橡胶类零件有限变形应力分析用的三维光弹性方法

在应力冻结法基础上，建立了橡胶类零件有限变形应力分析用的三维光弹性方法，被研究对象的拉格朗日应变可达１５％。用一个应力集中三维效应的实例说明了本方法的有效性。     

三维有限变形弹性问题的分析方法

至今还未见到用通常的应力函数和位移函数分析三维有限变形弹性问题的报导。利用Hasegawa的工作和Adkins的摄动法,本文将位移函数用于求解表面力或体积力作用下的有限变形轴对称弹性问题,提出一个分析可压缩和不可压缩材料三维弹性问题的新的解析法,并用两个简单例子验证了这种分析方法。     

用全息光弹性法解三维应力分析问题

本文介绍了进行三维应力分析的全息光弹性方法及有关技术,分析了全息光弹性方法的主要困难在于冻结材料的应力光学常数比B/A接近-0.5,并提供了一种新的光弹性材料制作和冻结工艺。这种材料冻结时的应力光学常数比可以远离-0.5。用这种材料制成的三维模型,可以通过全息光弹性方法获得三维应力的全应力实验解答。用这种方法测定了对径受压圆球和高压压头对称断面上的应力分布。实验结果和理论解进行了比较。     

有限变形下应力集中的三维效应

用三维有了奶变形光弹性方法研究了在有限变形下含半圆槽试件和含圆孔试件的应力集中的三维效应，考察了三维效应的基本规律，所得结果与Ｎｅｕｂｅｒ和Ｈｅｙｗｏｏｄ所提供的在小变形下的相应数据作了比较。     

有限空心截圆锥扭转变形问题解析解

对有限空心截圆锥扭转变形问题进行了力学分析，确定其外锥面的内柱面上的载荷分布规律，应用三维弹性理论求解了有限空心截圆锥扭转变形问题，得到了应力解析式。文中给出了实际算例。     

航空有机玻璃高阶弹性常数超声测定

从有限变形弹性动力学理论出发,认为超声在经历初始静态形变的各向同性弹性体中的传播是叠加在有限变形上的微小扰动,假设应变是应力的三次函数,导出以材料高阶弹性柔度系数为参数的超声纵波传播速度与初始应力关系式,针对YB-3航空有机玻璃试件,通过一组应力-速度测量数据,利用非线性最小二乘法优化方法确定了该材料的前四阶弹性柔度系数,并对实验及模拟计算结果进行了讨论。     

光弹性粘结材料的试验研究

在三维光弹性试验中，为模拟具有软弱夹层或由不同岩土构成的复杂地基问题，需用粘结材料将各种不同弹模的型材粘结成组合模型。本文提出三种新型光弹性粘结材料，并通过试验阐明其光学和力学性能，分析比较了它们的主要特点和差异，同时探讨了其粘结应力的作用与效果。     

吊车压轨器强度的实验测试

宽厚板厂房的行车轨道在行车运行时承受来自行车水平导向轮的水平推力，该水平推力可能导致压轨器破坏，为确保压轨器的安全设计，采用平面光弹性、三维光弹性进行实验测试，分析在最不利工况下，各种压轨器所承担的水平推力份额，压轨器的变形和应力分布，给出强度分析评估，确定系统中各个压轨器以及固定螺栓的关键部位的应力水平。     

用光弹性法测定复合应力强度因子

工程结构裂纹尖端应力强度因子(SIF)由于形状、荷载的复杂性及边界条件的不确定性,难以用解析法得到,数值计算也有困难,而光弹性法弥补了上述方法的不足。本文用环氧树脂制作圆轴模型,采用机加工的方法制作圆轴模型裂纹,然后将加载模型进行应力冻结,通过光弹性实验研究分析了圆轴裂纹尖端应力分布。由于带环形裂纹的圆轴在弯扭组合变形时,离中性轴最远的裂纹尖端处于复合裂纹状态,而三维光弹性应力冻结法是测定复杂三维问题复合裂纹的有效方法。本文用双参数法测定I型应力强度因子,用切片逐次削去法测定Ⅲ型应力强度因子,实验误差较小。     

正常及病态下静脉壁的力学特性分析

本文应用多束纤维加强超弹性复合材料应变能函数及厚壁圆筒模型,通过有限变形弹性理论研究了正常及病态下静脉壁在静脉压及轴向预拉伸作用下的变形和应力分布等力学特性,着重分析了静脉移植后自适应变化静脉壁在动脉压下的力学特性.首先利用超弹性材料厚壁圆筒模型得到了静脉壁在静脉压下的变形方程,给出了静脉压下静脉壁的变形和应力分布曲线,讨论了静脉壁的力学特性.给出了静脉移植后,正常和自适应变化静脉壁在动脉压下的变形和应力分布曲线,讨论了静脉移植后静脉壁的力学特性及其自适应性变化.然后给出了各种病态静脉壁的变形和应力分布曲线,讨论了材料参数的变化对静脉壁力学特性的影响规律.     

