Experimental and numerical investigation of the behaviour of articular cartilage under shear loading—Interstitial fluid pressurisation and lubrication mechanisms

In this paper, the mechanical and frictional responses of articular cartilage when subjected to alternating shearing forces under a constant load were investigated. Shear testing was performed at physiological contact pressures to ascertain the influence of interstitial fluid support on the evolution of frictional forces during cyclic loading.Numerical studies were also performed using the finite element software Abaqus. The tissue was modelled as a biphasic material with strain dependent permeability. The influence of the material characteristics on the lubrication mechanisms occurring when cartilage is subject to compression and shear was studied to corroborate the experimental findings.     

A Model for Intra-Articular Heat Exchange in a Knee Joint

A mathematical model has been developed for the understanding of temperature distribution in knee joint. Temperature rises in knee joint as a result of frictional energy. This heated synovial fluid enters into the articular cartilage by the process of filtration and supplies heat to cartilage and bone. This cooled fluid again mixes well with the lubricant in the joint cavity. The problem is formulated as a two-region flow and diffusion model: flow and thermal diffusion within the intra-articular gap; and within the porous matrix covering the approaching bones at the joint. The solution of the coupled mixed boundary value problem is solved by using perturbation method. It has been observed that, in certain diseased and or old synovial joints, the movement of the fluid into or out of the cartilage resisted, and therefore, the temperature does rise. The temperature does rise in old and diseased joints as observed by varying the values of parameters from its normal values. These values refer to old age and/or diseases affecting degeneration of synovial fluid and or cartilage.     

单搭接接头胶层间隙对强度和应力的影响

研究单搭接接头胶缝中预留间隙对接头拉剪强度和应力分布的影响。结果表明,随着间隙长度的增加,接头的承载能力趋于减小,但接头的实际剪切强度却持续上升;当间隙长度继续增加时,接头的实际强度趋于下降。研究中还发现间隙所处的位置对接头的抗剪强度有较大的影响,胶层端部预留间隙使接头的承载能力和实际强度均显著下降。有限元数值分析结果表明,间隙长度超过某特定值后胶层中的应力集中程度会急剧上升,间隙位于端部时胶层中的应力集中程度明显高于位于中部的场合。     

Effect of hole perpendicularity error and squeeze force on the mechanical behaviors of riveted joints

In the automatic drilling and riveting process, the perpendicular error of the hole is inevitable, which has a great influence on the assembly quality. In the current research, the shear and pull-out behaviors of riveted joints under different perpendicularity errors and squeeze forces were investigated and compared by the quasi-static tests. The fracture of the failed samples was characterized by a scanning electron microscope and the formation process of fracture was discussed. The failure mechanisms of riveted joints were analyzed in detail to guide engineering applications. The test results demonstrated that the shear load and pull-out load of riveted joints increased slightly with the increase of the tilt angle from 0° to 4°. The perpendicularity error did not affect the shear and pull-out failure modes of the riveted joints. However, the squeeze force had a significant effect on the failure modes of the pull-out samples. Fracture analysis showed that the failure of all shear samples occurred at the rivet shaft. Besides, when the squeeze force increased from 15 kN to 23 kN, the failure modes of the pull-out samples changed from the sheet to the rivet itself.     

Nonlinear in-plane elastic buckling of shallow circular arches under uniform radial and thermal loading

This paper presents a nonlinear in-plane elastic buckling analysis of circular shallow arches that are subjected both to a uniform temperature field and to a uniform radial load field. A virtual work method is used to establish nonlinear equilibrium equations and buckling equilibrium equations, and analytical solutions for the limit instability and bifurcation buckling loads are obtained. It is found that the temperature influences the limit instability, bifurcation buckling and postbuckling behaviour of shallow arches significantly. The limit instability and bifurcation buckling loads increase with an increase of the temperature. A maximum temperature is shown to exist for the occurrence of bifurcation buckling of shallow arches, and when the temperature is higher than this value, bifurcation buckling of an arch is not possible.An arch geometric parameter is introduced to define switches between the limit instability and bifurcation buckling modes, and between buckling and no buckling. Formulae and methods for the calculation of the limiting values of the arch geometric parameter are developed. It is also found that the limiting values of the arch geometric parameter decrease with an increase of the temperature.     

