Strain-coupling effects in branched polymers

The applicability of a strain-coupling integral constitutive equation to the analysis of the nonlinear viscoelasticity of branched polymers is evaluated. A simpler and more efficient method is proposed for evaluating the material functions of the strain-coupling constitutive equation.     

Strain-coupling effects in steady planar extension

This study is concerned with an evaluation of the capability of the strain-coupling model to predict steady shear and steady planar extensional flows. A comparison is made between the predictions of the K-BKZ and strain-coupling theories.     

光纤陀螺低温快速启动技术

光纤陀螺的启动时间与超辐射发光二极管(SLD)的输出性能密切相关。论文建立了SLD的ArcTan模型,并利用该模型分析光功率的温度敏感度和驱动电流敏感度。结果显示低温启动时,改变驱动电流可更快实现光功率稳定(与变温控制相比)。以此为指导设计了新型驱动电路,实现光功率自动控制,有效缩短光纤陀螺低温启动时间。论文描述了SLD的新型数学模型,设计出SLD的新型驱动电路。以低温(的40℃)启动时间较长(～8.5s)的陀螺仪表为应用对象,改进驱动电路后,该仪表可在2.5s内完成启动。     

The behaviour of field-responsive fluids during shear start-up

The application of an external field (magnetic or electric) to suspensions of particles in a carrier liquid often causes a dramatic increase in the flow resistance. The transient stress response of these systems during the start-up of shear flow was studied as a function of the shear rate, using a system of carbonyl iron particles dispersed in paraffinic spindle oil under magnetic flux densities up to 0.57 T. It was found that initially the stress increased in proportion to the applied strain, reaching a plateau value at a characteristic strain of 0.2. Similar strain dependence of the transient stress behaviour was observed for shear rates spanning the range 0.01 s^–1 to 10 s^–1, suggesting that strain-governed deformation and rupture of the particle aggregates in the fluid was the main contribution to the response. In addition, the steady state flow curves of these fluids were obtained over the shear rate range 0.1 to 100 s^–1.     

含有启动压力梯度的渗流问题及其无网格解法

针对两种典型的涉及启动压力梯度的渗流问题,给出了无量纲化的渗流控制方程、初始条件和边界条件,并使用无网格方法进行数值模拟。计算结果使用Gringarten—Bourdet图版进行井底压力分析,给出了一种计算动边界位置的方法,并详细讨论了动边界变化情况。     

Geometric nonlinear formulation for curved beams with varying curvature

Based on exact Green strain of spatial curved beam, the nonlinear strain-displacement relation for plane curved beam with varying curvature is derived. Instead of using the previous straight beam elements, curved beam elements are used to approximate the curved beam with varying curvature. Based on virtual work principle, rigid-flexible coupling dynamic equations are obtained. Physical experiments were carried out to capture the large overall motion and the strain of curved beam to verify the present rigid-flexible coupling formulation for curved beam based on curved beam element. Numerical results obtained from simulations were compared with those results from the physical experiments. In order to illustrate the effectiveness of the curved beam element methodology, the simulation results of present curved beam elements are compared with those obtained by previous straight beam elements. The dynamic behavior of a slider-crank mechanism with an initially curved elastic connecting rod is investigated. The advantage of employing generalized-α method is pointed out and the special nonlinear dynamic characteristics of the curved beam are concluded.     

粘弹性阻尼器动力设计及其应用的实验研究

本文提出一种圆柱式剪切型粘弹性阻尼器，给出其具有结构阻尼特性的单自由度动力学系统模型，用正弦扫频实验技术实现了对阻尼器动力学特性的测量。通过实验，研究了粘弹性材料动态特性与阻尼器动力学特性的关系，并给出这种关系的数学表示，给出了这类阻尼器的设计方法和基本公式。实验结果表明，应用这种阻尼器可有效控制桁架结构的振动，实现对结构的阻尼控制。     

Effect of ionic interaction on linear and nonlinear viscoelastic properties of ethylene based ionomer melts

The effect of ionic interaction on linear and nonlinear viscoelastic properties was investigated using poly(ethylene-co-methacrylic acid) (E/MAA) and its ionomers which were partially neutralized by zinc or sodium. Dynamic shear viscosity and step-shear stress relaxation studies were performed. Stress relaxation moduli G(t, y) of the E/MAA and its sodium or zinc ionomers were factorized into linear relaxation moduli G°(t) and damping functions h(y). The relaxation modulus at the smallest strain in each ionomer agreed with the linear relaxation modulus calculated from storage modulus G and loss modulus G. In the linear region, the ionic interaction shifted the relaxation time longer with keeping the same relaxation time distribution as E/MAA. In the nonlinear region, the ionic interaction had no influence on h(y) when the ion content was low. At higher ion content, however, the ion bonding enhanced the strain softening of h(y).     

