In-plane Shear Strain Research Articles

The effect of shoulder arthroplasty on humeral strength: An in vitro biomechanical investigation

Periprosthetic humeral fractures are a serious complication of shoulder arthroplasty. While adequate reaming of the canal and insertion of an oversized implant optimizes fit, such maneuvers also weaken the bone and predispose it to fracture. The impact of the humeral arthroplasty was assessed in vitro on human cadaveric specimens. Strain gauges were attached to the distal diaphyses and the specimens were mounted in a torsion-loading fixture throughout the tests. An initial series examined the effect of reaming of the canal to its clinically appropriate diameter using uniaxial strain gauges. A second series utilized strain rosettes to evaluate the cumulative effects of reaming, broaching, and implant insertion. Reaming of the canal to its clinically appropriate diameter significantly increased (P=0.007) uniaxial strain measurements by a mean of 30% with five of eight specimens showing increases of over 49% on at least one of four diaphyseal locations. In the second series, the surface strain was significantly affected by arthroplasty (P<0.008). Post-hoc analysis showed that the maximum in-plane shear strain following implant insertion was significantly increased relative to strain levels following reaming and broaching (P<0.009). The direction of the principal strain axes did not significantly change (P>0.46). Unexpected decreases in some strain measurements were observed as the arthroplasty procedure progressed perhaps reflecting overt mechanical failure within the humeral shaft. The strain increase following reaming suggests a reduction in torsional strength by over 33% which is further reduced following broaching and implant insertion. For the practicing surgeon, post-operative strength can be adversely affected by both canal preparation and implant insertion.

247 細胞膜チャネルのダイナミクスと高速膜動輸送機構のシミュレーション

The existence of a transendothelial channel, which is considered to be involved in specific transport of macromolecules is reported. In this study, the generation mechanism of vascular endothelial chained vesicles and the transendothelial channel is theoretically investigated based on minimization of bending and in-plane shear strain energy of the membrane. A system of nonlinear differential equations is derived according to the variational principle and is reduced to a two point boundary value problem. Simulated transendothelial channel changes its shape dramatically form chained vesicular channel to infundibular channel depending on lower opening radius.

Mechanics of Curved Plasma Membrane Vesicles: Resting Shapes, Membrane Curvature, and In-Plane Shear Elasticity

Highly curved cell membrane structures, such as plasmalemmal vesicles (caveolae) and clathrin-coated pits, facilitate many cell functions, including the clustering of membrane receptors and transport of specific extracellular macromolecules by endothelial cells. These structures are subject to large mechanical deformations when the plasma membrane is stretched and subject to a change of its curvature. To enhance our understanding of plasmalemmal vesicles we need to improve the understanding of the mechanics in regions of high membrane curvatures. We examine here, theoretically, the shapes of plasmalemmal vesicles assuming that they consist of three membrane domains: an inner domain with high curvature, an outer domain with moderate curvature, and an outermost flat domain, all in the unstressed state. We assume the membrane properties are the same in these domains with membrane bending elasticity as well as in-plane shear elasticity. Special emphasis is placed on the effects of membrane curvature and in-plane shear elasticity on the mechanics of vesicle during unfolding by application of membrane tension. The vesicle shapes were computed by minimization of bending and in-plane shear strain energy. Mechanically stable vesicles were identified with characteristic membrane necks. Upon stretch of the membrane, the vesicle necks disappeared relatively abruptly leading to membrane shapes that consist of curved indentations. While the resting shape of vesicles is predominantly affected by the membrane spontaneous curvatures, the membrane shear elasticity (for a range of values recorded in the red cell membrane) makes a significant contribution as the vesicle is subject to stretch and unfolding. The membrane tension required to unfold the vesicle is sensitive with respect to its shape, especially as the vesicle becomes fully unfolded and approaches a relative flat shape.

Geometrical Nonlinear Deformation Effects in Composite Sandwich Plates Subjected to In-Plane Shear Loads

An experimental and analytical study is presented to investigate the nonlinear behavior of foam core sandwich plates subjected to in-plane shear loads. Due to the low flexural stiffness of sandwich structures, the geometrical nonlinear deformation effects tend to appear earlier in foam core sandwich plates than in other laminated and sandwich plates. However, the analysis performed is applicable to any laminated or sandwich composite plate. In studies presented herein the Theorem of Minimum Potential Energy has been used to determine the deflections, strains, and stresses in the plate. Polynomial functions are used that satisfy all of the boundary conditions. It is seen from the analytical results that the lateral deflection and the in-plane shear strains and stresses are nonlinear functions of the applied loads. In addition, the in-plane normal strains do occur under the laterally applied loads which cause the inequality of principle strains between the compressive face strains and the tensile face strains.

