Biomechanical analysis of lumbar interbody fusion with an anisotropic hyperelastic model for annulus fibrosis

Based on computed tomography scanning images, this paper developed a detailed finite element model for the human L2–L4 lumbar spine segment with or without L3–L4 fusion. The model included vertebrae, intervertebral disc, facet articulating surfaces and various ligaments. A previously developed hyperelastic fibre-reinforced constitutive model was used to characterize the material property of annulus fibrosus. Numerical results of L3–L4 motion unit such as load–displacement curves and nucleus pressure were compared with experimental data to validate the FE model. The normal and fused lumbar spine segments under various loading conditions, such as flexion, extension and axial rotation, were analysed. The motion range and stress distribution of the L2–L4 models under different loading conditions were then obtained to investigate the effect of lumbar fusion operation. It was shown that under the same loading condition, the fused model had a much smaller body motion range. Interbody fusion brought out obviously different stress distribution in adjacent intervertebral disc annulus fibrosus. And it also increased the intradiscal pressure of adjacent intervertebral disc significantly.     

Development and validation of a viscoelastic finite element model of an L2/L3 motion segment

The prediction of the time dependent response of the spine to dynamic loading conditions is essential in understanding the injury mechanisms leading to occupationally related low back disorders (OLBD). Many previous finite element (FE) models of the lumbar spine have over-simplified the geometry and the material properties of their elements, yielding results limited generalizability. This study reports on the development and validation of a nonlinear viscoelastic FE model that can quantify the mechanical responses of the L2/L3 motion segment to time varying external loads. This model was developed by consideration of the intrinsic material properties of its individual constituents. A piecewise parameter identification method was adopted due to the inherent complexity in determining the role and contribution of each element to the overall behavior of the motion segment. The results of simulation of four loading conditions (quasistatic, constant loading rate, creep and cyclic relaxation) showed a satisfactory agreement with experimental observations in the literature. The detailed estimates of the state of stress/strain of this validated FE model can be used to test the role of epidemiological risk factors such as prolonged awkward posture, speed of lift (strain rate effect) and complex repetitive loading in OLBD.     

The behavior of viscoelastic squeeze films subject to normal oscillations, including the effect of fluid inertia

The problem of the squeeze film flow of a viscoelastic fluid between parallel, circular disks is analyzed. The upper disk is subject to small, axial oscillations. Lodge's “rubber-like liquid” is used as the viscoelastic fluid model, and fluid inertia forces are included. An exact solution to the equations of motion is obtained involving in-phase and out-of-phase components of velocity field and load, with respect to the plate velocity. Peculiar resonance phenomena in the load amplitude are exhibited at high Deborah number. At certain combinations of Reynolds number and Deborah number, the in-phase and/or out-of-phase velocity field components may attain an unusual circulating type of motion in which the flow reverses direction across the film. In the low Deborah number limit, and in the low Reynolds number limit, the results of this study reduce to those obtained by other workers.     

腰椎力学分析的数值模拟与实验研究

采用数值模拟和实验测试技术对两种不同内固定法的腰椎模型进行应力和变形分析,基于CT图像建立L4-S1的三维数值模型,经ANSYS计算分析得出五种工况下的终板应力值;在实验中采用了一种薄膜压力测试传感器结合图像处理的方法,提高测试椎间盘压力分布的精度;同时采用数字图像相关技术对腰椎骨上下关节突在承载情况下的空间位移进行了测量,获得了腰椎间盘（L3-L4）在承受轴压、前屈后伸和侧弯情况下的压力分布,以及对应的关节突的位移迹线。结果表明：本研究采用的数值分析技术和实验开发的测试技术可操作性强,精度满足要求,有望在类似的生物力学分析中得到应用。     

On dynamics and stability of continuous systems subjected to a distributed moving load

Summary The paper deals with an analysis of different models of continuous systems subjected to a load distributed over a given length and moving at a constant velocity.The general discussion concerns a beam resting on a viscoelastic semi-space. The motion of the body is described by polynomial differential operators. With body forces being disregarded, the motion of the beam lying on a viscoelastic foundation is discussed with either taking into account the effect of shear deflection and the inertia of rotation or with neglecting them. Consideration is also given to the cases of relative motion of two continuous systems and the stability of their interaction. The above cases represent the models of a number of mechanical systems applied in e.g. modern transportation facilities, technology of bonding of layer materials, etc.The analysis is substantially simplified because the equations of motion and the boundary conditions are written in a moving coordinate system related with the load and only stationary solutions are considered. With such an approach, the solutions depend only on the transformed space variable, while the velocity of the load appears as one of the parameters of the system. Interesting conclusions are drawn from the obtained solutions and numerical calculations.