Slip yield stress effects in start-up Newtonian Poiseuille flows

Analytical solutions are derived for various start-up Newtonian Poiseuille flows assuming that slip at the wall occurs when the wall shear stress exceeds a critical value, known as the slip yield stress. Two distinct regimes characterise the steady axisymmetric and planar flows, which are defined by a critical value of the pressure gradient. If the imposed pressure gradient is below this critical value, the classical no-slip, start-up solution holds. Otherwise, no-slip flow occurs only initially, for a finite time interval determined by a critical time, after which slip does occur. For the annular case, there is an additional intermediate (steady) flow regime where slip occurs only at the inner wall, and hence, there exist two critical values of the pressure gradient. If the applied pressure gradient exceeds both critical values, the velocity evolves initially with no-slip at both walls up to the first critical time, then with slip only along the inner wall up to the second critical time and finally with slip at both walls.     

New ill-posed problems in rheology

Many methods of material characterization by rheological methods lead to ill-posed problems. The nature of ill-posedness is discussed. In this light, some such new problems appearing in molecular weight characterization of homopolymers as well as in the characterization of size distribution of dispersed phases in polymer blends by rheological techniques are analyzed. The working capability of a nonlinear regularization method is demonstrated with examples of blend rheology. The role of Professor Meissner in motivating the research in the field of ill-posed problems as well as his important contribution to rheology of polymer blends is outlined.Dedicated to Prof. Dr. J. Meissner on the occasion of his retirement from the chair of Polymer Physics at the Eidgenössische Technische Hochschule (ETH) Zürich, Switzerland     

Absorbing Balls for Equations Modeling Nonuniform Deformable Bodies with Heavy Rigid Attachments

We study degenerate nonlinear partial differential equations with dynamical boundary conditions describing the forced motions of nonuniform deformable bodies with heavy rigid attachments. We prove that the dynamical system generated by a discretization of these equations has an absorbing ball whose size is independent of the order of the discretization. This result implies the existence of an absorbing ball for the infinite-dimensional dynamical system corresponding to the original degenerate partial differential equation and thereby serves as a critical step for establishing the existence of global attractors for this system. Our results also address the interesting mechanical question of how nonuniformity complicates the longterm dynamics of the coupled systems we consider.     

一维非线性黏弹体和黏塑性体中的最优应变路径

得出了一维非线性黏弹体和黏塑性体中最优应变路径方程，并揭示了它们的某些特性，如：（１）当非线性黏弹本构方程中的黏性部分与应变的关系具有上凸形式时，相应的最优应变路径具有下凸性质；（２）对于过应力和Ｂｏｄｎｅｒ－Ｐａｒｔｏｎ黏塑性体，它们的最优应变路径是塑性应变为线性形式，即塑性应变率为常数，而弹－黏塑性体的最优应变路径则不同。     

Molecular theories of nonlinear viscoelasticity of polymers

It is emphasized that considerable advances have been made recently in the development of the molecular theories of nonlinear viscoelasticity of concentrated solutions and melts of linear polymers. The new ideas in this exceptionally important field of the rheology of polymers are analysed. The methods by which the constraints (entanglements) imposed on the motion of macromolecules by the polymer environment are taken into account are also considered in the paper. The most detailed discussion is devoted to the model of topological constraints in the form of a tube and to the self-consistent theory of anisotropic micro-viscoelasticity which takes into account the relaxation nature of the interaction of macromolecules with their surrounding medium as well as the anisotropy of their mobility.Invited paper, presented at the XII-th All-Union Symposium on Rheology held in Riga (USSR), December 7–9, 1982.     

A nonlinear generalized continuum approach for electro-elasticity including scale effects

