夹层结构杆在弹性基础上的弹塑性变形

对位于弹性基底上的、具有可压缩非线性芯子的3层弹塑性杆的弯曲问题进行了研究．研究分析了由2个受力层和1个芯子层组成的3层构件的力学响应．解决了位于弹性基底上的3层杆弯曲的复杂问题．对所给出的弹性解法进行了收敛性检验,以保证该弹性解是可以接受的．计算结果表明,材料的塑性和物理非线性对位于弹性基底上的夹层结构杆的变形影响很大．     

单轴拉伸条件下细观非均匀性岩石损伤局部化和应力应变关系分析

岩石在拉应力状态下的力学特性不同于压应力状态下的力学特性．利用细观力学理论研究了细观非均匀性岩石拉伸应力应变关系包括:线弹性阶段、非线性强化阶段、应力降阶段、应变软化阶段.模型考虑了微裂纹方位角为Weibull分布和微裂纹长度的分布密度函数为Rayleigh函数时对损伤局部化和应力应变关系的影响,分析了产生应力降和应变软化的主要原因是损伤和变形局部化.通过和实验成果对比分析验证了模型的正确性和有效性．     

有限变形下的混凝土动态本构关系研究

讨论有限变形和小变形假设下本构关系的区别,并将其运用于混凝土的弹-粘塑性本构关系研究,提出了一个应变率相关的动态力学模型．模型基于Ottosen的4参数屈服准则,分别考虑混凝土在硬化阶段和软化阶段加载面的不同变化规律,建立冲击荷载下的混凝土本构关系．该模型可以应用于冲击载荷下混凝土材料响应的模拟．引进Green-Naghdi客观率建立有限变形的混凝土模型．根据大量实验结果对应变率和材料强度的关系提出合理假设,使模型可以反映混凝土大变形的动态力学行为,为相关工程问题的研究提供有益的思路和有效的工具．     

有限变形弹性圆杆中的孤波

在同时引入横向惯性和横向剪切应变的情况下,导出了有限变形弹性圆杆的非线性纵向波动方程,方程中包含了二次和三次的非线性项以及由横向剪切与横向惯性导致的两种几何弥散效应．借助Mathematica软件,利用双曲正割函数的有限展开法,对该方程和对应的截断的非线性方程进行求解,得到了非线性波动方程的孤波解,同时给出了这些解存在的必要条件．     

基于滑移与微纤维伸缩两种耗能机制的弹塑性本构模型

本文考虑了固体材料内以拉压和滑移方式消耗变形功的两种主要物理机制,提出了用纤维构元与滑移构元共同组集的弹塑性材料模型.两种构元都是单自由度变形体,其力学性质及塑性变形中的耦合硬化系数可由传统的材料力学实验确定.各种取向的构元在三维空间中均匀分布,并与宏观应变协调变形.从模型结构的力学响应导出了全量型和增量型本构方程,不必预先设定加载函数(塑性势函数).构元经历的变形历史与其取向有关,作为组合效应的应力应变关系能反映加载路径的影响.因此,本文得到的本构方程既保持了简洁的数学形式,又能模拟复杂加载条件下材料的宏观弹塑性力学行为. 本文预测了几种多晶金属材料在典型复杂加载路径下的应力应变响应与后继屈服面,与实验结果吻合良好.     

St.Venant-Levy-Mises材料塑性力学的Lagrange形式

将Ｓｔ．Ｖｅｎａｎｔ－Ｌｅｖｙ－Ｍｉｓｅｓ材料的塑性力学问题纳入Ｌａｇｒａｎｇｅ力学的理论体系,讨论了这一种材料的塑性力学三维问题,小挠度问题以及有限变形（大挠度）问题的基本微分方程。     

Cosserat生长弹性杆动力学的Gauss最小拘束原理

以自然界中具有生长、变形和运动特征的细长体为背景,用经典力学中的Gauss最小拘束原理研究生长弹性杆的动力学建模问题.在为生长弹性杆动力学建模提供新方法的同时,扩大了Gauss原理的应用范围.以Cosserat弹性杆为对象,分析弹性杆生长和变形的几何规则,表明生长应变和弹性应变是非线性耦合的;本构方程给出了截面的内力与弹性变形的线性关系;利用逆并矢,将经典力学中的Gauss原理和Gauss最小拘束原理用于生长弹性杆动力学,得到等价的两种表现形式,反映了时间和弧坐标在表述上的对称性,由此导出了封闭的动力学微分方程.给出了两种形式的最小拘束函数,表明生长弹性杆的实际运动使拘束函数取驻值,且为最小值.最后讨论了生长弹性杆的约束与条件极值等问题.     