Linear limit stresses of some photoelastic and mechanical model materials

Certain laws of similarity must be observed in structural-model analyses. In this paper, one aspect of model similarity—that of linearity—is examined quite extensively. Most model analyses assume that both prototype and model materials obey Hooke's law. But the plastics often used for structural or photoelastic models are viscoelastic or photoviscoelastic. The stress-strain and stress-birefringence relations are time dependent and may be nonlinear. Through careful calibration of model materials and proper design of model tests, potential errors due to the time dependence of material properties can usually be avoided. If the results of the test are to be interpreted conveniently and accurately, the stresses in the model material must be within the linear range. This range is limited and time dependent for most plastics. The linear range may extend only to stresses considerably below the ultimate or fracture strength of the material. Hence, analyses based don linearity may be in error if the initial stresses are too high and/or if given stresses are sustained too long before desired information is collected. The stresses which limit the linear range, called linear limit stresses, were determined for both stress-strain and stress-birefringence relations for four commonly used plastics: CR-39 (Cast Optics Co.), PS-1 and PS-2 (Photolastic, Inc.) and P6-K (B.A.S.F., Germany). A graphical presentation of the time-dependent photoelastic and mechanical properties is employed. It was concluded that linear limit stresses for birefringence are approximately equal to those based on strain and can therefore be used to establish, within reasonable bounds of accuracy, the linear range of behavior of the material.     

Growing avascular tumours as elasto-plastic bodies by the theory of evolving natural configurations

The aim of this article is to propose a simple way of describing a tumour as a linear elastic material from a reference configuration that is continuously evolving in time due to growth and remodelling. The main assumption allowing this simplification is that the tumour mass is a very ductile material, so that it can only sustain moderate stresses while the deformation induced by growth, that can actually be quite big, mainly induces a plastic reorganisation of malignant cells. In mathematical terms this means that the deformation gradient can be split into a volumetric growth term, a term describing the reorganisation of cells, and a term that can be approximated by means of the linear strain tensor. A dimensional analysis of the importance of the different terms also allows to introduce a second simplification consisting of decoupling the equations describing the growth of the tumour mass from those describing the flow of the interstitial fluid.     

End effects for anti-plane shear deformations of sandwich structures

The purpose of this research is to further investigate the effects of material inhomogeneity and the combined effects of material inhomogeneity and anisotropy on the decay of Saint-Venant end effects. Saint-Venant decay rates for self-equilibrated edge loads in symmetric sandwich structures are examined in the context of anti-plane shear for linear anisotropic elasticity. The problem is governed by a second-order, linear, elliptic, partial differential equation with discontinuous coefficients. The most general anisotropy consistent with a state of anti-plane shear is considered, as well as a variety of boundary conditions. Anti-plane or longitudinal shear deformations are one of the simplest classes of deformations in solid mechanics. The resulting deformations are completely characterized by a single out-of-plane displacement which depends only on the in-plane coordinates. They can be thought of as complementary deformations to those of plane elasticity. While these deformations have received little attention compared with the plane problems of linear elasticity, they have recently been investigated for anisotropic and inhomogeneous linear elasticity. In the context of linear elasticity, Saint-Venant's principle is used to show that self-equilibrated loads generate local stress effects that quickly decay away from the loaded end of a structure. For homogeneous isotropic linear elastic materials this is well-documented. Self-equilibrated loads are a class of load distributions that are statically equivalent to zero, i.e., have zero resultant force and moment. When Saint-Venant's principle is valid, pointwise boundary conditions can be replaced by more tractable resultant conditions. It is shown in the present study that material inhomogeneity significantly affects the practical application of Saint-Venant's principle to sandwich structures.     

Realizing the Willis equations with pre-stresses

This paper proves that the linear elastic behavior of the material with inhomogeneous pre-stresses can be described by the Willis equations. In this case, the additional terms in the Willis equations, compared with the classical linear elastic equations for homogeneous media, are related to the gradient of pre-stresses. In this way, the material length scale is naturally incorporated in the framework of continuum mechanics. All these findings also coincide with the results of transformation elastodynamics, so that they can meet the requirement of the principle of material objectivity and the principle of general invariance.     