A spatial model of the knee for the preoperative planning of knee surgery

A model on the spatial mechanical behaviour of the passive knee is presented. The femoral articular surfaces were represented by generalized, sagittally elliptical, toroidal surfaces. The medial and lateral tibial articular surfaces were represented by a dished spherical surface and the lower hemihyperbolic region of a torus respectively. Anatomical articular cartilage, knee ligaments and the posterior capsule were represented by spring-like deformable elements with non-linear load versus deflection characteristics. All the forces that act on the femur relative to the tibia were represented by three orthogonal forces and three associated moments. Spatial, articulation-dependent femorotibial kinematic constraint equations of the passive knee were formulated in an analytically explicit manner, based on the natural coordinates of the articular surfaces. The constraint equations were solved algebraically in closed form. Equations were derived that describe spatial femoro-tibial motion, ligament length, ligament strain, ligament-based elastic potential energy and the quasi-static equilibrium of the passive knee. Software was written, simulations on the motion characteristics and load versus deflection characteristics of the knee were carried out and graphical results were presented. The simulation of planar flexion/extension was almost spontaneous. The time taken to simulate spatial six-degree-of-freedom femoro-tibial motion was less than 2.5 min. The models were found to be capable of representing real-life passive knees to a high degree of satisfaction. It has been demonstrated that the models can provide knee surgeons with additional information on major aspects of the preoperative planning of knee surgery. The models can be used to enhance the preoperative planning of ligament reconstruction, articular surfaces related surgery, osteotomy and patellar tendon transfer surgery.     

磨粒分析技术在骨关节炎评估中的应用研究

鉴于磨损颗粒在机械系统以及人造膝关节的磨损过程中起着主要作用,由此可以在理论上进行假设,膝关节中产生的磨粒对骨关节炎的产生和发展中有一定的影响。通过多学科领域的创新拓展探讨这种假设:利用羊的膝关节和磨损试验台进行磨损实验;对羊关节软骨和磨粒样本进行采集和分析;将磨粒样本和关节软骨样本的表面特征进行如下的关联:磨粒和关节软骨磨损特征间的关系;磨粒样本磨损特征与骨关节炎程度间的关系。为探讨硬度与骨关节炎发展的关系,对磨粒进行硬度试验。结果证明在磨损过程中产生的磨粒所携带的信息,对骨关节炎的评估和诊断是很有价值的。     

Temperature stability of elasticity moduli for piezoceramics

The temperature dependences of elasticity and shear moduli for TsTBS-3 and TsTSNV-1 piezoceramics were obtained by the resonance method for flexural and torsional vibrations of a specimen fixed on a single-sided support. The dependences were interpreted and their empirical polynomial relationships were derived. A region of constant elasticity and shear moduli was found for TsTSNV-1 piezoceramics in the temperature range of 330–360 K. The electrode-coated layer on the piezoelectric element was found to affect the elasticity moduli of TsTBS-3 and TsTSNV-1. The data obtained may be useful for the development of vibrational and piezoelectric transducers.Translated from Defektoskopiya, Vol. 40, No. 8, 2004, pp. 56–65. Original Russian Text Copyright © 2004 by Akopyan.     

Analysis of the elastic punch-substrate contact under fretting: Monotonic and cyclic loading of the punch