Luminescent Strain-Sensitive Coatings

The use of novel luminescent coatings and digital imaging to map the in-plane strain field on structural components under static load is described. The technology, referred to as strain-sensitive skin by Visteon Corporation, employs two different approaches: the first uses a luminescent brittle coating (LBC), and the second uses a luminescent photoelastic coating (LPC). A coating consisting of a binder, generally polymeric in nature, and luminescent dye is applied to the surface of a test part by conventional aerosol techniques. The LBC is excited with incoherent ultraviolet or blue illumination, and the corresponding emission is imaged via a digital camera. The relative change in emission intensity is related to the in-plane volumetric strain response for moderate strain levels. The I,PC is excited by the same sources after being conditioned with polarizing and retarding optics to create circularly polarized light. The relative change in emission ellipticity, both in magnitude and phase as measured after passing through an analyzing polarizer, are related to the in-plane shear strain and its corresponding principal direction. These techniques offer quantitative, repeatable, and high spatial resolution measurements. Additionally, they are applicable to complex three-dimensional geometries, cost efficient to implement, and suitable to be integrated in the product design cycle in conjunction with finite element analysis tools. Results from a test conducted on an automobile suspension control arm under static loads are presented and discussed.

Luminescent photoelastic coatings

In this paper we describe a new technique to measure the surface strain field on complex three-dimensional structural components under static load. It is cost-efficient to implement and suitable to be integrated in the product design cycle in conjunction with finite element analysis tools. The technique employs novel luminescent photoelastic coatings and digital imaging to map the in-plane strain field. The coatings consist of a binder, generally polymeric in nature, and luminescent dyes that are applied to the surface of a test part using conventional aerosol techniques. When excited with circular polarized ultraviolet or blue illumination, the corresponding emission intensity from the coating is measured via a digital camera. The relative change in emission magnitude and phase as measured after passing through an analyzing polarizer is related to the in-plane shear strain and its corresponding principal direction. Several basic test results are presented and discussed, showing quantitative, repeatable, and high spatial resolution measurements.

Elastic properties of a Poisson–Shear material

A Poisson–Shear material is one which displays significant in-plane shear strain when loaded in the outof-plane direction. Hence for a prescribed out-of-plane strain (e3), we have e1 ≈ −e2. To attain this behavior a Poisson–Shear material should, for example, possess a positive Poisson’s ratio in the 1–3 plane but a negative Poisson’s ratio in the 2–3 plane, or vice versa, such that the magnitudes are almost equal. A Poisson–Shear material, therefore, can be used as a micro-capsule for squeezing into veins or any small ducts such that axis-1 is parallel to the micro-duct. Hence when squeezed along axis-3 the micro-capsule contracts along axis-2, or vice versa, such that the transverse cross-section of the micro-capsule contracts to ease entry. Allowance for expansion along axis-1, on the other hand, prevents excessive densification, hence enabling the micro-capsule to perform as drugdelivery media or for any storage purposes during transport (see Fig. 1 for illustration). Based on strain energy formulation, the Poisson’s ratio is in the range −1 0 in 2–3 plane, we let 0 < θ2 < (π/2) < θ1 < π . Recently, a unified study on the elastic stiffness of a generalized honeycomb structure, applicable for Poisson’s ratio of either signs, has been performed [30], whereby the mode of deformation is confined to be two-dimensional. In this paper, we extend a similar approach [30] for the case of Poisson–Shear material [29], in which deformation is three-dimensional. For brevity, we employ the notation θi for i = 1, 2. By virtue of symmetry, one quarter of the RVE is isolated for analysis, as shown in Fig. 5. A kinematics proof for Poisson–Shearing is given in the Appendix. In the following analysis, we consider i, j = 1, 2 = 3 unless specified otherwise. Since (OC) = [bi − (li − bi ) cos θi ]/2 and (OA) = [(li − bi ) sin θi ]/2, we have the in-plane extensions

636 連結シェル状チャネルによる細胞内高速膜動輸送機構のシミュレーション(バイオ・人間と板シェル構造,OS-9:板・シェルアナリシス基礎への再訪)

The existence of a transendothelial channel, which is considered to be involved in specific transport of macromolecules is reported. In this study, the generation mechanism of vascular endothelial chained vesicles and the transendothelial channel is theoretically investigated based on minimization of bending and in-plane shear strain energy of the membrane. A system of nonlinear differential equations is derived according to the variational principle and is reduced to a two point boundary value problem. Simulated transendothelial channel changes its shape dramatically form chained vesicular channel to infundibular channel depending on lower opening radius.

