A NOTE ON MORI-TANAKA＇S METHOD

Explicit expressions of Mori-Tanaka＇s tensor for a transversely isotropic fiber rein- forced UD composite are presented. Closed-form formulae for the effective elastic properties of the composite are obtained. In a 3D sense, the resulting compliance tensor of the composite is symmetric. Nevertheless, the 2D compliance tensor based on a deteriorated Mori-Tanaka＇s tensor is not symmetric. Nor is the compliance tensor defined upon a deteriorated 2D Eshelby＇s tensor. The in-plane effective elastic properties given by those three approaches are different. A detailed comparison between the predicted results obtained from those approaches with experimental data available for a number of UD composites is made.     

Prediction of steady-state viscous and elastic properties of polyolefin melts in shear and elongation

The linear and nonlinear steady-state viscosities and elastic compliances were measured in shear and elongational flows for two low-density polyethylenes, a linear polypropylene, and two metallocene catalyzed polyethylenes (one linear and one long-chain branched) by Wolff et al. (Rheol Acta 49:95?C103, 2010) and Resch (dissertation, 2010). Comprehensive data of this type are rarely found in the literature, and comprehensive modeling of both viscous and elastic effects is even rarer. In this contribution, the reliability of a modeling approach proposed by Laun (J Rheol 30(3):459?C501, 1986) and based on the damping function concept is tested. The strain hardening seen for the long-chain branched polymers and its absence in the case of the linear polymer, the stronger decrease of the tensile compliance in comparison to the shear compliance with increasing stress, as well as the extended linear-viscoelastic regime of the shear viscosity in contrast to the shear compliance are correctly modeled. While the modeling of the nonlinear response in shear can be achieved with only one material parameter for most of the polymers considered here, the nonlinear modeling in elongation is achieved with two parameters. The same parameter values are shown to describe viscous as well as elastic properties of the melts, and thus the relations of Laun can be used to test the consistency of viscosity and compliance measurements.     

Constitutive Model Calibration for Powder Compaction Using Instrumented Die Testing

Calibration procedures for constitutive models for powder compaction are presented. A practical calibration method based on a die compaction experiment is presented. A newly developed apparatus consisting of a die instrumented with radial stress sensors is described. The paper proposes two contributions to account for errors present in instrumented die testing, which are due to 1) elastic compliance of the testing frame, influencing the measurement of axial strain and 2) the presence on non-homogeneous stress state in the test specimen. It is shown that system compliance is important for generating an accurate stress-strain curve for compression. The effect of different compliance correction methods is evaluated with regard to the accuracy of models predicting pressing forces. The system compliance becomes more significant during unloading in the die; this information is used to determine the elastic properties. A new compliance correction method is introduced following a detailed analysis of the forces and deformations of different parts of the loading frame. In instrumented die compaction the axial and radial stresses are measured at fixed locations and the specimen is subject to non-homogeneous stresses and strains due to the effect of friction between the powder and die wall. Starting from the Janssen-Walker method of differential slices a method to account for non-homogeneous stress and strain is developed.     

Effective elastic properties of solids with defects of irregular shapes

Pores and defects in real materials often have very irregular shapes. Thus, micromechanical modeling based on the analytical solutions of elasticity becomes inapplicable. The objective of this paper is to present a computational procedure to calculate the contribution of the irregularly shaped defects into the effective moduli of two-dimensional elastic solids. In this procedure, the cavity compliance tensor is constructed numerically for an individual defect, and then used in the elastic potential-based approach to predict the effective moduli of porous solids. Two computational methods are used in this paper to calculate the components of a cavity compliance tensor: finite element analysis and numerical conformal mapping. Application of this procedure to the regular hole shapes produces results that are in good correspondence with analytical predictions.     

