webs are tested. This test and shear-deformation tests available in the literat...

Homogenization of fin layers in tube-fin structures subjected to compression and bending: Analyses and experiments

This paper verifies fin-homogenization for finite element analysis of heat exchanger cores with stacking of flat tubes and thin wavy fins. A first-order homogenization method is proposed on the assumption that uniform deformation prevails a short distance away from each fin layer in the stacking direction while the wavy fins have periodicity in the in-layer directions. Using this homogenization method, the homogenized elastic stiffness values of outer and inner fin layers in an intercooler are evaluated by considering real and sinusoidal shapes of the wavy fins. The homogenized elastic stiffness values attained are examined by performing fin-homogenization-based (fin-h-based) analyses, full-scale analyses, and experiments of tube-fin layered specimens subjected to compression and bending. It is shown that the fin-h-based and full-scale analyses give good agreements to each other even in the presence of macro-strain gradients in the outer and inner fin layers though the homogenization method is of first-order. Moreover, it is shown that the fin-h-based analyses reproduce well the experiments if the homogenized elastic stiffness values obtained for the real shapes of outer and inner fins are used in the analyses. It is also shown that the Bernoulli-Euler assumption is not satisfied in the homogenized outer fin layers under longitudinal bending because the homogenized elastic shear stiffness responsible for the bending is very low.

Assessment and comparison of experimental and numerical model studies of cross-laminated timber mechanical connections under cyclic loading

Earthquake engineering is a major consideration for structures along the west coast of North America. The current building code of Canada is based on design criteria, which are defined by stresses and member forces calculated from prescribed levels of applied lateral shear force. Traditional wood-frame buildings are known to perform well in earthquakes. However, with the development of new engineered wood products, such as CLT (cross-laminated timber) and more consideration to build higher than the existing six stories limit in wood-frame structures, highlights the need to use innovative hybrid techniques for buildings. Hybrid buildings with steel frame structures incorporated with CLT infill walls offer one possible solution to residential and commercial multi-level buildings to overcome the height limitation. In order to make such a structure applicable for an earthquake prone area, it is important to understand the structural performance of the connection between steel and CLT elements. In this research, six connection combinations have been tested and modeled in a finite element program. The load–displacement test results are assessed with two evaluation methods. The first method follows the American Society of Testing Method, where ductility ratio, elastic shear stiffness, and the EEEP-curve (equivalent energy elastic–plastic curve) are generated and assessed. The second method follows an energy-based accumulation principle, where the test results are used to calculate a damage index at each time step. Both methods are used to compare test and model results and assess the accuracy of the model as well as addressing the capability of each assessment method. Depending on the purpose of the model one or the other assessment method might be suitable. For an analysis of the overall ductility or elastic shear stiffness, applying the method provided by ASTM will give relatively accurate results to assess a hysteretic load–displacement model such as the SAWS model in this research. The assessment with a damage accumulation method is a great tool to capture more details of the hysteretic load–displacement curve. Energy dissipation is valuable indicator besides ductility and elastic shear stiffness to evaluate the model.

Modeling of the stress-strain state of layered orthotropic plates on elastic foundation

The problem of the analysis of the stress-strain state of hinged layered plates on elastic foundation is considered. Bending of the layered plate on the Pasternak foundation at its mechanical loading is investigated. Original two-dimensional discrete-structural generalized theory of multi-layered plates is used to study the orthotropic plate bending. This theory is based on developing the displacement vector components of each layer in the power series along transverse coordinate. It allows to calculate displacement and stress tensor components of each layer with the required accuracy. The possibilities of the proposed approach are demonstrated on the examples of studying the response of layered plates on elastic foundation. The reliability of the results, obtained on its basis is determined through comparison with the data, presented in known scientific publications. The effect of the elastic foundation parameters on the stress-strain state of multi-layer structures is investigated. It was found that with an increase in the number of power series terms, displacement and stress demonstrate good convergence. It is shown that the elastic foundation shear stiffness significantly affects the stress-strain state of the hinged layered plates.