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Zur Dynamik und Stabilität von kontinuierlichen Systemen unter verteilten bewegten Lasten

Übersicht Der vorliegende Beitrag behandelt die Analyse von kontinuierlichen Systemen, die verteilten bewegten Lasten ausgesetzt sind. Es wird zunächst ein Balken auf viskoelastischem Halbraum behandelt. Die Bewegung des Körpers wird beschrieben durch Differentialoperatoren in Polynomform, wobei der Einfluß von Schubverformung und Drehträgheit diskutiert wird. Der Fall der Relativbewegung von zwei kontinuierlichen Systemen und ihre Stabilität wird ebenfalls diskutiert. Die untersuchten Fälle stellen Modelle zahlreicher mechanischer Systeme dar, wie zum Beispiel moderne Schnelltransportsysteme, Fügevorrichtungen von Schichtmaterialien, usw.Die Analyse der Probleme wird wesentlich dadurch vereinfacht, daß die Bewegungsgleichungen und Randbedingungen in einem mitbewegten Koordinatensystem formuliert werden und nur stationäre Lösungen betrachtet werden. Auf diese Weise hängen die Lösungen nur von der transformierten Ortsvariablen ab; die Geschwindigkeit der Belastung tritt als ein Parameter des Systems auf.Aufschlußreiche Schlußfolgerungen werden anhand der erhaltenen Lösungen und numerischen Berechnungen dargestellt.

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This paper was presented at the Second Symposium on Inelastic Solids and Structures, Bad Honnef, September 1981     

钢筋混凝土箱梁非线性及剪滞效应的试验研究

制作了钢筋混凝土简支箱梁模型,试验包括模型梁开裂范围内的加载及开裂后的加载。在开裂范围内,对该试验梁分别进行了顶板满布均布荷载、均布荷载作用于肋板上方、集中力作用于跨中以及对称集中力作用下的加载;对开裂后的试验梁,进行了对称集中力作用下的加载。用应变采集仪与电脑连接,并用半桥测量,温度自补偿方法测取应变值,采用百分表测试梁体挠度,采用读数显微镜观测裂缝。测量得到应力、应变的分布规律,验证了钢筋混凝土箱梁中存在剪滞效应。试验结果与考虑混凝土非线性的有限段法的计算结果吻合较好,验证了有限段法在混凝土箱梁剪滞效应分析中的适用性。     

Non-linear dynamic response of a rotating radial Timoshenko beam with periodic pulse loading at the free-end

Consideration is given to the dynamic response of a Timoshenko beam under repeated pulse loading. Starting with the basic dynamical equations for a rotating radial cantilever Timoshenko beam clamped at the hub in a centrifugal force field, a system of equations are derived for coupled axial and lateral motions which includes the transverse shear and rotary inertia effects, as well. The hyperbolic wave equation governing the axial motion is coupled with the flexural wave equation governing the lateral motion of the beam through the velocity-dependent skew-symmetric Coriolis force terms. In the analytical formulation, Rayleigh-Ritz method with a set of sinusoidal displacement shape functions is used to determine stiffness, mass and gyroscopic matrices of the system. The tip of the rotating beam is subjected to a periodic pulse load due to local rubbing against the outer case introducing Coulomb friction in the system. Transient response of the beam with the tip deforming due to rub is discussed in terms of the frequency shift and non-linear dynamic response of the rotating beam. Numerical results are presented for this vibro-impact problem of hard rub with varying coefficients of friction and the contact-load time. The effects of beam tip rub forces transmitted through the system are considered to analyze the conditions for dynamic stability of a rotating blade with intermittent rub.     