Deformations in wide, center-notched, thin panels, part I: three-dimensional shape and deformation measurements by computer vision

The response of wide, thin, center-notched, 2024-T3 aluminum panels undergoing far-field tensile load is investigated. Three panels with a notch length to panel width of 0.33 and widths of 305, 610, and 1016 mm were subjected to far-field tensile loading. As part of the experimental program, two pairs of cameras were configured into separate stereovision systems and used to simultaneously capture both the global response of the sheet and the local response near a notch tip. Global areas, ranging in size from 250x 250 mm to 550x 550 mm, were imaged for each panel. A second stereovison system recorded images of a small area, 10×20 mm, ahead of one notch tip. Postprocessing of the stereovision measurement data from global and local systems using three-dimensional digital image correlation was used to obtain the complete displacement field at each point in the region of interest. In general, results demonstrate that the combination of stereovision and three-dimensional digital image correlation is capable of accurately measuring true, three-dimensional structural deformations in regions undergoing both large out-of-plane displacements and large displacement gradients. Furthermore, 3-D measurements on the panel specimen near the grip location are shown to provide an independent assessment of the true boundary conditions, with specimen slippage clearly noted in the 1016-mm specimen. Results from the extensive notched, wide panel experimental program demonstrate that (a) each panel has an initial shape that deviates up to 3 mm from planarity, with the greatest deviations occurring at the center of the notch, (b) the global load-displacement response is essentially linear for load levels that are well beyond the onset of large, out-of-plane displacements in the notch region, and (c) increasing the size of the notched, thin panel specimen results in distinctly different surface deformations and deformed shapes, with three separate maxima/minima in the out-of-plane component of the largest panel. The region where tensile opening strains are above 2% extends several millimeters ahead of the hole, while compressive strains parallel to the notch direction are contained within a few millimeters of the hole. The in-plane shear strains are concentrated along circular lobes at +/-45 deg from the horizontal direction, a trend which is generally consistent with plane stress conditions.

323 血管内皮細胞内チャネルの形成メカニクス

The existence of a transendothelial channel, which is considered to be involved in specific of macromolecules, is reported. In this study, the generation mechanism of vascular endothelial chained vesicles and the transendothelial channel is theoretically investigated based on minimization of bending and in-plane shear strain energy of the membrane. A system of nonlinear differential equations is derived according to the variational principle and is reduced to a two point boundary value problem. The equations are solved through the Shooting method along with Newton-Raphson and Runge-Kutta method. The computed shape suggests that the effect of in-plane shear elasticity and outer cytoplasmic membrane are significant and these should be taken into account in numerical simulation.

Determination of regional pulmonary parenchymal strain during normal respiration using spin inversion tagged magnetization MRI.

In clinical practice, the assessment of lung mechanics is limited to a global physiological evaluation, which measures, in the aggregate, the contributions of the pulmonary parenchyma, pleura, and chest wall. In this study, we used an MR imaging methodology which applies two-dimensional bands of inverted magnetization directly onto the pulmonary parenchyma, thus allowing for the quantification of local pulmonary tissue deformation, or strain, throughout inhalation. Our results showed that the magnitude of strain was maximal at the base and apex of the lung, but was curtailed at the hilum, the anatomical site of the poorly mobile bronchial and vascular insertions. In-plane shear strain mapping showed mostly positive shear strain, predominant at the apex throughout inhalation, and increasing with expanding lung volume. Anisotropy mapping showed that superior-inferior axial strain was greater than medial-lateral axial strain at the apex and base, while the opposite was true for the middle lung field. This study demonstrates that localized pulmonary deformation can be measured in vivo with tagging MRI, and quantified by applying finite strain definitions from continuum mechanics.

Bioengineering. Large Deformation Mechanics of Plasma Membrane Chained Vesicles in Cells.