The object of this paper is to analyze the elastic behaviour of a 2-D contact problem between a right-angled flat punch and a semi-infinite substrate, subjected to a constant normal compressive load and a cyclic shear load using a finite element code. The knowledge of the stress and strain fields produced close to the corners of the punch under different loading conditions as a function of the friction coefficient will allow insight to be gained into the fretting fatigue problem associated to this cyclic loading. In order to better understand the behaviour and analyze the possibility of using fracture mechanics approaches to study the stress field close to the punch corners, two different models have been compared to each other: one without continuity solution between the punch and the substrate and the other with a couple of contact surfaces between them. Using the continuous model, a particularization of the general analytic solutions of Williams has been proposed. The complete stress field around the corners of the punch for this model has been obtained for any values of the punch size, normal and shear loads. Some general guides for understanding and systematizing the punch-substrate behaviour have been extracted from the above solution and that of a sliding wedge, provided by the literature, which enable a systematic numerical analysis of the problem. Further on, a more detailed study of the slip between punch and substrate, as well as of the stress field, has been accomplished using finite element analysis guided by the previous semi-analytical results. The study has been completed for the whole load process: compressive normal load, monotonic shear load, and cyclic shear load.     

The contact behaviour of surfaces of small nominal area

In treating the problem of surface contact it is usually assumed that the asperity radius remains constant during the deformation process. Such an assumption may be valid for the contact of surfaces of large nominal area subjected to moderate normal loads; however, with surfaces of small area where the population of asperities is small the amount of asperity deformation is expected to be relatively large and the displaced material may play an effective role in determining the contact behaviour. In this paper the asperity radius is assumed to increase with deformation and analyses are presented for determining the variation of normal approach with load for rough flat surfaces. The results of such analyses suggest that the deformation process produces increasingly suffer surfaces and are shown to have better agreement with experiment than those results obtained from analyses based on a constant asperity radius.     

Nanomechanical properties of alginate-recovered chondrocyte matrices for cartilage regeneration

Tissue-engineered cartilage constructs designed for in-vivo applications intuitively should mimic the mechanical properties of native cartilage. The objective of the present work was to characterize the nanomechanical properties of alginate-recovered chondrocyte matrices as a function of ex-vivo incubation time. Chondrocytes isolated from the articular cartilage of the mature bovine metacarpophalangeal joints were cultured with alginate hydrogel to allow for the formation of extracellular matrices. The recovered chondral constructs after 2, 4, 8, and 12 weeks of ex-vivo incubation were analysed using nanoindentation with atomic force microscopy to determine their mechanical properties. Chondral constructs had average Young's moduli of 123 +/- 22 kPa, 174 +/- 31 kPa, 373 +/- 40 kPa, and 564 +/- 79 kPa after incubation for 2, 4, 8, and 12 weeks respectively, indicating the gradual attainment of mechanical stiffness. This escalating trend of micromechanical properties as a function of increasing ex-vivo incubation time suggests that chondral constructs via a tissue-engineering approach are capable of elaborating extracellular matrices and increase mechanical stiffness. The relationship between Young's modulus and incubation time of the chondral constructs is useful in the design and fabrication of tissue-engineered cartilage constructs.     

Determination of representative dimension parameter values of Korean knee joints for knee joint implant design

Knee joint implants developed by western companies have been imported to Korea and used for Korean patients. However, many clinical problems occur in knee joints of Korean patients after total knee joint replacement owing to the geometric mismatch between the western implants and Korean knee joint structures. To solve these problems, a method to determine the representative dimension parameter values of Korean knee joints is introduced to aid in the design of knee joint implants appropriate for Korean patients. Measurements of the dimension parameters of 88 male Korean knee joint subjects were carried out. The distribution of the subjects versus each measured parameter value was investigated. The measured dimension parameter values of each parameter were grouped by suitable intervals called the "size group," and average values of the size groups were calculated. The knee joint subjects were grouped as the "patient group" based on "size group numbers" of each parameter. From the iterative calculations to decrease the errors between the average dimension parameter values of each "patient group" and the dimension parameter values of the subjects, the average dimension parameter values that give less than the error criterion were determined to be the representative dimension parameter values for designing knee joint implants for Korean patients.     

A study of the cracking sounds from the metacarpophalangeal joint

The familiar cracking sounds produced by distraction of the metacarpophalangeal joints were studied using accelerometers and a computerized signal analysis system. The joints were distracted in a controlled manner using a motorized device which simultaneously monitored the load on the joint and its extension. The load and extension parameters and those from the signal analysis were used to examine diurnal variation, the effects of multiple distractions, distraction speed, hand temperature and loading between distractions, and to show that in many cases, the energy contained in a crack signal, expressed as a ratio of the articular cartilage volume, exceeded a known level needed to produce articular cartilage damage.     