Longitudinal shear of a composite with elliptic nanofibers: Local stresses and effective stiffness

The paper addresses calculation of the local elastic fields and effective longitudinal shear stiffness of elliptic nano fiber composite with Gurtin–Murdoch interface. The series solutions are obtained for three most widely used model geometries of fibrous composite, namely, single inclusion, finite cluster of inclusions and a representative unit cell. Both the periodic and random microstructures are considered. The developed analytical method combines the superposition principle, multipole expansion and the technique of complex potentials. For the effective stiffness evaluation, both the Maxwell’s and Rayleigh’s approaches have been implemented. In the latter case, the exact formulas for the effective elastic moduli have been derived by analytical averaging the local strain and stress fields. The results show substantial effect of the inclusion shape and interface elasticity on the local stress concentration and effective elastic behavior of fibrous nano composite.

Three dimensional vibration and bending analysis of carbon nanotubes embedded in elastic medium based on theory of elasticity

This paper studies free vibration and bending behavior of singlewalled carbon nanotubes (SWCNTs) embedded on elastic medium based on three-dimensional theory of elasticity. To accounting the size effect of carbon nanotubes, non-local theory is adopted to shell model. The nonlocal parameter is incorporated into all constitutive equations in three dimensions. The surrounding medium is modeled as two-parameter elastic foundation. By using Fourier series expansion in axial and circumferential direction, the set of coupled governing equations are reduced to the ordinary differential equations in thickness direction. Then, the state-space method as an efficient and accurate method is used to solve the resulting equations analytically. Comprehensive parametric studies are carried out to show the influences of the nonlocal parameter, radial and shear elastic stiffness, thickness-to-radius ratio and radiusto-length ratio.

Effective elastic shear stiffness of a periodic fibrous composite with non-uniform imperfect contact between the matrix and the fibers

In this contribution, effective elastic moduli are obtained by means of the asymptotic homogenization method, for oblique two-phase fibrous periodic composites with non-uniform imperfect contact conditions at the interface. This work is an extension of previous reported results, where only the perfect contact for elastic or piezoelectric composites under imperfect spring model was considered. The constituents of the composites exhibit transversely isotropic properties. A doubly periodic parallelogram array of cylindrical inclusions under longitudinal shear is considered. The behavior of the shear elastic coefficient for different geometry arrays related to the angle of the cell is studied. As validation of the present method, some numerical examples and comparisons with theoretical results verified that the present model is efficient for the analysis of composites with presence of imperfect interface and parallelogram cell. The effect of the non uniform imperfection on the shear effective property is observed. The present method can provide benchmark results for other numerical and approximate methods.

Two-dimensional discrete element modelling of bender element tests on an idealised granular material

The small-strain (elastic) shear stiffness of soil is an important parameter in geotechnics. It is required as an input parameter to predict deformations and to carry out site response analysis to predict levels of shaking during earthquakes. Bender element testing is often used in experimental soil mechanics to determine the shear (S-) wave velocity in a given soil and hence the shear stiffness. In a bender element test a small perturbation is input at a point source and the propagation of the perturbation through the system is measured at a single measurement point. The mechanics and dynamics of the system response are non-trivial, complicating interpretation of the measured signal. This paper presents the results of a series of discrete element method (DEM) simulations of bender element tests on a simple, idealised granular material. DEM simulations provide the opportunity to study the mechanics of this testing approach in detail. The DEM model is shown to be capable of capturing features of the system response that had previously been identified in continuum-type analyses of the system. The propagation of the wave through the sample can be monitored at the particle-scale in the DEM simulation. In particular, the particle velocity data indicated the migration of a central S-wave accompanied by P-waves moving along the sides of the sample. The elastic stiffness of the system was compared with the stiffness calculated using different approaches to interpreting bender element test data. An approach based upon direct decomposition of the signal using a fast-Fourier transform yielded the most accurate results.