The clathrin-coated pits, vesicles and chained vesicles on the inner surface of the plasma membrane facilitate the cell to transport specific extracellular macromolecules. This cellular process is strongly involved with large mechanical deformations of the plasma membrane accompanied by changes in membrane curvature. The assembly of the clathrin coat is thought to provide curvature into the membrane. Hence, effects of in-plane shear elasticity due to these coat structure may be significant on the vesicular mechanics. In this study, large deformation mechanics of plasma membrane chained vesicles in cells have been formulated based on minimization of bending and in-plane shear strain energy of the membrane. Effects of outer surrounding cytoplasmic flat membrane upon mechanically stable shapes of the vesicles were revealed, while effects of in-plane shear elasticity were partly discussed.

Parametric Study of the Behavior of Graphite/Epoxy Panels with Stiffener Terminations

The results of a parametric study examining six types of stiffener terminations for stiffened graphite/epoxy panels are presented. Stiffener blades are terminated by attaching to another blade, by tapering the stiffener height, by tapering the stiffener thickness, or by a combination of these methods. Stiffener flanges are also terminated abruptly or by tapering their thickness. Flange length is also varied. Both thin-skin panels and thick-skin panels are considered. Panels were analyzed with a nonlinear finite element analysis code to determine panel response and failure modes. Midplane axial and shear strains, surface strains, interlaminar strains, and failure predictions for the panels are discussed. These results indicate that the mechanism initiating failure is dependent on the stringer configuration of the panel. Interlaminar stresses and bending must be considered to predict the failure of thin-skin panels, and interlaminar stress, in-plane shear strains, and axial strains must be considered to predict the failure of thick-skin panels.

A method for planar biaxial mechanical testing that includes in-plane shear.

A limitation in virtually all planar biaxial studies of soft tissues has been the inability to include the effects of in-plane shear. This is due to the inability of current mechanical testing devices to induce a state of in-plane shear, due to the added cost and complexity. In the current study, a straightforward method is presented for planar biaxial testing that induces a combined state of in-plane shear and normal strains. The method relies on rotation of the test specimen's material axes with respect to the device axes and on rotating carriages to allow the specimen to undergo in-plane shear freely. To demonstrate the method, five glutaraldehyde treated bovine pericardium specimens were prepared with their preferred fiber directions (defining the material axes) oriented at 45 deg to the device axes to induce a maximum shear state. The test protocol included a wide range of biaxial strain states, and the resulting biaxial data re-expressed in material axes coordinate system. The resulting biaxial data was then fit to the following strain energy function W: [equation: see text] where E'ij is the Green's strain tensor in the material axes coordinate system and c and Ai are constants. While W was able to fit the data very well, the constants A5 and A6 were found not to contribute significantly to the fit and were considered unnecessary to model the shear strain response. In conclusion, while not able to control the amount of shear strain independently or induce a state of pure shear, the method presented readily produces a state of simultaneous in-plane shear and normal strains. Further, the method is very general and can be applied to any anisotropic planar tissue that has identifiable material axes.

Internally pressurized elliptical composite cylinders

Presented is the development of a semi-analytical solution based on minimization of the total potential energy, the Rayleigh–Ritz procedure, and the Kantorovich method, to study the response of elliptical composite cylinders to internal pressure. Using the solution, the response of a quasi-isotropic elliptical cylinder is compared with the response of a quasi-isotropic circular cylinder to study the effects of noncircular geometry. The distinguishing features of the response of an ellipse are the inward normal displacement at the ends of the major diameter that occur despite the outward force of the internal pressure, the presence of circumferential displacements, and the presence of inplane shear strains. These effects lead to spatial variations, including sign reversals, of a number of displacement, strain, and curvature responses. To study the influence of material orthotropy, the responses of axially stiff and circumferentially stiff elliptical cylinders are also examined. It is shown that in some instances material orthotropy can be used to mitigate the influence of the elliptical geometry, and make particular responses look like those of a circular cylinder.

Determination of surface strains by speckle shear photography

The aim of the paper is to put forward the idea of speckle shearing photography. The method provides a precise measurement of the in-plane strains and in-plane shear strains. The method is discussed from a theoretical point of view. Configurations for implementing the method are described and experimental results are presented to show the feasibility of the method.