Materials characterized by an electro-mechanically coupled behaviour fall into the category of so-called smart materials. In particular, electro-active polymers (EAP) recently attracted much interest, because, upon electrical loading, EAP exhibit a large amount of deformation while sustaining large forces. This property can be utilized for actuators in electro-mechanical systems, artificial muscles and so forth. When it comes to smaller structures, it is a well-known fact that the mechanical response deviates from the prediction of classical mechanics theory. These scale effects are due to the fact that the size of the microscopic material constituents of such structures cannot be considered to be negligible small anymore compared to the structure's overall dimensions. In this context so-called generalized continuum formulations have been proven to account for the micro-structural influence to the macroscopic material response. Here, we want to adopt a strain gradient approach based on a generalized continuum framework [Sansour, C., 1998. A unified concept of elastic-viscoplastic Cosserat and micromorphic continua. J. Phys. IV Proc. 8, 341-348; Sansour, C., Skatulla, S., 2007. A higher gradient formulation and meshfree-based computation for elastic rock. Geomech. Geoeng. 2, 3-15] and extend it to also encompass the electro-mechanically coupled behaviour of EAP. The approach introduces new strain and stress measures which lead to the formulation of a corresponding generalized variational principle. The theory is completed by Dirichlet boundary conditions for the displacement field and its derivatives normal to the boundary as well as the electric potential. The basic idea behind this generalized continuum theory is the consideration of a micro- and a macro-space which together span the generalized space. As all quantities are defined in this generalized space, also the constitutive law, which is in this work conventional electro-mechanically coupled nonlinear hyperelasticity, is embedded in the generalized continuum. In this way material information of the micro-space, which are here only the geometrical specifications of the micro-continuum, can naturally enter the constitutive law. Several applications with moving least square-based approximations (MLS) demonstrate the potential of the proposed method. This particular meshfree method is chosen, as it has been proven to be highly flexible with regard to continuity and consistency required by this generalized approach.     

非线性粘弹性拟静态问题与非线性弹性静力问题对应原理

本文应用多重单边拉氏变换导出了非线性粘弹性拟静态问题与非线性弹性静力问题的对应关系,从而把过去认为只有线性条件下存在的粘弹性——弹性对应原理拓展到了非线性范畴     

Predicting the nonlinear hereditary viscoelasticity of polymers

A mathematical model for the nonlinear hereditary viscoelasticity of polymer materials is proposed to predict deformation processes of various complexity — from simple relaxation and simple creep to complex deformation-relaxation and reverse relaxation processes with alternative loading and unloading. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 6, pp. 147–157, November–December, 2007.     

温度对介电弹性体材料力电耦合变形的影响

介电弹性体(Dielectric Elastomer,简称DE)材料是一类在电场激励下可以产生大幅度尺寸或形状变化的新型柔性功能材料.DE材料具有非常宽的温度应用范围,这种宽的温度工作范围和快速大变形性能为各种柔性致动器结构提供了良好的基础,但作为一种粘弹性高分子材料,温度对其性能的影响也是非常明显的.然而到目前为止,所有关于DE材料驱动性能的研究仅局限于室温条件下,温度变化对DE材料力电耦合稳定性的影响几乎没有相关报道.基于此,通过实验研究了温度对最常用的DE材料(VHB 4910,3M)力电耦合变形的影响,结果表明:升高温度可以提高DE材料的力电耦合变形;温度越高,DE材料越容易发生力电耦合失稳.然后,从热力学和粘弹性力学出发,建立了考虑温度影响后的DE材料的粘弹性力电耦合模型,数值模拟理论结果和实验结果定性地吻合.     

Torsion and normal force responses of glassy polymers in the sub-yield regime

While there is a major body of literature relating the non-linear response of both elastomers and polymer melts with the molecular structure and topology of the chains, the same cannot be said of the non-linear response, especially that below the yield point, for polymer glasses. Here we take an approach that uses ideas of finite deformation elasticity and apply them to the isochronal response of glassy polymers in torsional deformations. We find that, while the torsional (shear) responses are similar for different molecular structures, there seems to be a strong effect of side group relaxations on the normal forces. The results are discussed in terms of the strain energy density function and the opportunities for future research.     

The indenter tip radius effect in micro- and nanoindentation hardness experiments.

Nix and Gao established an important relation between the microindentation hardness and indentation depth. Such a relation has been verified by many microindentation experiments (indentation depths in the micrometer range), but it does not always hold in nanoindentation experiments (indentation depths approaching the nanometer range). Indenter tip radius effect has been proposed by Qu et al. and others as possibly the main factor that causes the deviation from Nix and Gao's relationship. We have developed an indentation model for micro- and nanoindentation, which accounts for two indenter shapes, a sharp, conical indenter and a conical indenter with a spherical tip. The analysis is based on the conventional theory of mechanism-based strain gradient plasticity established from the Taylor dislocation model to account for the effect of geometrically necessary dislocations. The comparison between numerical result and Feng and Nix's experimental data shows that the indenter tip radius effect indeed causes the deviation from Nix-Gao relation, but it seems not be the main factor. The project supported by the National Natural Science Foundation of China (10121202) and the Ministry of Education of China (20020003023)     

对不可压黏弹材料非线性本构关系的探讨

运用张量分析,证明了适合描述不可压缩黏弹性材料非线性本构关系的3种理论：BKZ理论、Lianis理论和Chirstensen理论,运用到各向同性材料中它们的单轴拉伸具有一样的表现形式,同时也验证了3种理论在解释非线性本构关系时具有统一性．