Shear behavior of partially encased composite I-girder with corrugated steel web: Experimental study

A new type of partially encased composite I-girder with corrugated steel web has been proposed to improve the structural performance of continuous girders under hogging moment. The shear behavior of such partially encased composite I-girders under anti-symmetric loading has been experimentally and analytically investigated. Experimental results show that the partially encased composite girders has superior shear strength compared to steel I-girders, since shear bucking of steel web is restricted by concrete encasement. The shear stiffness of the composite section is based on the total summation of corrugated web and concrete encasement with average thickness before cracking, and the ratio of shear resistance shared by the steel web and the concrete encasement depends on their shear stiffness. In addition, predicted shear strength of the partially encased composite girder with corrugated web is proposed according to the experimental failure mode and strain distribution. The analytical shear stiffness and shear resistance ratio at the elastic stage are verified by experimental results. And the calculated shear strength for steel and composite girders agree well with the experimental results. The comparison shows that the proposed analytical methods can be applied in predicting elastic shear stiffness and design shear strength for such partially encased composite girders with corrugated web.

Seismic performance of CFST column to steel beam joint with RC slab: Joint model

Based on the previous experimental and numerical investigations presented in Han and Li (2010)and Li and Han (2011), this paper studies the joint model for the composite joint consisted of circular concrete filled steel tubular (CFST) column and steel beam with external diaphragm. The elastic shear stiffness and the shear deformation of the joint panel zone are investigated by parametric study using the finite element analysis (FEA) model. A hysteretic model incorporating the shear stiffness, shear strength, shear deformation and the hysteretic rules is proposed for the panel zone of the composite joint. This hysteretic model is then integrated in a fiber-based joint macro element. The joint macro element is validated by both FEA and experimental results. The overall and the local behavior of CFST joints and frame with macro elements are investigated. The proposed model is featured with a favorable accuracy and amenable modeling method, and could be applied to simulate the seismic behavior of large-scale and complex composite structural systems.

Flexural Rigidity and Shear Stiffness of Flagella

Cilia are thin subcellular organelles that line airways and other passages and bend actively to propel fluid and foreign materials. The ciliary cytoskeleton (the axoneme) consists of nine outer microtubule doublets surrounding a central pair of singlet microtubules. Large bending deformations of the axoneme involve relative sliding of the outer doublets driven by the motor protein dyneins. The genetics and cell biology of the ciliary structure and function have been studied extensively, but the mechanics of the axoneme remain unclear. In this study, we used the unicellular alga Chlamydomonas reinhardtii as the model system for their flagellum replicates the highly conserved molecular structure of the ciliary axoneme. Piconewton forces were applied perpendicularly on the tip of a single flagellum (length L) through a microsphere trapped in optical tweezers. Dividing the force (P) by the corresponding deflection of the flagellar tip (δ) yields the flexural stiffness of the flagellum (K = P/δ), which was then used to calculate the apparent flexural rigidity (EI = KL3/3). The contributions of major structural components to passive mechanical properties were quantified by testing on flagella of specific mutations. The average apparent flexural rigidity of wild-type, pf-3 (without nexin links), and pf-13 flagella (without outer dynein arms) was about 2700 ± 1100, 1300 ± 550, and 650 ± 140 pN·μm2, respectively. In addition, the ratio of elastic shear stiffness (resistance to interdoublet sliding) to true flexural rigidity was estimated by the counterbend response in bent flagella manipulated with a glass microneedle. The quantitative understanding of axonemal mechanics will help illuminate the roles of certain genes and molecular structures in the normal and abnormal axoneme.

