THE INVERSE PROPOSITION ABOUT THE SYMMETRY OF LINEAR CONSTITUTIVE LAW

基于线弹性体本构方程系数矩阵的对称性,提出了其对应的逆命题问题,即若材料本构方程是线性且对称的,能否由此确定物体是完全弹性的?论文通过构造势函数的方法对该问题给出了肯定的回答,从而论证了对于符合线性本构关系的材料,其本构方程的对称性与物体的完全弹性相互蕴含,因而是相互等价的.     

第二届全国"三流"学术会议非牛顿流体力学论文介绍

非牛顿流体力学是流体力学中的一个新领域,它在国民经济,尤其是在化学工业中获得广泛应用。1982年4月举行的第二届全国多相流体力学、非牛顿流体力学、物理-化学流体力学(简称"三流")学术会议上,收到这方面的论文有十七篇。分别介绍如下: 本构方程是非牛顿流体动力学的基础理论。陈文芳在"非牛顿流体的一些本构方程"一文中综述各向同性的不可压缩流体的各种本构方程,包括非弹性液体、...     

功能梯度半空间体的热弹性问题研究

本文研究半空间非均匀各向同性功能梯度弹性体的热弹性问题.根据功能梯度材料热弹性体的运动方程,热传导方程以及本构方程,利用状态空间法推导出功能梯度材料的热力耦合微分方程,进一步利用特征值分析法和拉普拉斯逆变换进行求解,得到功能梯度热弹性体在分别只受温度和应力荷载作用时,时域内位移,温度,应力三个物理量的解析解.通过图表,数值分析了半空间功能梯度材料弹性体在热-力荷载作用下各物理场的响应,数值曲线的变化趋势反映了热-力荷载之间的耦合效应.这可以很好的利用在材料设计领域,通过控制材料的梯度参数来控制物理场的极值,从而为未来该材料的工厂加工设计提供理论支持.     

电磁热弹性介质的一些基本理论─电磁热动力理论

具有电磁热弹性耦合性质的介质是许多传感器及机敏结构或系统中的关键材料，本文则是力争对这种耦合材料的基本理论进行系统的研究。第一部分基于被推广的经典热动力学理论推导和归纳了电磁热弹性体的几个守恒方程、动力学方程、本构方程和热平衡方程。第二部分则是系统地讨论了在数值计算中具有极重要意义的电磁热弹性变分原理。     

电磁热弹性介质的一些基本理论电磁热动力理论

具有电磁热弹性耦合性质的介质是许多传感器及机敏结构或系统中的关键材料，本文则是力争对这种耦合材料的基本理论进行系统的研究。第一部分基于被推广的经典热动力学理论推导和归纳了电磁热弹性体的几个守恒方程、动力学方程、本构方程和热平衡方程。第二部分则是系统地讨论了在数值计算中具有极重要意义的电磁热弹性变分原理。     

修正的偶应力线弹性理论及广义线弹性体的有限元方法

以含偶应力的弹性理论为基础,考虑小变形情况下变形体的平动变形和旋转变形,提出关于偶应力与曲率张量的线性本构关系,建立一般弹性体的线性模型。为满足有限单元C1连续性要求,考虑转角为独立变量,利用罚方法引入约束条件,构造一般弹性体的约束变分形式。应用8节点48个自由度的实体等参元,建立一般弹性体力学响应分析的有限元方程。对悬臂梁的静力和动力分析表明,一般弹性体模型较之经典弹性力学更适合结构分析;较之Timoshenko梁模型,一般弹性体模型能够计及结构尺度对结构动力特性和动力响应造成的显著影响。     

丙烯酸弹性体的率相关分数阶黏弹性模型研究

丙烯酸弹性体VHB 4910作为一种重要的介电弹性体,在软体机器人、致动器、俘能器和智能隔振器等领域有很好的应用前景.但材料的非线性黏弹性对其力学行为有显著影响.近来分数阶模型在复杂材料的建模中取得了成功.本文基于分数阶有限变形Kelvin-Voigt流变学模型建立弹性体的三维张量本构,并进一步推导单向拉伸情况下的本构...     

