Notes on the X-ray Theory

My aim is to better compare thermoelasticity theory with a continuum theory of X-ray observations of crystals, to be described, to make it easier to adapt ideas and techniques from one to the other. To this end, I will present some different ways of formulating the X-ray theory. Also, I will adapt symmetry considerations from the former, partly to analyze problems of a kind not considered in thermoelasticity theory. This revised version was published online in August 2006 with corrections to the Cover Date.     

关于非局部场论的几个新观点及其在断裂力学中的应用(Ⅲ)——重论线性非局部弹性理论

证明了在线性非局部弹性力学中能量平衡方程是动量平衡方程的首次积分,论证了在非局部场论中局部化体力残余恒为零。详细推导了线性非局部弹性理论的本构方程,得到了反对称应力存在的新结果。     

Nonlinear vibration analysis of viscoelastic cable with small sag

Both the inplane and out-of-plane transverse vibrations of a viscoelastic cable subjected to an initial stress distributing uniform on the cross section are studied. The constitution of the cable material is assumed to be of the hereditary integral type. The partial differential-integral equations of motion are derived first. Then by applying Galerkin's method, the governing equations are reduced to a set of second-order nonlinear differential-integral equations which are solved by finite difference numerical integration procedures. Finally, the effects of the viscosity parameter and the elastic parameter on the transient amplitudes of the first mode are investigated by numerical simulation. Project supported by the National Natural Science Foundation of China (No. 59635140) and the National Postdoctoral Foundation of China.     

现代统一塑性理论

经典的本构理论不能精确描述材料表现出的率相关性和非线性本构关系,导致现代统一塑性理论的出现.各派现代统一塑性理论形式不相同,但最根本的观点接近:①材料变形由弹性变形与非弹性变形两部分组成,不再将非弹性变形区分为塑性变形与蠕变;②存在着两种物理参量:背应力X与粘滞系数K_0 σ—X构成非弹性形变的动力,K是非弹性应变的阻力,因而ε~(in)=f((σ-X)/K);③原始材料X= 0,K=K_0,K_0为较大的标量,所以加载初始表现出线弹性,续继加载X与K按演化规律变化导致非线性形变规律的出现.各派统一塑性理论的主要差异在于X与K的演化公式不同.各有其长亦有其短.在大量试验基础上取各派之长,舍各派之短,融合为一科学的理论是今后发展的方向.      

考虑材料非线性的两端固支柱后屈曲载荷优化算法

针对满足Ramberg-Osgood本构关系的6082-T6铝合金固支柱的后屈曲问题进行了研究。利用泰勒展开式得到了用于计算横截面上弯矩的应力显式表达式,并通过弯矩-曲率关系导出了用剪力表示的控制方程。由于同时考虑材料非线性和几何非线性,此时控制方程为二阶非线性微分方程,本文提出了求解包含屈曲载荷的控制方程的优化算法。以屈曲载荷和固支端处的曲率为设计变量,以固支柱中点处的转角和挠度形成目标函数。利用进退法和黄金分割法改变设计变量的值,通过程序中包含的R-K法输出不同的结果,然后将输出的结果代入到目标函数中进行比较,获得包含目标函数极小值的最小区间,最终实现了对满足计算精度的设计变量值的确定。相较于打靶法复杂的分析过程,该优化算法优化过程简单,计算速度较快。为了验证本文算法的正确性,与两端固支6082-T6铝合金柱后屈曲时的数值解进行了对比。     

A New Molecular Theory of Non‐Linear Viscoelasticity for Vitrifiable (or Crystallizable) Thermoplastic Polyurethane Elastomers

The molecular theory of non‐linear viscoelasticity for vitrifiable thermoplastic polyurethane elastomers (VTPUE) is a refinement and extension of viscoelastic theory of thermoplastic elastomers and polyurethanes to glassy transition, a structural model and a mechanism of vitrification for glassy polymers were proposed. Five kinds of constituent chains with Nagai chain constraint consisting of soft‐domains, hard‐domains, and entanglements are used as the elementary structural and statistical ensemble units for the correlation of molecular and phase‐domain structures to the static and dynamic mechanical behaviors. So the influences of non‐Gaussian in character, the phase separation of domain, the network topology of structure, the affined deformation of constituent chains, and the thermal history are all taken into account in the constituent chains of the theory. Free energies of deformation for the VTPUE segment copolymer were calculated by the statistical mechanics with the probability distribution functions of the sizes for the five kinds of constituent chains. Then the static constitutive equations and modulus of four types of deformation and the dynamic shear viscosity, modulus and loss tangent of VTPUE are derived from the proposed theory. The theory is successful in relating the molecular chain parameters C₁₀₀, C₀₂₀, and C₂₀₀ to the constitutive equations and modulus under large deformations and the micro‐domain structure to the complex shear viscosity and modulus and the loss tangent. The dynamic shear modulus and loss tangent of VTPUE are related to the domain structures through the fraction of hard segments (W_h), the molecular weight of soft segment (M_ns), and the growth dimensional parameters of hard and soft domains (β). Two series of linear VTPUE copolymers (ES and ET) with different fractions(W_h) of hard segments and molecular weight (M_ns) of soft segments were prepared. Their static and dynamic mechanical properties were studied by uni‐axial extension and dynamic analysis tests. Then the constitutive equation at uni‐axial extension and the expressions of shear modulus and loss tangent are verified by these experimental data, and excellent agreement between the theory and experiments is achieved. It is shown, that the proposed theory can predict the viscoelastic behavior of vitrifiable thermoplastic polyurethanes.     

Identification of quasi-static displacement for constitutive models of viscoelasticity

I.IntroductionQuasi-staticdisplacementbasedtechniqueofinverseanalysisfortheconstitutlveparametersisbeingwidlyusedintheundergroundengineeringandsomeotherfields.Anumberofprogresshasbeenachievedinthefieldofidentificationfortheviscoelasticconstitutiveparallleters.XueandYang(1986)l'].Liu(1986)l=lemployedintegraltransformationtechniquetoidentifyviscoelasticconstitutiveparameters;a3-DinverseanalysisfortheviscoelasticconstitutiveparameterswasconductedbyYang(199I)l'];YallgandWu(1996)l'Jproposedagen…     

饱和砂土动本构理论研究进展

饱和砂土由于它对动载荷作用的特殊敏感性在土动力学和土工抗震问题研究中占据了重要的地位,本文介绍了饱和砂土的基本动力学特性,并对当前饱和砂土动本构理论的研究进展作了较为系统的评述,以期对进一步的研究有所稗益．      

岩土力学的公理化理论体系*

本文以混合物理论为基础,融理性力学、不可逆过程热力学和土力学的精华于一体,提出了岩土力学的公理化理论体系。该理论体系包括5个基本定律和8个本构原理,它们在纯力学理论和工程实际的鸿沟之间架起了一道桥梁。     

多相固体弹塑性本构方程的同类性

本文以复合材料为背景,讨论多相固体即混合物的等效弹塑性本构方程.按照所提出的等效本构方程的定义,文章证明,由服从广义正交法则的多种均匀的弹塑性介质组成的混合物具有与它的组分介质同类的、也服从广义正交法则的等效本构方程.