FE modeling of the interfacial behaviour of composite concrete members

The accurate prediction of the shear strength between concrete layers is important in: (i) new concrete bridges with precast and cast in-situ members as well as in (ii) existing concrete bridges strengthened with a concrete overlay. The monolithic behaviour of these composite members depends only on the interface strength. There are several experimental studies dealing with the influence of different parameters on the bond strength of the concrete-to-concrete interfaces. However, an adequate numerical model concerning the behaviour of these structural interfaces is still missing. In this paper such a numerical model is presented, which is calibrated with experimental data. Results of push-off tests performed to evaluate the longitudinal shear strength between two concrete layers are considered. Different ratios of steel reinforcement crossing the interface were adopted. The comprehensive identification of the influence of the following parameters is achieved: elastic shear stiffness; internal friction angle; dilatancy angle; cohesion; fracture energy; and bond–slip relation between steel connectors and concrete. The most relevant conclusions are presented.

Performance of Wood-Frame Wall with Thin ECC Shear Panel

The study evaluates an alternative to traditional wood-framed shear wall construction, an innovative use of a water and seismic damage resistant, wood-concrete-composite (WCC). The WCC design consisted of a thin layer of engineered cementitious composite (ECC) cast in a traditional wood frame. Structural performance and damage sustained during lateral loading and cost were evaluated, and compared to a traditional wood frame with OSB sheathing. Monotonic tests of WCC walls show that the average maximum load was 47.5 kN (10,700 lb) , average elastic shear stiffness was 1.78 kN∕mm (10,200 lb∕in.) and average energy absorbed was 4,810 J (42,600 lb-in.) . Tests show WCC is comparable with or superior to the OSB wall in shear strength and stiffness, energy absorption and ductility. During lateral loading the WCC appeared to sustain less damage than the OSB wall. Panelized construction of the WCC may increase cost but yield benefits such as decreased construction time and greater durability. WCC appears to be a ...

Theoretical calculations of phase transitions and optical properties of solid iodine underhigh pressures

The structural stability and optical properties of solid iodine under pressure havebeen studied using the ab initio pseudopotential plane-wave method. Thedependence of lattice parameters on pressure indicates that the first structural phasetransition from phase I to phase V occurs at about 20 GPa. From the pressuredependence of our elastic constants for solid iodine in phase I, it is found thatthe first structural transformation from molecular phase I to the intermediatephase V occurs at about 20 GPa due to the softening of the elastic constantC44, which is very close to the transition pressure of 20 GPa obtained by geometry optimizationsand 23.2 GPa obtained by experimental measurements. The optimized structure for phaseV is a face-centered orthorhombic (fco) phase with equal interatomic distancesd1 = d2 = d3, but this fco structure is mechanically unstable, with shear elastic stiffness coefficientC44<0. To understand the modulated phase V, we use a periodic crystal structure to mimic theincommensurate phase V and obtain some quantitative information. In our calculation, themodulated phase is thermodynamically and mechanically stable. It is believed that phase Vis not a monatomic phase but an intermediate state between a molecular and a monatomicstate.

Ab initiostudies of solid bromine under high pressure

Crystal structures of bromine under high pressure have been studied by employing plane-wave pseudopotential method with the generalized gradient approximation. It is found that the band overlap in the molecular $Cmca$ phase, which causes the pressure-induced insulator-to-metal transition, occurs at about $55\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$. Geometry optimization shows that the bromine changes to a face-centered orthorhombic (fco) phase with equal interatomic distances ${d}_{1}={d}_{2}={d}_{3}$ at about $75\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$, but this fco structure is mechanically unstable with shear elastic stiffness coefficient ${C}_{66}&lt;0$. For understanding the structure of this phase, we have modeled an incommensurate structure by a rational approximation with modulation vector $k=(0.25,0,0)$ according to the previous research results in solid iodine. Our results show that the enthalpy of this modulated phase is lower than that of the fco solid, and the elastic stiffness coefficients $({C}_{ij})$ satisfy the Born stability criteria, indicating that the modulated structure is more thermodynamically stable and mechanically stable. In addition, through comparing the x-ray diffraction patterns of our structure with the experimental one, we conclude that the structure of bromine phase V is close to our modulated structure. It is clearly illustrated that the phase transition from $Cmca$ phase to the incommensurate phase is associated with the instability of the shear elastic stiffness coefficient ${C}_{44}$ which is related to the softening of the long-wavelength part of the transverse branch near the center of the first Brillouin zone. With the increasing of pressure, the modulated phase transforms into the monatomic phase II with body-centered orthorhombic structure at about $100\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$, which is in agreement with the experimental result.