率相关本构方程积分新算法

提出一种积分率相关本构方程的隐式积分新算法,引入0～1范围内的缩放因子λ对本构方程进行间接求解,可以避免直接求解等效塑性应变或等效塑性应变率时,由于其数值过大或过小而造成的收敛困难或收敛失败,实现对率相关本构方程的快速准确求解.以B-P统一本构方程及双曲正弦本构方程为例,验证了算法的可行性.结果表明,新算法对于准静态变形条件下的无硬化本构方程也可以得出准确的解.     

土本构关系的尖点突变模式

本文首次应用突变理论的尖点突变模型分析土的本构特性,建立了土相应的统一本构关系方程。该方程可以考虑软化土的应力路径,亦可分析硬化土的应力路径,统一本构方程通过试验检验是令人满意的。     

Oldroyd速率型本构方程显式化的微分算符形式

本文建立了一种条件,在这种条件下,隐式的Oldroyd本构方程是等价于微分型本构方程。并且解释了这些条件的物理意义。最后给出了Maxwell型及Oldroyd型本构方程显式化的微分算符形式。     

利用分形相关法测量股骨头剖开面的面内位移

由于股骨头内松质骨结构的复杂性,对股骨头内骨小梁的应力和变形的分析与测试十分困难。在已经开展的这一方面的研究工作中主要是进行松质骨试样的宏观力学性能测试。随着计算机和图像技术的发展,图像及图像相关方法开始被用来进行松质骨的生物力学研究,这是非接触的测量方法,可以用来测量松质骨的表面位移场。本文利用图像相关方法在宏观尺度下测量了股骨头受外力作用时冠状面的面内的位移分布,作为进一步探索的开端。尽管松质骨表面的凹凸不平性对测量精度有影响,但是,还是可以分析出面内位移的分布特点。     

The Anisotropic Hooke's Law for Cancellous Bone and Wood

A method of data analysis for a set of elastic constant measurements is applied to data bases for wood and cancellous bone. For these materials the identification of the type of elastic symmetry is complicated by the variable composition of the material. The data analysis method permits the identification of the type of elastic symmetry to be accomplished independent of the examination of the variable composition. This method of analysis may be applied to any set of elastic constant measurements, but is illustrated here by application to hardwoods and softwoods, and to an extraordinary data base of cancellous bone elastic constants. The solid volume fraction or bulk density is the compositional variable for the elastic constants of these natural materials. The final results are the solid volume fraction dependent orthotropic Hooke's law for cancellous bone and a bulk density dependent one for hardwoods and softwoods. This revised version was published online in August 2006 with corrections to the Cover Date.     

Stress analysis of an elastic cracked layer bonded to a viscoelastic substrate

The effect of a viscoelastic substrate on an elastic cracked layer under an in-plane concentrated load is solved and discussed in this study. Based on a correspondence principle, the viscoelastic solution is directly obtained from the corresponding elastic one. The elastic solution in an anisotropic trimaterial is solved as a rapidly convergent series in terms of complex potentials via the successive iterations of the alternating technique in order to satisfy the continuity condition along the interfaces between dissimilar media. This trimaterial solution is then applied to a problem of a thin layer bonded to a half-plane substrate. Using the standard solid model to formulate the viscoelastic constitutive equation, the real-time stress intensity factors can be directly obtained by performing the numerical calculations. The results obtained in this paper are useful in studying the problem with bone defects where a crack is assumed to exist in an elastic body made of the cortical bone that is bonded to a viscoelastic substrate made of the cancellous bone.     

Ultrasound propagation in cancellous bone

Wave propagation in fluid-saturated cancellous bone is studied on the basis of two approaches: The thermodynamic-consistent Theory of Porous Media (TPM) and Biot’s theory. Phase velocities in the low-frequency range, calculated with the Biot-Gassmann relations, Wyllie’s equation and the TPM, are demonstrating that a simple, so-called hybrid biphasic TPM model is able to capture the main acoustical effects in cancellous bones. Furthermore, an extension towards high-frequency wave propagation is discussed on the basis of the constitutive relations for the momentum exchange of the fluid and the solid phases. Further numerical results show that, in the high-frequency (ultrasound) range a viscous correction as well as an added mass effect (tortuosity) needs to be taken into account to explain experimentally obtained results.     