The Micromechanics of Short-Term Damageability of Fibrolaminar Composites

A theory of microdamageability is constructed for fibrous laminated composites consisting of transversally isotropic fibers and a microdamaged isotropic porous binder. Microdamages in the binder are simulated by pores filled with compression-resisting particles of the destroyed material. Damage in a microvolume of the binder is described by the Schleicher–Nadai strength criterion, which allows for the difference between the ultimate tensile and compressive loads. The ultimate strength is a random function of coordinates with the Weibull distribution. The stress–strain state and effective characteristics of the material are determined by solving the stochastic equations of elastic theory for a fibrous laminated composite with a porous binder. The equations of deformation and microdamageability are closed by the equations of porosity balance in the binder. Nonlinear diagrams of the concurrent processes of deformation of the fibrous laminated material and microdamage of the matrix for various physical and geometrical parameters are constructed     

有限元分析中的最优离散化

系统的最优离散化具有很大的实用价值和理论意义。采用这种方法可以用最少的自由度得到最精确的数值解。本文给出了两种有代表性的方法,并收集了一些应用实例,其中包括笔者和刘永成、朱建中在Zienkiewicz指导下所作的一些工作。这种方法作为一种重分析方法不仅可用于线性问题,而且也可以用于具有表面非线性的弹性接触问题。      

Identification of the elastic and damping characteristics of carbon fiber-reinforced plastic based on a study of damping flexural vibrations of test specimens

A theoretical and experimental method for determining the elastic and damping characteristics of materials is proposed based on analysis of vibrograms of damping flexural vibrations of test specimens with different structures. It is shown that during tension–compression and shear of a carbon fiber-reinforced plastic made of Porcher 3692 carbon fabric and EDT-69NM polymer binder, its dynamic elastic modulus decreases considerably with increasing frequency of deformation in the range of 0–120 Hz. The amplitude dependences of the logarithmic vibration decrements of the carbon fiber-reinforced plastic are determined by minimizing the discrepancy between the experimental and calculated internal-damping parameters of the test specimens in tension–compression and shear.     

三维机织复合材料的弹性性能预报模型

建立了基于等效响应比拟技术的三维机织复合材料弹性性能预报模型．首先将三维机织物的结构单元分解为4个子元(经纱、纬纱、填充纱和接结纱),用几何模型去估算这些子元的体积分数．然后依据不同的外载形式,将复合材料的应力-应变关系等效地表达为3组诸子元所组成的三维弹簧网络．根据刚度系数的物理意义,采用不同的弹簧网络连接形式,并按体积平均化方法获得材料总体刚度矩阵中相应的刚度系数,进而计算得到三维机织复合材料的9个弹性系数．该模型考虑了层内交织经纱、层间交织接结纱的弯曲以及材料内部纯树脂区对三维机织复合材料弹性性能的影响．试验结果与模型的理论预测值进行比较,表明这个模型是有效的。     

The Effect of the Elastic Compliance of Actuator Components on the Dynamics of a Robot

Kinematic and dynamic control problems for a pedestal-mounted robot with a multilink arm are formulated. The robot is considered a system of perfectly rigid bodies controlled by a combined actuating system. The mathematical model of robot dynamics accounts for the elastic properties of actuator components based on the formalism of Lagrange equations of the second kind. The effect of the elastic compliance of the actuator components on the dynamics of manipulator links and actuator motors is discussed. A robot with a two-link arm is considered as an example     

On estimation methods for effective moduli of microcracked solids

Summary  Most of the conventional methods for estimating the overall elastic moduli of microcracked solids are defined based on the concept of effective medium or effective field. The formal similarity of these methods is examined in this paper. A one-to-one correspondence relation exists between the effective medium methods and the effective field methods in the sense that they yield identical results. In addition to the conventional estimation techniques, any other number of such approaches may be constructed by appropriately specifying the effective matrix compliance (or stiffness) tensor and the effective stress (or strain) field which a microcrack is assumed to be subjected to. To generate continuous spectra of new methods for estimating the effective elastic moduli, two simple and straightforward approaches are proposed, which contain one or two adjustable parameters in order to yield results of good accuracy. The discussion in this paper can be extended to other kinds of heterogeneous materials. Received 4 October 2000; accepted for publication 30 January 2001     

Spectral decomposition of the compliance fourth-rank tensor for orthotropic materials

Summary The compliance tensor related to orthotropic media is spectrally decomposed and its characteristic values are determined. Further, its idempotent tensors are estimated, giving rise to energy orthogonal states of stress and strain, thus decomposing the elastic potential in discrete elements. It is proven that the essential parameters, required for a complete characterisation of the elastic properties of an orthotropic medium, are the six eigenvalues of the compliance tensor, together with a set of three dimensionless parameters, the eigenangles θ, ϕ and ω. In addition, the intervals of variation of these eigenangles with respect to different values of the elastic constants are presented. Furthermore, bounds on Poisson's ratios are obtained by imposing the thermodynamical constraint on the eigenvalues to be strictly positive, as specified from the positive-definite character of the elastic potential. Finally, the conditions are investigated under which a family of orthotropic media behaves like a transversely isotropic or an isotropic one. Received 5 January 1999; accepted for publication 22 June 1999     