Thermodynamic nature and control of the elastic limit in solids

The elastic limit of a solid is implicit in its thermo-elastic properties and can be determined from the constitutive equations of internal energy and entropy in the elastic range. The second law of thermodynamics is responsible for this, as it sets an upper bound to the internal energy that a material can store during isothermal elastic deformation processes. A link between irreversibility and elasticity can thus be established, which allows for a better control of the properties of strength, ductility and elastic limit of the material. For elastic-plastic materials of practical interest it implies that the yield limit cannot be assigned independently of the elastic constitutive equations, although the current approaches do so. An application to elastic-plastic materials with linear thermo-elastic properties reveals that, in the one-dimensional case, all information on the entropy of the material can be drawn from standard uniaxial tests. An easy procedure can then be devised to design the preparation process of the material so that the desired combination of strength, ductility and elastic limit can be achieved within the admissible values for these quantities.     

基于近场动力学理论的准脆性材料的本构力函数的构建

近场动力学理论(PD)是基于非局部思想的连续介质力学新理论,用于研究材料破坏问题。根据准脆性材料破坏的线性和非线性的力学行为,在初始微观弹脆性材料(PMB)的本构力函数中引入了键的损伤模型,将键的断裂过程分成了线性的弹性变形阶段和非线性的损伤变形阶段,以此构建了准脆性材料的本构力函数的基本形式。以典型的准脆性材料为例构建了其本构力函数,通过在压缩载荷下对含预制不同角度单裂纹缺陷的类岩材料的裂纹扩展进行PD数值模拟仿真,裂纹起裂位置和扩展方向与试样试验结果在一定程度上保持了一致,证明了该基于近场动力学理论的典型准脆性材料的本构力函数可用于该类材料的破坏分析。     

A double inclusion model for microcrack arrest in fibre reinforced brittle materials

A model for the prediction of microcrack growth in a fibre reinforced brittle matrix composite material is suggested. The model is based on composite material theory and linear elastic fracture mechanics. The microcracks in question are so-called large microcracks, i.e. microcracks which are bridged by the reinforcing fibres. The crack bridging fibres are “smeared” out to form a homogeneous medium. This homogeneous medium constitutes together with the matrix crack an ellipsoidal so-called “double inclusion.” Matrix cracking as well as interfacial debonding can be analysed and this analysis can be synthesized and interpreted as a determination of the strength of the reinforced matrix. The model is compared with some experimental results, and good agreement is found. The model can serve as a tool for the design of brittle matrix composite materials because it identifies the significance of fibre geometry, volume fraction of fibres, and adhesion between fibres and matrix.     

Evolution of the rheological properties during the reactive processing of thermoplastic/thermoset epoxy

The melt state reaction, or fusion process of bisphenol-A and the diglycidyl ether of bisphenol-A can produce both linear phenoxy backbone chains and crosslinked network structures. The linear chains can be thought of as thermoplastic polymer, while the crosslinked molecular matrix is a thermoset; therefore, this resin system can be termed a thermoplastic/thermoset epoxy.Rheological analysis has been performed on this system to determine the occurrence of the crossover of the storage and loss moduli during the reaction using three techniques: isothermal cure, interval frequency sweep, and interval stress relaxation.Determination of the activation energy of the reaction by consideration of the conventional gel-point determination prove unsatisfactory as compared to that which is determined by FTIR. An alternative technique is presented which yields a value in good agreement with that obtained by following epoxide consumption. The thermoplastic/thermoset nature of this material leads to the deviation from traditional thermoset cure behavior.     

Dynamic rheological properties of a fumed silica grease

The thermo-rheological characteristics of a fumed silica lubricating grease in linear and nonlinear oscillatory experiments have been investigated. The material rheological behavior represents a soft solid being thermo-rheologically complex. There is an abnormal temperature dependency in the range of ??10 to 10 °C which is related to the phase transition of the base oil. The dynamic moduli data in linear viscoelastic envelop (LVE) have been modeled using mode-coupling theory (MCT) in the whole temperature range. Two main relaxation mechanisms can be identified through linear and nonlinear viscoelastic properties related to interaction of the primary particle and its neighbor particles as well as a slow relaxation process which represents the escape of this particle from its “cage”. Finally, it is demonstrated that the dominant yielding process in large amplitude oscillatory experiments can be explained based on either particle cage rupture (consistent with MCT framework) or particle “hopping” out of its cage proposed in soft glassy rheology (SGR) model. It will be discussed that the governing mechanism depends on the applied frequency.     

脆性无序介质冲击破碎过程及其非线性动力学特性的细观模拟

为了模拟脆性无序介质的冲击破碎过程以及揭示其所伴随的非线性动力学特性，提出了梁－颗粒细观数值模型。在该模型中，介质被随机地离散成Ｖｏｒｏｎｏｉ多边形单元，相邻多边形采用弹脆性梁单元联结，介质的连续损伤和破坏由梁单元的断裂来模拟。算例表明，梁－颗粒细观数值模型不仅能实时给出介质的破碎图象及其分形维数，而且还能模拟介质内部应力和质点运动速度随时间的演化过程。