轴向拉伸细长杆的非线性力学模型

聚酯系泊缆是深海工程中具备一定抗弯刚度、易拉伸变形的细长杆件结构.聚酯缆的轴向变形属大拉伸范畴,分析中应当区分变形前后状态,特别是缆索长度的改变使得基于小拉伸假设的细长杆模型需要予以改进.因此,基于Garrett细长杆模型,应用总体坐标和斜率取代Euler-Bernoulli(欧拉 伯努利)梁元的转角,解决缆索在空间中大转动变形的几何非线性问题;使用轴向拉伸变形前后物质点对应的方法,借助单元两个节点和一个中点,以及3个二次多项式形函数描述轴向拉伸变形下细长杆元的运动微分方程.通过与轴向拉伸悬臂梁的对比分析,验证了该拉伸杆元的收敛性和准确性.     

钱氏定理在有限变形极矩弹性力学广义变分原理的应用

应用Lagrange乘子法和钱伟长证明的两类广义变分原理的等价定理,在本文中导出有限变形极矩弹性力学的广义变分原理.文中采用了在拖带坐标系描述法建立的有限变形应变张量(称为Biot有限变形应变定义的准确形式)和应变速率定义与拖带系应力张量构成完整的数学描述.     

非保守力作用下杆的塑性动态稳定性

本文用Liapunov第二方法分析非保守力作用下直杆的塑性动态稳定性.杆处于粘性阻尼介质中,并受到切向均布的随动载荷作用.分析中在应力-应变关系中引入了应变率效应.导出了一个稳定性条件,并求出了临界失稳载荷,讨论了应变率效应对杆的稳定性的影响.     

Stability of strain gradient elastic bars in tension

Equilibrium of a bar under uniaxial tension is considered as optimization problem of the total potential energy. Uniaxial deformations are considered for a material with linear constitutive law of strain second gradient elasticity. Applying tension on an elastic bar, necking is shown up in high strains. That means the axial strain forms two homogeneously deformed sections in the ends of the bars and a section in the middle with high variable strain. The interactions of the intrinsic (material) lengths with the non linear strain displacement relations develop critical states of bifurcation with continuous Fourier’s spectrum. Critical conditions and post-critical deformations are defined with the help of multiple scales perturbation method. An erratum to this article can be found at     

SPH method applied to compression of solid materials for a variety of loading conditions

Smoothed Particle Hydrodynamics (SPH) is a numerical method that does not use a mesh or grid when solving a set of partial differential equations. This makes it particularly useful in application to solid mechanics problems where the sample undergoes large deformation. Whereas mesh-based methods have difficulty when the sample becomes severely distorted, SPH naturally deals with this important engineering scenario. We implement the SPH method for compressional deformation of solid samples and focus on uniaxial, biaxial and triaxial loading. We develop numerical procedures that naturally deal with these three different sets of boundary conditions and apply it to both small and larger strains in elastic and more complex materials. The method is shown to be robust up to large strains of 30%. Under uniaxial loading, a cylindrical sample tends to deform by bulging while under triaxial loading the cylindrical sample will remain cylindrical, but the diameter of the sample increases accordingly.     

Axisymmetric deformation of cylinders made of homogeneous and fiber-reinforced elastic materials in butt-end torsion

The equations of axisymmetric deformation of a circular cylinder made of homogeneous and weakly fiber-reinforced materials in a macroscopically two-dimensional problem statement are presented. The fibers are placed in the axial, circumferential, and radial directions and along spirals in the cylinder wall. They also can lie along opposite spirals in adjacent cylindrical layers, forming an angle-ply reinforcement scheme. At a low content of fibers, it is assumed that they are in the uniaxial stress state, determined by the axial tension or constraint compression in the deformed cylinder. Based on this mathematical model, the deformation of homogeneous and fiber-reinforced elastic cylinders of various length, with free outer surfaces, in butt-end torsion is investigated. The effect of length of the cylinders on their deformation character in torsion is evaluated. The torsion of the cylinders under the conditions of sliding fit along the inner surface and under the action of pressure on the surface, when the initial and deformed configurations are practically congruent, is considered.     