A non-linear finite element model of human L4-L5 lumbar spinal segment with three-dimensional solid element ligaments

This paper establishes a non-linear finite element model (NFEM) of L4-L5 lumbar spinal segment with accurate three-dimensional solid ligaments and intervertebral disc. For the purpose, the intervertebral disc and surrounding ligaments are modeled with four-nodal three-dimensional tetrahedral elements with hyper-elastic material properties. Pure moment of 10 N·m without preload is applied to the upper vertebral body under the loading conditions of lateral bending, backward extension, torsion, and forward flexion, respectively. The simulate relationship curves between generalized forces and generalized displacement of the NFEM are compared with the in vitro experimental result curves to verify NFEM. The verified results show that: (1) The range of simulated motion is a good agreement with the in vitro experimental data; (2) The NFEM can more effectively reflect the actual mechanical properties than the FE model using cable and spring elements ligaments; (3) The NFEM can be used as the basis for further research on lumbar degenerative diseases.     

纳米颗粒增强镍基MEMS器件材料的蠕变性能研究

利用同步辐射LIGA微铸复合工艺,将纳米氧化物增强颗粒复合到微电子机械系统(MEMS)结构材料中。制作了专用夹具,采用微力材料试验机测量了纳米Al2O3颗粒增强镍基复合材料的强度为1GPa;将恒加载速率/载荷法和恒载荷法相结合,利用纳米压痕仪测量了该材料的室温蠕变速率敏感指数m。结果表明,LIGA复合技术得到的纳米颗粒增强镍基复合材料具有较高的强度;MEMS器件材料在室温下会发生蠕变;材料在相同压深下最大载荷不随加载速率而改变,加载段粘弹性和粘塑性变形极少;主要由局部高应力导致压痕蠕变;材料的蠕变速率敏感指数m值为0.004,说明纳米Al2O3颗粒可有效增强基体材料的抗蠕变能力;且不同恒.P/P下获得的m值基本相同,表示此种材料对加载速率不敏感。     

粘弹性桩的混沌运动分析

研究了在轴向载荷和周期性横向载荷共同作用下非线性粘弹性嵌岩桩的混沌运动情况。假定桩和土体分别满足Leaderman非线性粘弹性和线性粘弹性本构关系，得到的运动方程为非线性偏微分．积分方程；利用Galerkin方法将方程简化为非线性常微分一积分方程，同时利用非线性动力系统中的数值方法，进行了数值计算，得到了不同载荷参数、几何参数、材料参数时粘弹性桩发生周期运动、多周期运动及混沌运动的时程曲线、相图、功率谱、Poincare截面图，同时得到了挠度-载荷、挠度-几何参数、挠度-材料参数等分叉图，考察了各种参数的影响。数值结果表明非线性粘弹性桩在一定的条件下可以通过倍周期分叉的方式进入混沌运动状态，且桩的载荷参数、几何参数、材料参数对其运动状态有较大的影响。     

Tensorial generalized Stokes–Einstein relation for anisotropic probe microrheology

In thermal “passive” microrheology, the random Brownian motion of anisotropically shaped probe particles embedded within an isotropic viscoelastic material can be used to extract the material’s frequency-dependent linear viscoelastic modulus. We unite the existing theoretical frameworks for separately treating translational and rotational probe motion in a viscoelastic material by extending the generalized Stokes–Einstein relation (GSER) into a tensorial form that reflects simultaneous equilibrium translational and rotational fluctuations of one or more anisotropic probe particles experiencing viscoelastic drag. The tensorial GSER provides a formal basis for interpreting the complex Brownian motion of anisotropic probes in a viscoelastic material. Based on known hydrodynamic calculations of the Stokes mobility of highly symmetric shapes in a simple viscous liquid, we show simple examples of the tensorial GSER for spheroids and half-stick, half-slip Janus spheres.     