Finite element stress analysis of left ventricular mechanics in the beating dog heart

A three-dimensional finite element model was used to explore whether or not transmural distributions of end-diastolic and end-systolic fiber stress are uniform from the apex to the base of the canine left ventricular wall. An elastance model for active fiber stress was incorporated in an axisymmetric model that accurately represented the geometry and fiber angle distribution of the anterior free wall. The nonlinear constitutive equation for the resting myocardium was transversely isotropic with respect to the local fiber axis. Transmural distributions of end-diastolic fiber stress became increasingly nonuniform from midventricle toward the apex or the base. At a typical diastolic left ventricular pressure (1 kPa), the differences between largest and smallest fiber stresses were only 0.5 kPa near midventricle, compared with 4.6 kPa at the apex, and 3.3 kPa at the base. Transmural fiber stress differences at end-systole (14 kPa) were relatively small in regions from the base to the midventricle (13–22 kPa), but were larger between midventricle and the apex (30–43 kPa). All six three-dimensional end-diastolic strain components were within or very close to one standard deviation of published measurements through the midanterior left ventricular free wall of the passive canine heart [Omens et al., Am. J. Physiol. 261, H918–H928 (1991)]. End-systolic in-plane normal and shear strains also agreed closely with published experimental measurements in the beating dog heart [Waldman et al., Circ. Res. 63, 550–562 (1988)]. The results indicate that, unlike in the midventricle region that has been studied most fully, there may be significant regional nonhomogeneity of fiber stress in the normal left ventricle associated with regional variations in shape and fiber angle.

Measuring the Twisting Rigidity of Woven Fabrics

An apparatus has been developed to determine twisting rigidities of woven fabrics by subjecting fabric samples to monotonically increasing twist. In order to avoid slack in the test specimen and permit a reliable measurement, tensioning weights are applied. The twisting moment acting on the fabric is measured, along with the in-plane load that is simultaneously developed by the coupling effect between the in-plane and out- of-plane deformation modes. The twisting deformation of the fabric is described to correlate the complex deformation with properties that can be measured, based on an elastic plate model. A plot of measured twisting rigidities versus preload yields a straight line that does not pass through the origin, and a small twisting rigidity at zero preload is graphically determined. The in-plane load caused by the twisting process is connected with the in-plane shear strain that relates twisting moment through one of the coupling rigidities.

Comparative in-plane shear behaviour of long-carbon-fibre composites with thermoset or thermoplastic matrix

This paper presents a comparative study of the in-plane shear behaviour of the AS4/PEEK thermoplastic and the thermoset T300/914 material. Tensile tests with several unloadings on (±45) 2 S specimens have shown that the laminae orientation, θ, varies greatly during the test, particularly in APC2 laminates which exhibit substantial plastic behaviour. These irreversible deformations induce considerable residual stresses in the plies of the unloaded specimens. The in-plane shear stresses and strains therefore need to be calculated, at each step of the tensile test, with the actual θ value. With this precaution, and taking into account the residual stresses, the elastic, damaged and plastic behaviour in shear of the thermoset and thermoplastic composites have been characterized for strain values below 10%. It is shown that T300/914 and AS4/PEEK materials exhibit very similar shear behaviour at the beginning of loading, with small variations of laminae orientation, θ, very scarce and short matrix cracks, but a very significant loss in shear stiffness associated with the development of large plastic strains. As soon as matrix cracks appear, damage development differs in the two materials: the precise observation, on the specimen edges, of matrix cracks and interply delaminations has shown that the earlier failure of the T300/914 specimens is primarily due to the lower shear strength of the thermoset matrix. Because of a much delayed failure, the (±45) 2 S PEEK matrix laminates can develop more pronounced plastic behaviour.

Dynamic analysis and design of laminated composite beams with multiple damping layers

This paper describes the formulation of a theory for the prediction of damping and natural frequencies of laminated composite beams with multiple viscoelastic damping layers. The damping layers are constrained (or sandwiched) by anisotropic laminates. The in-plane shear strains of the damping layers and the constraining layers are included in the model. Closed-form solutions for the resonance frequencies and modal loss factors of the composite beam system under simple supports are derived using the energy and Ritz method. A parametric study has been conducted to study the variation of dynamic stiffness and modal loss factor of the system with structural parameters (e.g., the ply orientations of laminas, thickness of the damping layers and the laminates), operating temperature, and damping material properties. The design of composite beams for maximizing the damping capacity is also presented in this paper which includes the determination of operating temperature range corresponding to given structural parameters and finding optimal structural parameters corresponding to given temperature range. Finally, some experimental results are compared with theory for the cases of single and double damping layer beam systems that show good agreement between predicted and measured natural frequencies.