Modelling of the deformation processes and the localization of plastic deformations in the torsion–tension of solids of revolution

Generalized two-dimensional problems of the torsion of elastoplastic solids of revolution of arbitrary shape for large deformations under non-uniform stress-strain conditions are formulated and a method for their numerical solution is proposed. The use of this method to construct strain diagrams of materials based on experiments on the torsion of axisysmmetric samples of variable thickness until fracture occurs is described. Experimental and numerical investigations of processes of elastoplastic deformation, loss of stability and supercritical behaviour of solid cylindrical steel samples of variable thickness under conditions of monotonic kinematic loading with a torque, a tension and a combined load are presented. The mutual influence of torsion and tension on the deformation process and the limit states is estimated, and the universality (the independence of the form of the stress-strain state) of the “stress intensity – Odqvist parameter” diagram for steel for large deformations is proved.     

The conservation energy principle in description of stable and unstable states for aluminium

In the paper the physical model based on the energy conservation principle is proposed. On the basis of this principle the division of energy on volumetric and deviatory parts is presented. In this model a concept of energy division is recognised as important. Using the strain energy density function we can formulate criteria of the material equilibrium stability. Considerations are carried out for aluminium. All assumptions are based on uniaxial tension test supported by transverse deformation measurements. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

不同应变率下PC,ABS和PC/ABS合金拉伸变形行为研究

采用实验方法研究了PC(聚碳酸酯)、ABS(丙烯腈-丁二烯-苯乙烯)和PC/ABS合金(PC与ABS共混率为80∶20,60∶40,50∶50和40∶60),在不同应变率条件下的拉伸变形行为.采用MTS-810万能材料试验机和分离式Hopkinson拉杆实验系统分别进行了PC,ABS和PC/ABS合金室温条件下的准静态和冲击拉伸实验,得到了上述材料在不同应变率条件下的真应力-真应变曲线;通过对其变形特点的详细分析,讨论了应变率和ABS含量对拉伸变形的影响,并且给出了10-4s-1～103s-1应变率范围内屈服应力与应变率的线性关系式.     

Method of investigating the extension of high-elastic polymers

A method has been developed for studying the deformation of polymers in a field with a longitudinal velocity gradient. The changes in the longitudinal viscosity and modulus of high elasticity of polyisobutylene in uniaxial tension at constant extension and strain rates are compared.Mekhanika Polimerov, Vol. 4, No. 2, pp. 343–348, 1968     

薄壳非线性变形理论

对薄壳的非线性变形,给出了应变与位移之间的精确关系.经过合理的简化,给出了壳的挠度与厚度同级的大变形基本公式.当薄壳为无限长柱形且作柱形变形时,精确地求得了壳的挠度与长度同级的大变形基本公式.     

New damage evolution model of rock material

As a kind of natural engineering material with original defects, there are distinctly nonlinear and anisotropic mechanical behaviors for rock materials. Nevertheless, the rock damage mechanics can solve this problem well. However, for the complexity of mechanical property of rock material, the mature and applicable model to describe the rock failure process and the method to determine the maximum damage value have not been established very well. To solve this problem, one new damage evolution model for rock material has been proposed. In this model, the least energy consumption principle proposed to describe the fracture process of materials is used. Using the experimental data of granite sample under uniaxial compression and the results of numerical tests under uniaxial tension and uniaxial compression, this model is verified. Moreover, the results of the new model have been compared with the results of the tests (numerical test and real test) and the traditional damage model. The comparison shows that the new model has the higher accuracy and better reflects for the fracture process of the granite sample. Moreover, the released damage energies of the new model and Mazars model are different, and the released damage energy of the new model is slightly less than that of the Mazars model.