Identification of viscoelastic properties by means of nanoindentation taking the real tip geometry into account

Motivated by recent progress in viscoelastic indentation analysis, the identification of viscoelastic properties from nanoindentation test data taking the real tip geometry into account is presented in this paper. Based on the elastic solution of the indentation problem, the corresponding viscoelastic solution is obtained by the application of the method of functional equations. This general solution, which accounts for the real geometric properties of the indenter tip, is specialized for the case of a trapezoidal load history, commonly employed in nanoindentation testing. Three deviatoric creep models, the single dash-pot, the Maxwell, and the three-parameter model are considered. The so-obtained expressions allow us to determine viscoelastic model parameters via back calculation from the measured load–penetration history. The presented approach is illustrated by the identification of short-term viscoelastic properties of bitumen. Hereby, the influence of loading rate, maximum load, and temperature on the model parameters is investigated.     

A dynamic biaxial testing machine

The development of generalized constitutive equations for materials requires additional experimental data. A testing machine is described which is capable of applying biaxial, tension-torsion loading to thin-walled tubular specimens over a wide range in loading rates. Both components of the load are independently controlled. The objective is to obtain information on the effect of the rate of loading on viscoplastic or viscoelastic behavior of materials. Some preliminary data are given on the effect of loading rate on the yielding of mild steel. Paper was presented at 1966 SESA Spring Meeting held in Detroit, Mich., on May 4–6. The work presented herein was performed under Contract DA31-124-ARO-D-273 with the Army Research Office, Durham, Durham, N. C.     

基于波传播系数构建填实爆炸下花岗岩中运动及变形场

为利用球面波实验测得的有限个粒子速度信息来分析地下爆炸下介质的运动及变形特性，基于黏弹性球面波理论和局部黏弹性等效假设，提出了一种构建地下爆炸运动及变形场的新方法。首先，利用0.125 g TNT填实爆炸下花岗岩中相邻测点的粒子速度频谱给出相应的频谱比；其次，结合黏弹性球面波理论给出的理论频谱比求解出相邻测点之间区域内等效的球面波传播系数；再次，利用局部黏弹性等效假设给出相邻测点之间任意一点的粒子速度频谱，再通过傅里叶逆变换给出粒子速度的时域波形；最后，利用运动场和变形场的物理关系，完成整个分析区域内运动场和变形场的构建。结果表明:由相邻测点反演得到的波传播系数，可高精度地构建相应测点之间区域内介质的运动及变形场；在半径15～50 mm区域内，径向压缩应变峰值约从1.7×10?2降为2.1×10?3，切向拉伸应变峰值约从4.7×10?3降为0.4×10?3，径向压缩应变率峰值约从5.1×104 s?1降为2.5×103 s?1，切向拉伸应变率峰值约从5.0×103 s?1降为1.4×102 s?1，涵盖了高应变（率）到中低应变（率）加、卸载的全过程。     

A model for the viscoelastic behavior of polymers at finite strains

Summary A constitutive model is derived for the isothermal nonlinear viscoelastic response in polymers, which do not possess the separability property. The model is based on the concept of transient networks, and treats a polymer as a system of nonlinear elastic springs (adaptive links), which break and emerge due to micro-Brownian motion of chains. The breakage and reformation rates for adaptive links are assumed to depend on some strain energy density. The viscoelastic behavior is described by an integral constitutive equation, where the relaxation functions satisfy partial differential equations with coefficients depending on the strain history. Adjustable parameters of the model are found by fitting experimental data for a number of polymers in tension at strains up to 400 per cent. To validate the constitutive relations, we consider loading with different strain rates, determine adjustable parameters at one rate of strains, and compare prediction of the model with observations at another rate of strains. Fair agreement between experimental data and results of numerical simulation is demonstrated when the rates of strains differ by more than a decade. Received 1 July 1997; accepted for publication 7 October 1997     