Comparison of viscous and elastic properties of polyolefin melts in shear and elongation

Viscous and elastic properties of a linear polypropylene (PP) and a long-chain branched low-density polyethylene (LDPE) have been investigated by creep and creep–recovery experiments in shear and elongation. The data obtained verify the ratios between the linear values of the viscosities and the steady-state elastic compliances in shear and elongation predicted by the theory of linear viscoelasticity. In the nonlinear range, no simple correlation between the viscous behaviour in shear and elongation exists. The elongational viscosity of the PP decreases with increasing stress analogously to the shear thinning observed; the linear range extends to higher stresses in elongation than in shear, however. The LDPE shows thinning in shear and strain hardening in elongational flow. For the LDPE, a linear steady-state elastic tensile compliance corresponding to one third of the linear steady-state elastic compliance in shear was determined. For the PP, this theoretically predicted value is approximately reached. Analogous to the viscous behaviour, the linear range extends to higher stresses in elongation than in shear. For both materials, the steady-state elastic compliances in the nonlinear range decrease with increasing stress in shear as well as in elongation. However, the decrease in elongation is more pronounced.     

Elastic beam in adhesive contact

Dynamic and quasistatic processes of contact with adhesion between an elastic or viscoelastic beam and a foundation are considered. The contact is modeled with the Signorini condition when the foundation is rigid, and with normal compliance when it is deformable. The adhesion is modeled by introducing the bonding function β, the evolution of which is described by an ordinary differential equation. The existence and uniqueness of the weak solution for each of the problems is established using the theory of variational inequalities, fixed point arguments and the existence and uniqueness result in Commun. Contemp. Math. 1(1) (1999) 87–123. The numerical approximations of the quasistatic problem with normal compliance are considered, based on semi-discrete and fully discrete schemes. The convergence of the solutions of the discretized schemes is proved and error estimates for these approximate solutions are derived.     

Characteristics of local compliance of an elastic body under a small punch indented into the plane part of its boundary

An asymptotic solution of the contact problem of an elastic body indented (without friction) by a circular punch with a flat base is obtained under the assumption of a small relative size of the contact zone. The resulting formulas involve integral characteristics of the elastic body, which depend on its shape, dimensions, fixing conditions, Poisson's ratio, and location of the punch center. These quantities have the mechanical meaning of the coefficients of local compliance of the elastic body. Relations that, generally, reduce the number of independent coefficients in the asymptotic expansion are obtained on the basis of the reciprocal theorem. Some coefficients of local compliance at the center of an elastic hemisphere are calculated numerically. The asymptotic model of an elastic body loaded by a point force is discussed.     

Elastic coiled-coils act as energy buffers in the ATP synthase

In the ATP synthase, transmission of energy from the membrane-embedded F0 sector to the catalytic F1 sector is accomplished by two stalks composed of coiled-coils. The great efficiency of the enzyme, despite the presence of a symmetry mismatch between the F1 and F0 sectors, suggests the involvement of elastic elements that store energy during the catalytic cycle. Here, the stalk subunits γ and b are investigated as the source of this elastic compliance using a continuum mechanical model of coiled-coils and energy arguments. The analysis shows that the compliance of both subunits is required for efficient energy transmission between F0 and F1. In addition, the predicted mechanical properties of coiled-coils in the ATP synthase suggest mechanisms whereby regulatory subunits influence the enzyme activity.     