Fluid Flow Analysis of Integrated Porous Bone Scaffold and Cancellous Bone at Different Skeletal Sites: In Silico Study

The dynamic characteristic of bone is its ability to remodel itself through mechanobiological responses. Bone regeneration is triggered by mechanical cues from physiological activities that generate structural strain and cause bone marrow movement. This phenomenon is crucial for bone scaffold when implanted in the cancellous bone as host tissue. Often, the fluid movement of bone scaffold and cancellous bone is studied separately, which does not represent the actual environment once implanted. In the present study, the fluid flow analysis properties of bone scaffold integrated into the cancellous bone at different skeletal sites are investigated. Three types of porous bone scaffolds categorized based on pore size configurations: 1 mm, 0.8 mm and hybrid (0.8 mm interlaced with 0.5 mm) were used. Three different skeletal sites of femoral bone were selected: neck, lateral condyle and medial condyle. Computational fluid dynamics was utilized to analyze the fluid flow properties of bone scaffold integrated cancellous bone. The results of this study reveal that the localization and maximum value of shear stress in an independent bone scaffold are significantly different compared to the bone scaffold integrated with cancellous bone by about 160% to 448% percentage difference. Low shear stress and high permeability were found across models that have higher Tb.Sp (trabecular separation). Specimen C and femoral lateral condyle showed the highest permeability in their respective category.

     

Hall effects on hydromagnetic falling liquid film

An investigation is made of flow of an electrically conducting falling liquid film over a smooth vertical surface taking Hall effects into account, the liquid being permeated by a transverse magnetic field. Consideration of Hall current into the flow indicates a similarity between the flow of a rotating liquid and that due to the non-rotating system in presence of Hall currents. Discussion has been made for electrically conducting falling film in presence of cross-flow due to hall effect in non-rotating system.     

Finite Element Simulation of the Fatigue Behaviour of Cancellous Bone*

Meccanica - Fatigue failure of bone has been implicated in a number of clinical failure scenarios. At the material level, the fatigue behaviour of cancellous bone is poorly understood. At the...     

利用松质骨理想化模型对骨小梁刚度的研究

利用结构张量的概念建立了考虑松质骨结构各向异性的理想模型，将杆型与板型两种传统模型统一起来．采用均匀化理论，通过有限单元的数值计算建立了松质骨弹性常数与结构张量、固体体积比之间的数值关系，并预测了骨小梁的弹性模量．结果表明，本文模型较好地体现了松质骨的各向异性力学性质．对骨小梁的计算结果表明，骨小梁的弹性模量在６７６ＧＰａ～１０９ＧＰａ范围内，平均意义上的结果是９２１ＧＰａ．     

Dynamics of liquid membranes. II: Adaptive finite difference methods

Two domain-adaptive finite difference methods are presented and applied to study the dynamic response of incompressible, inviscid, axisymmetric liquid membranes subject to imposed sinusoidal pressure oscillations. Both finite difference methods map the time-dependent physical domain whose downstream boundary is unknown onto a fixed computational domain. The location of the unknown time-dependent downstream boundary of the physical domain is determined from the continuity equation and results in an integrodifferential equation which is non-linearly coupled with the partial differential equations which govern the conservation of mass and linear momentum and the radius of the liquid membrane. One of the finite difference methods solves the non-conservative form of the governing equations by means of a block implicit iterative method. This method possesses the property that the Jacobian matrix of the convection fluxes has an eigenvalue of algebraic multiplicity equal to four and of geometric multiplicity equal to one. The second finite difference procedure also uses a block implicit iterative method, but the governing equations are written in conservation law form and contain an axial velocity which is the difference between the physical axial velocity and the grid speed. It is shown that these methods yield almost identical results and are more accurate than the non-adaptive techniques presented in Part I. It is also shown that the actual value of the pressure coefficient determined from linear analyses can be exceeded without affecting the stability and convergence of liquid membranes if the liquid membranes are subjected to sinusoidal pressure variations of sufficiently high frequencies.     

松质骨的细观力学研究评述

用细观力学方法分析松质骨的力学性能，研究松质骨的弹性模量、压缩强度与其相对密度之间的关系，这是骨力学的一个重要研究方向．