A knife-edge load traveling on the surface of an elastic halfspace

A load moving on the surface of an elastic halfspace forms a basic problem that is related to different fields of engineering, such as the subsoil response due to vehicle motion or the ultrasound field due to an angle beam transducer. Many numerical techniques have been developed to solve this problem, but these do not provide the fundamental physical insights that are offered by closed form solutions, which are very rare in comparison. This paper describes the development and analysis of the closed form space-time domain solution for a knife-edge load, i.e. a line segment of normal traction, moving at a constant speed on the surface of an elastic halfspace. The various contributions making up the exact solution, obtained with the Cagniard-De Hoop method, produce all the complicated wave patterns from this distributed type of loading. Examples are the transient wave field at the starting position of the load, angled conical and plane waves propagating into the solid, Rayleigh waves propagating along the surface, and head waves spreading and attenuating in specific directions from the loading path. The influence of the load speed on the wave field is investigated by considering the singularities in the relevant complex domains, for each sonic range relative to the bulk wave velocities. The characteristic wave fronts and wave patterns as exhibited by the particle displacements are evaluated for subsonic, transonic and supersonic load speeds.     

大型偏心结构吊装欠约束问题研究

吊装施工过程中被吊模块的水平度是作业要求的重要指标,通常需要增加配重调平。传统有限元方法需要补充约束以消除单元刚体位移,且需要重复计算平衡方程来求解调平载荷,效率不高。将模块的运动分解为随动坐标系的整体运动以及相对该坐标系的弹性变形,可将欠约束问题化为多体系统的静平衡问题。基于虚功率原理推导了吊装平顺时刻的节点力平衡方程以及相应的切线刚度矩阵,并将配重表示为基础配重与载荷系数相乘的形式。通过对节点力平衡方程求导,得到一组以载荷系数为自变量的微分方程,通过求解微分方程并结合水平度判据,可快速搜寻满足水平度要求的载荷系数。数值算例表明,该方法在解决偏心模块吊装欠约束问题方面具有明显的优势,在确定配重载荷方面具有较快的速度和合理的精度。     

PREDICTION OF MECHANICAL PROPERTIES OF FISH MUSCLE IN VIVO DURING STEADY SWIMMING

在综合游动力学的框架下采用整体模化分析方法,对比研究了鳗鲡鱼类和鲹科鱼类巡游中红肌（驱动鱼类巡游的骨骼肌）的力学性能异同. 该方法将观测总结的鱼体动态变形规律作为已知条件,首先确定鱼游中体外作用（包括流体动力响应和惯性力）,然后间接预测活体的体内作用（包括肌肉主动力和生物组织被动应力）. 研究结果显示,鳗鲡鱼类尾部的肌肉强度明显低于其躯干部分,而鲹科鱼类尾部和躯干部分肌肉强度相当,这与各自的体内作用主导机制相适应. 且体外作用的区别也导致了鲹科鱼类的能效更高. 同时发现,两种模式游动下都存在鱼体躯干内部从头至尾的能量传递,其肌肉输出净功沿鱼体轴向都呈“钟形” 分布. 总体上沿轴向各点的肌肉都输出正的净功.     

功能梯度材料的黏弹性断裂问题

功能梯度材料(FGM)是一种不同于传统复合材料的新型工程复合材料 [1], 国内外关于FGM的断裂力学方面的研究发展非常迅速. 关于FGM静态裂纹问题,学者们研究了不同类型裂纹尖端场的应力强度因子 [2-5], 探讨了有限长裂纹在不用载荷作用下的传播等问题. 而关于动态裂纹问题,也已经取得很大成就 [6-9]. FGM一个很重要的应用是高温结构材料,在强大的热环境中,很多材料都呈现出黏弹性. 因此,研究FGM的黏弹性断裂力学非常具有实际价值.对此,众多研究 [10-14]提出不同的分析模型,并在不同受载条件,通过理论计算,分析了黏弹性裂纹尖端场的力学 行为.本文考查了功能梯度材料板条中界面裂纹垂直于梯度方向时的黏弹性断裂问题,首先利用有限元法求解线弹性功能梯度材料板条的裂纹尖端场,然后根据黏弹性的对应性原理,求解出黏弹性功能梯度材料板条裂纹问题的应力场强度因子.      

Stability of plane Poiseuille flow of a slightly viscoelastic fluid

Consideration is given to the stability of planePoiseuille flow of a slightly viscoelastic fluid which has a constant viscosity and normal stress differences varying nearly with the shear rate. It is shown that the presence of elasticity lowers the criticalReynolds number at which instability occurs.