The influence of continuous sliding and subsequent surface wear on the friction of articular cartilage.

Reciprocating motion friction tests were conducted upon cartilage-on-metal contacts while subjected to a constant load. Initial friction coefficients were compared with repeat friction coefficients following a sufficient load removal period. The repeat friction coefficients were marginally higher than the initial values and both were primarily dependent on the loading time. It was concluded that while a wear component had been identified, which modestly increased friction coefficients, the overriding parameter influencing friction was loading time. The authors postulate that fluid phase load carriage (being dependent on loading time) within the articular cartilage is largely responsible for low friction coefficients in the mixed and boundary lubrication regimes. This mechanism has been referred to as biphasic lubrication. Both synovial fluid and Ringer's solution were used as lubricants. Over the assessed 120 min loading time friction coefficients rose from 0.005 (for both lubricants) after 5 s to 0.50 and 0.57 for synovial fluid and Ringer's solution respectively. Synovial fluid was found to significantly reduce friction coefficients compared to Ringer's solution over broad ranges of the assessed loading times (p < 0.05). Stylus and non-contacting laser profilometry were successfully employed to provide reliable, quantitative and accurate measures of surface roughness. Laser profilometry before and after a continuous sliding friction test revealed a significant increase in surface roughness from Ra = 0.8 (+/- 0.2) micron to Ra = 2.1 (+/- 0.2) microns, (p < 0.0005); confirming that surface wear was occurring. Scanning electron microscopy (SEM) revealed the typical highly orientated collagen fibres of the superficial tangential zone. Environmental SEM (ESEM) of fully hydrated cartilage specimens provided largely featureless images of the surface which suggested that sample preparation for conventional SEM was detrimental to the authenticity of the cartilage surface appearance using SEM. Two distinct acellular, non-collagenous surface layers were identified using ESEM and transmission electron microscopy (TEM); respectively referred to as the boundary layer and surface lamina. The phospholipid/glycoprotein based boundary layer will provide boundary lubrication during intimate contact of opposing cartilage surfaces. The surface lamina, being a continuum of the proteoglycan interfibrillar matrix, is present to prevent fibrillation of the underlying collagen fibres. Both layers may contribute to the time dependent frictional response of articular cartilage. Although laser profilometry did reveal surface wear which was consistent with a small increase in friction, the primary variable controlling the friction coefficient was the period of loading.     

Dynamic relaxation method for nonlinear buckling analysis of moderately thick FG cylindrical panels with various boundary conditions

Using new approach proposed by Dynamic relaxation (DR) method, buckling analysis of moderately thick Functionally graded (FG) cylindrical panels subjected to axial compression is investigated for various boundary conditions. The mechanical properties of FG panel are assumed to vary continuously along the thickness direction by the simple rule of mixture and Mori-Tanaka model. The incremental form of nonlinear formulations are derived based on First-order shear deformation theory (FSDT) and large deflection von Karman equations. The DR method combined with the finite difference discretization technique is employed to solve the incremental form of equilibrium equations. The critical mechanical buckling load is determined based on compressive load-displacement curve by adding the incremental displacements in each load step to the displacements obtained from the previous ones. A detailed parametric study is carried out to investigate the influences of the boundary conditions, rule of mixture, grading index, radius-to-thickness ratio, length-to-radius ratio and panel angle on the mechanical buckling load. The results reveal that with increase of grading index the effect of radius-to-thickness ratio on the buckling load decreases. It is also observed that effect of distribution rules on the buckling load is dependent to the type of boundary conditions.