An analytical elastic-perfectly plastic contact model

A new formulation for elastic-perfectly plastic contact in the normal direction between two round surfaces that is solely based on material properties and contact geometries is developed. The problem is formulated as three separate domains: the elastic regime, mixed elastic–plastic behavior, and unconstrained (fully plastic) flow. Solutions for the force–displacement relationship in the elastic regime follow from Hertz’s classical solution. In the fully plastic regime, two well supported assumptions are made: that there is a uniform pressure distribution and there is a linear force–deflection relationship. The force–displacement relationship in the intermediate, mixed elastic–plastic regime is approximated by enforcing continuity between the elastic and fully plastic regimes. Transitions between the three regimes are determined based on empirical quantities: the von Mises yield criterion is used to determine the initiation of mixed elastic–plastic deformation, and Brinell’s hardness for the onset of unconstrained flow. Unloading from each of these three regimes is modeled as an elastic process with different radii of curvature based on the regime in which the maximum force occurred. Simulation results explore the relationship between the impact velocity and coefficient of restitution. Further comparisons are made between the model, experimental results found in the literature, and other existing elastic–plastic models. The new model is well supported by the experimental measurements of compliance curves for elastic–plastic materials and of coefficients of restitution from impact studies, and in elastic-perfectly plastic regimes is demonstrated to be more accurate than existing models found in the literature.     

The role of binder mobility in spontaneous adhesive contact and implications for cell adhesion

The standard view of mechanical adhesive contact is as a competition between a reduction in free energy when surfaces with bonding potential come into contact and an increase in free energy due to elastic deformation that is required to make these surfaces conform. An equilibrium state is defined by an incremental balance between these effects, akin to the Griffith crack growth criterion. In the case of adhesion of biological cells, the molecules that tend to form surface-to-surface bonds are confined to the cell wall but they are mobile within the wall, adding a new phenomenon of direct relevance to adhesive contact. In this article, the process of adhesive contact of an initially curved elastic plate to a flat surface is studied for the case in which the binders that account for adhesion are able to migrate within the plate. This is done by including entropic free energy of the binder distribution in the total free energy of the system. By adopting a constitutive assumption that binders migrate at a speed proportional to the local gradient in chemical potential, the transient growth of an adhesion zone due to binder transport is analyzed. For the case of a plate of very large extent, the problem can be solved in closed form, whereas numerical methods are invoked for the case of a plate of limited extent. Results are presented on the rate of growth of an adhesion zone in terms of system parameters, on the evolution of the distribution of binders and, in the case of a plate of limited extent, on the long-term limiting size of the adhesion zone.     

New Type of Optimal Topologies by Iterative Method

ABSTRACT

Optimal design with thousands of variables is a great challenge in engineering calculations. In this paper beside the short history of optimality criteria methods, a solution technique is introduced for the topology optimization of elastic disks under single parametric static loading. Different boundary conditions and thousands of design variables are applied. Due to a simple mesh construction technique, the checker-board pattern is avoided. The Michell-type problem is investigated minimizing the weight of the structure subjected to a compliance condition. The numerical procedure is based on an iterative formula that is formed by the use of the first-order optimality condition of the Lagrangian function. The application is illustrated by numerical examples. The effect of the different loading conditions is studied for the Michell-type topologies as well.     

配置柔顺机构空间机器人双臂捕获卫星操作力学模拟及基于神经网络的全阶滑模避撞柔顺控制

讨论了空间机器人双臂捕获卫星操作过程避免关节冲击破坏的避撞柔顺控制问题. 为此在关节电机与机械臂之间设计了一种旋转 型串联弹性执行器(rotatory series elastic actuator, RSEA)--柔顺机构,其作用在于:(1) 通过其内置弹簧的拉伸或压缩变形来吸收捕获操作过程中被捕获卫星对空间机器人关节产生的冲击能量;(2) 可以利用合理设计的与之配合的避撞柔顺控制策略来保证关节冲击力矩受限在安全范围. 首先,利用第二类Lagrange方程分别建 立了捕获操作前含柔顺机构双臂空间机器人的开环分系统动力学模型与目标卫星的分系统动力学模型;之后,基于系统动量 守恒关系、闭链系统位置与速度几何约束关系,获得了捕获操作后空间机器人与被捕获卫星闭链混合体系统综合动力学方程; 最后,基于RBF神经网络提出了一种捕获操作后两者混合体系统镇定运动的全阶终端滑模避撞柔顺控制方案. 所提方案结合柔 顺机构在有效吸收、缓冲被捕获卫星冲击能量的同时,还在冲击能量过大时适时开、关空间机器人关节驱动器,以避免关节驱 动器过载、破坏;此外,还通过最小权值范数法分配了机械臂各关节力矩,以保证双臂协调操作. Lyapunov稳定性理论证明了 系统的全局稳定性,系统计算机数值仿真也验证了上述避撞柔顺控制策略的有效性.