Defining Yield from Bender Element Measurements in Triaxial Stress Probe Experiments

This paper describes the elastic response of a block sample of compressible Chicago glacial clay under a variety of stresses and its relationship with the deformation characteristics at relatively large strains. The elastic shear stiffness was obtained from bender element tests during consolidation and shearing in drained triaxial stress probe tests. An empirical correlation was established based on the elastic shear stiffness in a preyield condition. By comparing the empirical correlation with the measured elastic shear stiffness in the stress region during probing, the changes of elastic shear stiffness were investigated. The departure of elastic shear stiffness from values computed by the empirical relation based on K0 loading directly relates to the yielding characteristics of the clay. The large-scale change of soil structure at yielding alters the well-established relationship between the elastic shear stiffness and stresses in the preyield condition. The mechanical yielding response of clays can be detected based on the systematic analysis of the elastic shear wave velocities.

Influence of transverse reinforcement on elastic shear stiffness of cracked concrete elements

Various truss models for calculating the cracked elastic shear stiffness due to transverse reinforcement are investigated to determine the threshold of the geometrical configuration of concrete beams and columns, in which the more convenient continuum truss model can substitute for the discrete truss model without losing accuracy. For this purpose, a comparison is made between continuum and discrete truss models, between constant and variable angle truss models, and between rectangular hoops and circular hoops and spirals. For the continuum truss model to substitute for the discrete truss model, the center-to-center space between transverse reinforcements should be limited to s ≤ d c / 5 for rectangular hoops and s ≤ d c / 3 for circular hoops and spirals. The minimization of energy due to combined flexure and shear mechanisms leads to the construction of formulae for the inclination of diagonal cracks. This angle, θ , is a key parameter for a shear strength and stiffness analysis. The validity of the crack angle formulae is verified through a comparison of the theoretical crack angles with those measured from experimental results reported in a number of earlier studies.

Equilibrium figures of spinning bodies with self-gravity

The study of the equilibrium and stability of spinning ellipsoidal fluid bodies with gravity began with Newton in 1687, and continues to the present day. However, no smaller bodies of the Solar System are fluid. Here I model those bodies as elastic–plastic solids using a cohesionless Mohr–Coulomb yield envelope characterized by an angle of friction. This study began in Holsapple 2001. Here new closed-form algebraic formulas for the spin limits of ellipsoidal shapes are derived using an energy method. The fluid results of Maclaurin and Jacobi are again recovered as special cases. I then consider the stability of those equilibrium states. For elastic–plastic solids the common methods cannot be used, because the constitutive equations lack sufficient smoothness at the limiting plastic states. Therefore, I propose and study a new measure of the stability of dynamic processes in general bodies. An energy-based approach is introduced which is shown to include stability approaches used in the statics of nonlinear elastic and elastic–plastic bodies, spectral definitions and the Liapunov methods used for finite-dimensional dynamical systems. The method is applied to spinning, solid, strained bodies. In contrast to the special fluid case, it is found that the strain energy term of solid materials generally induces stability of all equilibrium shapes, except for two possible cases. First, strain softening in the elastic–plastic law can result in instability at the plastic limit spin. Second, a loss of shear stiffness can give unstable states at specific spins less than the limit equilibrium spins. In the latter case, a solid spinning ellipsoidal body without elastic shear stiffness can spin no faster than with a period of about 3.7 hr, else it will fail by shearing deformations. That is distinctly slower than the oft-quoted limit of 2.1 hr at which material would be flung off the equator by tensile forces. However, the final conclusion is that neither cohesion nor tensile strength is required for the shapes and spins of almost all of the larger observed asteroids: we cannot rule out rubble-pile structures.