     

Postbuckling of shear deformable laminated plates under biaxial compression and lateral pressure and resting on elastic foundations

Postbuckling analysis is presented for a simply supported, shear deformable laminated plate subjected to biaxial compression combined with uniform lateral pressure and resting on an elastic foundation. The lateral pressure is first converted into an initial deflection and the initial geometrical imperfection of the plate is also taken into account. The formulations are based on the Reddy's higher-order shear deformation plate theory, and including the plate-foundation interaction. The analysis uses a perturbation technique to determine the buckling loads and the postbuckling equilibrium paths. Numerical examples are presented that relate to the performances of perfect and imperfect, antisymmetrically angle-ply and symmetrically cross-ply laminated plates under combined loading and resting on Pasternak-type or softening nonlinear elastic foundations from which results for Winkler elastic foundations are obtained as a limiting case. The effects played by foundation stiffness, transverse shear deformation, plate aspect ratio, total number of plies, fiber orientation, the biaxial load ratio and initial lateral pressure are studied.     

Buckling analysis of FGM plates under uniform,linear and non-linear in-plane loading

The paper investigates the buckling responses of functionally graded material (FGM) plate subjected to uniform, linear, and non-linear in-plane loads. New nonlinear in-plane load models are proposed based on trigonometric and exponential function. Non-dimensional critical buckling loads are evaluated using non-polynomial based higher order shear deformation theory. Navier’s method, which assures minimum numerical error, is employed to get an accurate explicit solution. The equilibrium conditions are determined utilizing the principle of virtual displacements and material property are graded in the thickness direction using simple Voigt model or exponential law. The present formulation is accurate and efficient in analyzing the behavior of thin, thick and moderately thick FGM plate for buckling analysis. It is found that with the help of displacement-buckling load curve, critical buckling load can be derived and maximum displacement due to the instability of inplane load can be obtained. Also, the randomness in the values of transverse displacement due to inplane load increases as the extent of uniformity of the load on the plate is disturbed. Furthermore, the parametric varying studies are performed to analyse the effect of span-to-thickness ratio, volume fraction exponent, aspect ratio, the shape parameter for non-uniform inplane load, and non-dimensional load parameter on the non-dimensional deflections, stresses, and critical buckling load for FGM plates.

     

Cold drawing of regular polygonal tubular sections from round tubes

An analytical solution is obtained for the problem of cold drawing through flat idle rolls of regular polygonal metal tubular sections from round tube. The solution is based on obtaining a compatible velocity field that satisfies kinematic conditions to yield the strain-rate components. The stresses are obtained by combining the material constitutive law with Levy–Mises flow rule and integrating the equations of equilibrium. The solution is applied to the case of a low-carbon steel standard round pipe to investigate the effects of drawn section shape, friction at the roll interface, roll radius and wall thickness on the roll load and drawing force. The results obtained have shown that for different section shapes the roll load and drawing force decrease with the increase of the number of sides and increase with the decrease of corners radius. Surface friction has no appreciable effect on the loads which allows dry drawing. An increase in the roll radius increases the roll load but the drawing force remains unchanged. Increasing the wall thickness does not proportionally increase the roll load and drawing force; the tube wall behaves as a thin shell subjected to biaxial combined membrane and bending stresses.     

Buckling and vibration of anisotropic or isotropic plate assemblies under combined loadings

This paper describes the underlying theory, and a general-purpose computer program, VIPASA, for determining the critical buckling stresses or natural frequencies of vibration of thin prismatic structures, consisting of a series of plates rigidly connected together along longitudinal edges. Each plate may be either isotropic or anisotropic and may carry a basic stress system consisting of longitudinal and transverse direct stress combined with shear. The structure is assumed to be subjected to a “dead load” system which does not cause buckling; in addition a “live load” system, defined in magnitude by a single load factor, may be applied and the value of the load factor at buckling is determined. Alternatively the natural frequencies of vibration of the structure when subjected to the dead load system are determined. Any number of critical load factors or natural frequencies can be obtained. The theory is based upon the assumption that all modes are sinusoidal, in the sense that all three components of displacement vary sinusoidally along any longitudinal line, but phase differences are incorporated to allow for the effects of anisotropy and shear. Apart from this assumption no further approximations are made other than those inherent in thin plate theory.